TSTP Solution File: HEN010-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : HEN010-2 : TPTP v8.1.0. 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  : 600s
% DateTime : Sat Jul 16 12:57:28 EDT 2022

% Result   : Unsatisfiable 3.05s 3.21s
% Output   : CNFRefutation 3.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  195 ( 111 unt;   9 typ;   0 def)
%            Number of atoms       : 1129 ( 325 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives : 2005 ( 282   ~; 373   |;   0   &;1350   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   8 con; 0-3 aty)
%            Number of variables   :  642 (   0   ^ 642   !;   0   ?; 642   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_divide,type,
    divide: $i > $i > $i ).

thf(tp_idQ_idQa,type,
    idQ_idQa: $i ).

thf(tp_idQa,type,
    idQa: $i ).

thf(tp_idQa_Q__idQ_idQa,type,
    idQa_Q__idQ_idQa: $i ).

thf(tp_identity,type,
    identity: $i ).

thf(tp_less_equal,type,
    less_equal: $i > $i > $o ).

thf(tp_quotient,type,
    quotient: $i > $i > $i > $o ).

thf(tp_zero,type,
    zero: $i ).

thf(1,axiom,
    ! [X: $i,Y1: $i,Y2: $i,Y3: $i] :
      ( ~ ( quotient @ identity @ X @ Y1 )
      | ~ ( quotient @ identity @ Y1 @ Y2 )
      | ~ ( quotient @ identity @ Y2 @ Y3 )
      | ( Y1 = Y3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).

thf(2,axiom,
    ! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
      ( ~ ( less_equal @ X @ Y )
      | ~ ( quotient @ X @ Z @ W1 )
      | ~ ( quotient @ Y @ Z @ W2 )
      | ( less_equal @ W1 @ W2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy_implies_xQzLEyQz) ).

thf(3,axiom,
    ! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
      ( ~ ( less_equal @ X @ Y )
      | ~ ( quotient @ Z @ Y @ W1 )
      | ~ ( quotient @ Z @ X @ W2 )
      | ( less_equal @ W1 @ W2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).

thf(4,axiom,
    ! [X: $i,Y: $i,W1: $i,Z: $i,W2: $i] :
      ( ~ ( quotient @ X @ Y @ W1 )
      | ~ ( less_equal @ W1 @ Z )
      | ~ ( quotient @ X @ Z @ W2 )
      | ( less_equal @ W2 @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).

thf(5,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( less_equal @ X @ Y )
      | ~ ( less_equal @ Y @ Z )
      | ( less_equal @ X @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).

thf(6,axiom,
    ! [X: $i] : ( quotient @ X @ zero @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).

thf(7,axiom,
    ! [X: $i] : ( quotient @ X @ X @ zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).

thf(8,axiom,
    ! [X: $i] : ( quotient @ zero @ X @ zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).

thf(9,axiom,
    ! [X: $i] : ( quotient @ X @ identity @ zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).

thf(10,axiom,
    ! [X: $i,Y: $i,Z: $i,W: $i] :
      ( ~ ( quotient @ X @ Y @ Z )
      | ~ ( quotient @ X @ Y @ W )
      | ( Z = W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).

thf(11,axiom,
    ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).

thf(12,axiom,
    ! [X: $i] : ( less_equal @ X @ identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).

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

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

thf(15,axiom,
    ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i,V5: $i] :
      ( ~ ( quotient @ X @ Y @ V1 )
      | ~ ( quotient @ Y @ Z @ V2 )
      | ~ ( quotient @ X @ Z @ V3 )
      | ~ ( quotient @ V3 @ V2 @ V4 )
      | ~ ( quotient @ V1 @ Z @ V5 )
      | ( less_equal @ V4 @ V5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).

thf(16,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( quotient @ X @ Y @ Z )
      | ( less_equal @ Z @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).

thf(17,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( quotient @ X @ Y @ zero )
      | ( less_equal @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).

thf(18,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( less_equal @ X @ Y )
      | ( quotient @ X @ Y @ zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).

thf(19,axiom,
    quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).

thf(20,axiom,
    quotient @ identity @ idQa @ idQ_idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).

thf(21,axiom,
    quotient @ identity @ a @ idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).

thf(22,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(23,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[22]) ).

thf(24,negated_conjecture,
    idQa != idQa_Q__idQ_idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).

thf(25,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ! [X: $i,Y1: $i,Y2: $i,Y3: $i] :
          ( ~ ( quotient @ identity @ X @ Y1 )
          | ~ ( quotient @ identity @ Y1 @ Y2 )
          | ~ ( quotient @ identity @ Y2 @ Y3 )
          | ( Y1 = Y3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ~ ( quotient @ X @ Z @ W1 )
          | ~ ( quotient @ Y @ Z @ W2 )
          | ( less_equal @ W1 @ W2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(28,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ~ ( quotient @ Z @ Y @ W1 )
          | ~ ( quotient @ Z @ X @ W2 )
          | ( less_equal @ W1 @ W2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i,W1: $i,Z: $i,W2: $i] :
          ( ~ ( quotient @ X @ Y @ W1 )
          | ~ ( less_equal @ W1 @ Z )
          | ~ ( quotient @ X @ Z @ W2 )
          | ( less_equal @ W2 @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ~ ( less_equal @ Y @ Z )
          | ( less_equal @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(31,plain,
    ( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(32,plain,
    ( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(33,plain,
    ( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(34,plain,
    ( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(35,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
          ( ~ ( quotient @ X @ Y @ Z )
          | ~ ( quotient @ X @ Y @ W )
          | ( Z = W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(36,plain,
    ( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(37,plain,
    ( ( ! [X: $i] : ( less_equal @ X @ identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(38,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ~ ( less_equal @ Y @ X )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(39,plain,
    ( ( ! [X: $i] : ( less_equal @ zero @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(40,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i,V5: $i] :
          ( ~ ( quotient @ X @ Y @ V1 )
          | ~ ( quotient @ Y @ Z @ V2 )
          | ~ ( quotient @ X @ Z @ V3 )
          | ~ ( quotient @ V3 @ V2 @ V4 )
          | ~ ( quotient @ V1 @ Z @ V5 )
          | ( less_equal @ V4 @ V5 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(41,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( quotient @ X @ Y @ Z )
          | ( less_equal @ Z @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(42,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( quotient @ X @ Y @ zero )
          | ( less_equal @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(43,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ( quotient @ X @ Y @ zero ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(44,plain,
    ( ( quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(45,plain,
    ( ( quotient @ identity @ idQa @ idQ_idQa )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(46,plain,
    ( ( quotient @ identity @ a @ idQa )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(47,plain,
    ( ( ( idQa != idQa_Q__idQ_idQa ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(48,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[25]) ).

thf(49,plain,
    ( ( ! [X: $i,Y1: $i] :
          ( ~ ( quotient @ identity @ X @ Y1 )
          | ! [Y2: $i] :
              ( ~ ( quotient @ identity @ Y1 @ Y2 )
              | ! [Y3: $i] :
                  ( ~ ( quotient @ identity @ Y2 @ Y3 )
                  | ( Y1 = Y3 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[26]) ).

thf(50,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ! [W1: $i] :
              ( ~ ( quotient @ X @ Z @ W1 )
              | ! [W2: $i] :
                  ( ~ ( quotient @ Y @ Z @ W2 )
                  | ( less_equal @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ! [W1: $i] :
              ( ~ ( quotient @ Z @ Y @ W1 )
              | ! [W2: $i] :
                  ( ~ ( quotient @ Z @ X @ W2 )
                  | ( less_equal @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[28]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i,W1: $i] :
          ( ~ ( quotient @ X @ Y @ W1 )
          | ! [Z: $i] :
              ( ~ ( less_equal @ W1 @ Z )
              | ! [W2: $i] :
                  ( ~ ( quotient @ X @ Z @ W2 )
                  | ( less_equal @ W2 @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(53,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( less_equal @ Y @ Z )
              | ( less_equal @ X @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(54,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( quotient @ X @ Y @ Z )
          | ! [W: $i] :
              ( ~ ( quotient @ X @ Y @ W )
              | ( Z = W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[35]) ).

thf(55,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i] :
          ( ~ ( quotient @ X @ Y @ V1 )
          | ~ ( quotient @ Y @ Z @ V2 )
          | ~ ( quotient @ X @ Z @ V3 )
          | ! [V4: $i] :
              ( ~ ( quotient @ V3 @ V2 @ V4 )
              | ! [V5: $i] :
                  ( ~ ( quotient @ V1 @ Z @ V5 )
                  | ( less_equal @ V4 @ V5 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(56,plain,
    ( ( ( idQa != idQa_Q__idQ_idQa ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(57,plain,
    ( ( ( idQa != idQa_Q__idQ_idQa ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(58,plain,
    ( ( quotient @ identity @ a @ idQa )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(59,plain,
    ( ( quotient @ identity @ idQa @ idQ_idQa )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(60,plain,
    ( ( quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(61,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ( quotient @ X @ Y @ zero ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(62,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( quotient @ X @ Y @ zero )
          | ( less_equal @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(63,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( quotient @ X @ Y @ Z )
          | ( less_equal @ Z @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(64,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i] :
          ( ~ ( quotient @ X @ Y @ V1 )
          | ~ ( quotient @ Y @ Z @ V2 )
          | ~ ( quotient @ X @ Z @ V3 )
          | ! [V4: $i] :
              ( ~ ( quotient @ V3 @ V2 @ V4 )
              | ! [V5: $i] :
                  ( ~ ( quotient @ V1 @ Z @ V5 )
                  | ( less_equal @ V4 @ V5 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(65,plain,
    ( ( ! [X: $i] : ( less_equal @ zero @ X ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(66,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ~ ( less_equal @ Y @ X )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(67,plain,
    ( ( ! [X: $i] : ( less_equal @ X @ identity ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(68,plain,
    ( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(69,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( quotient @ X @ Y @ Z )
          | ! [W: $i] :
              ( ~ ( quotient @ X @ Y @ W )
              | ( Z = W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(70,plain,
    ( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(71,plain,
    ( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(72,plain,
    ( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(73,plain,
    ( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(74,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( less_equal @ Y @ Z )
              | ( less_equal @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(75,plain,
    ( ( ! [X: $i,Y: $i,W1: $i] :
          ( ~ ( quotient @ X @ Y @ W1 )
          | ! [Z: $i] :
              ( ~ ( less_equal @ W1 @ Z )
              | ! [W2: $i] :
                  ( ~ ( quotient @ X @ Z @ W2 )
                  | ( less_equal @ W2 @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(76,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ! [W1: $i] :
              ( ~ ( quotient @ Z @ Y @ W1 )
              | ! [W2: $i] :
                  ( ~ ( quotient @ Z @ X @ W2 )
                  | ( less_equal @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(77,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less_equal @ X @ Y )
          | ! [W1: $i] :
              ( ~ ( quotient @ X @ Z @ W1 )
              | ! [W2: $i] :
                  ( ~ ( quotient @ Y @ Z @ W2 )
                  | ( less_equal @ W1 @ W2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(78,plain,
    ( ( ! [X: $i,Y1: $i] :
          ( ~ ( quotient @ identity @ X @ Y1 )
          | ! [Y2: $i] :
              ( ~ ( quotient @ identity @ Y1 @ Y2 )
              | ! [Y3: $i] :
                  ( ~ ( quotient @ identity @ Y2 @ Y3 )
                  | ( Y1 = Y3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(79,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(80,plain,
    ( ( idQa = idQa_Q__idQ_idQa )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(81,plain,
    ! [SV1: $i] :
      ( ( ! [SY51: $i] :
            ( ~ ( less_equal @ SV1 @ SY51 )
            | ( quotient @ SV1 @ SY51 @ zero ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(82,plain,
    ! [SV2: $i] :
      ( ( ! [SY52: $i] :
            ( ~ ( quotient @ SV2 @ SY52 @ zero )
            | ( less_equal @ SV2 @ SY52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(83,plain,
    ! [SV3: $i] :
      ( ( ! [SY53: $i,SY54: $i] :
            ( ~ ( quotient @ SV3 @ SY53 @ SY54 )
            | ( less_equal @ SY54 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(84,plain,
    ! [SV4: $i] :
      ( ( ! [SY55: $i,SY56: $i,SY57: $i,SY58: $i,SY59: $i] :
            ( ~ ( quotient @ SV4 @ SY55 @ SY56 )
            | ~ ( quotient @ SY55 @ SY57 @ SY58 )
            | ~ ( quotient @ SV4 @ SY57 @ SY59 )
            | ! [V4: $i] :
                ( ~ ( quotient @ SY59 @ SY58 @ V4 )
                | ! [V5: $i] :
                    ( ~ ( quotient @ SY56 @ SY57 @ V5 )
                    | ( less_equal @ V4 @ V5 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(85,plain,
    ! [SV5: $i] :
      ( ( less_equal @ zero @ SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(86,plain,
    ! [SV6: $i] :
      ( ( ! [SY62: $i] :
            ( ~ ( less_equal @ SV6 @ SY62 )
            | ~ ( less_equal @ SY62 @ SV6 )
            | ( SV6 = SY62 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(87,plain,
    ! [SV7: $i] :
      ( ( less_equal @ SV7 @ identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(88,plain,
    ! [SV8: $i] :
      ( ( ! [SY63: $i] : ( quotient @ SV8 @ SY63 @ ( divide @ SV8 @ SY63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(89,plain,
    ! [SV9: $i] :
      ( ( ! [SY64: $i,SY65: $i] :
            ( ~ ( quotient @ SV9 @ SY64 @ SY65 )
            | ! [SY66: $i] :
                ( ~ ( quotient @ SV9 @ SY64 @ SY66 )
                | ( SY65 = SY66 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(90,plain,
    ! [SV10: $i] :
      ( ( quotient @ SV10 @ identity @ zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(91,plain,
    ! [SV11: $i] :
      ( ( quotient @ zero @ SV11 @ zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(92,plain,
    ! [SV12: $i] :
      ( ( quotient @ SV12 @ SV12 @ zero )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(93,plain,
    ! [SV13: $i] :
      ( ( quotient @ SV13 @ zero @ SV13 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(94,plain,
    ! [SV14: $i] :
      ( ( ! [SY67: $i] :
            ( ~ ( less_equal @ SV14 @ SY67 )
            | ! [SY68: $i] :
                ( ~ ( less_equal @ SY67 @ SY68 )
                | ( less_equal @ SV14 @ SY68 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(95,plain,
    ! [SV15: $i] :
      ( ( ! [SY69: $i,SY70: $i] :
            ( ~ ( quotient @ SV15 @ SY69 @ SY70 )
            | ! [SY71: $i] :
                ( ~ ( less_equal @ SY70 @ SY71 )
                | ! [SY72: $i] :
                    ( ~ ( quotient @ SV15 @ SY71 @ SY72 )
                    | ( less_equal @ SY72 @ SY69 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(96,plain,
    ! [SV16: $i] :
      ( ( ! [SY73: $i,SY74: $i] :
            ( ~ ( less_equal @ SV16 @ SY73 )
            | ! [SY75: $i] :
                ( ~ ( quotient @ SY74 @ SY73 @ SY75 )
                | ! [SY76: $i] :
                    ( ~ ( quotient @ SY74 @ SV16 @ SY76 )
                    | ( less_equal @ SY75 @ SY76 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(97,plain,
    ! [SV17: $i] :
      ( ( ! [SY77: $i,SY78: $i] :
            ( ~ ( less_equal @ SV17 @ SY77 )
            | ! [SY79: $i] :
                ( ~ ( quotient @ SV17 @ SY78 @ SY79 )
                | ! [W2: $i] :
                    ( ~ ( quotient @ SY77 @ SY78 @ W2 )
                    | ( less_equal @ SY79 @ W2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(98,plain,
    ! [SV18: $i] :
      ( ( ! [SY81: $i] :
            ( ~ ( quotient @ identity @ SV18 @ SY81 )
            | ! [Y2: $i] :
                ( ~ ( quotient @ identity @ SY81 @ Y2 )
                | ! [Y3: $i] :
                    ( ~ ( quotient @ identity @ Y2 @ Y3 )
                    | ( SY81 = Y3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(99,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(100,plain,
    ! [SV19: $i,SV1: $i] :
      ( ( ~ ( less_equal @ SV1 @ SV19 )
        | ( quotient @ SV1 @ SV19 @ zero ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(101,plain,
    ! [SV20: $i,SV2: $i] :
      ( ( ~ ( quotient @ SV2 @ SV20 @ zero )
        | ( less_equal @ SV2 @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(102,plain,
    ! [SV21: $i,SV3: $i] :
      ( ( ! [SY84: $i] :
            ( ~ ( quotient @ SV3 @ SV21 @ SY84 )
            | ( less_equal @ SY84 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(103,plain,
    ! [SV22: $i,SV4: $i] :
      ( ( ! [SY85: $i,SY86: $i,SY87: $i,SY88: $i] :
            ( ~ ( quotient @ SV4 @ SV22 @ SY85 )
            | ~ ( quotient @ SV22 @ SY86 @ SY87 )
            | ~ ( quotient @ SV4 @ SY86 @ SY88 )
            | ! [V4: $i] :
                ( ~ ( quotient @ SY88 @ SY87 @ V4 )
                | ! [V5: $i] :
                    ( ~ ( quotient @ SY85 @ SY86 @ V5 )
                    | ( less_equal @ V4 @ V5 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(104,plain,
    ! [SV23: $i,SV6: $i] :
      ( ( ~ ( less_equal @ SV6 @ SV23 )
        | ~ ( less_equal @ SV23 @ SV6 )
        | ( SV6 = SV23 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(105,plain,
    ! [SV24: $i,SV8: $i] :
      ( ( quotient @ SV8 @ SV24 @ ( divide @ SV8 @ SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(106,plain,
    ! [SV25: $i,SV9: $i] :
      ( ( ! [SY91: $i] :
            ( ~ ( quotient @ SV9 @ SV25 @ SY91 )
            | ! [SY92: $i] :
                ( ~ ( quotient @ SV9 @ SV25 @ SY92 )
                | ( SY91 = SY92 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(107,plain,
    ! [SV26: $i,SV14: $i] :
      ( ( ~ ( less_equal @ SV14 @ SV26 )
        | ! [SY93: $i] :
            ( ~ ( less_equal @ SV26 @ SY93 )
            | ( less_equal @ SV14 @ SY93 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(108,plain,
    ! [SV27: $i,SV15: $i] :
      ( ( ! [SY94: $i] :
            ( ~ ( quotient @ SV15 @ SV27 @ SY94 )
            | ! [SY95: $i] :
                ( ~ ( less_equal @ SY94 @ SY95 )
                | ! [SY96: $i] :
                    ( ~ ( quotient @ SV15 @ SY95 @ SY96 )
                    | ( less_equal @ SY96 @ SV27 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(109,plain,
    ! [SV28: $i,SV16: $i] :
      ( ( ! [SY97: $i] :
            ( ~ ( less_equal @ SV16 @ SV28 )
            | ! [SY98: $i] :
                ( ~ ( quotient @ SY97 @ SV28 @ SY98 )
                | ! [SY76: $i] :
                    ( ~ ( quotient @ SY97 @ SV16 @ SY76 )
                    | ( less_equal @ SY98 @ SY76 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(110,plain,
    ! [SV29: $i,SV17: $i] :
      ( ( ! [SY100: $i] :
            ( ~ ( less_equal @ SV17 @ SV29 )
            | ! [SY101: $i] :
                ( ~ ( quotient @ SV17 @ SY100 @ SY101 )
                | ! [SY102: $i] :
                    ( ~ ( quotient @ SV29 @ SY100 @ SY102 )
                    | ( less_equal @ SY101 @ SY102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(111,plain,
    ! [SV30: $i,SV18: $i] :
      ( ( ~ ( quotient @ identity @ SV18 @ SV30 )
        | ! [SY103: $i] :
            ( ~ ( quotient @ identity @ SV30 @ SY103 )
            | ! [SY104: $i] :
                ( ~ ( quotient @ identity @ SY103 @ SY104 )
                | ( SV30 = SY104 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(112,plain,
    ! [SV19: $i,SV1: $i] :
      ( ( ( ~ ( less_equal @ SV1 @ SV19 ) )
        = $true )
      | ( ( quotient @ SV1 @ SV19 @ zero )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(113,plain,
    ! [SV20: $i,SV2: $i] :
      ( ( ( ~ ( quotient @ SV2 @ SV20 @ zero ) )
        = $true )
      | ( ( less_equal @ SV2 @ SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(114,plain,
    ! [SV31: $i,SV21: $i,SV3: $i] :
      ( ( ~ ( quotient @ SV3 @ SV21 @ SV31 )
        | ( less_equal @ SV31 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(115,plain,
    ! [SV32: $i,SV22: $i,SV4: $i] :
      ( ( ! [SY105: $i,SY106: $i,SY107: $i] :
            ( ~ ( quotient @ SV4 @ SV22 @ SV32 )
            | ~ ( quotient @ SV22 @ SY105 @ SY106 )
            | ~ ( quotient @ SV4 @ SY105 @ SY107 )
            | ! [SY108: $i] :
                ( ~ ( quotient @ SY107 @ SY106 @ SY108 )
                | ! [SY109: $i] :
                    ( ~ ( quotient @ SV32 @ SY105 @ SY109 )
                    | ( less_equal @ SY108 @ SY109 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(116,plain,
    ! [SV23: $i,SV6: $i] :
      ( ( ( ~ ( less_equal @ SV6 @ SV23 ) )
        = $true )
      | ( ( ~ ( less_equal @ SV23 @ SV6 )
          | ( SV6 = SV23 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(117,plain,
    ! [SV33: $i,SV25: $i,SV9: $i] :
      ( ( ~ ( quotient @ SV9 @ SV25 @ SV33 )
        | ! [SY110: $i] :
            ( ~ ( quotient @ SV9 @ SV25 @ SY110 )
            | ( SV33 = SY110 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(118,plain,
    ! [SV26: $i,SV14: $i] :
      ( ( ( ~ ( less_equal @ SV14 @ SV26 ) )
        = $true )
      | ( ( ! [SY93: $i] :
              ( ~ ( less_equal @ SV26 @ SY93 )
              | ( less_equal @ SV14 @ SY93 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[107]) ).

thf(119,plain,
    ! [SV34: $i,SV27: $i,SV15: $i] :
      ( ( ~ ( quotient @ SV15 @ SV27 @ SV34 )
        | ! [SY111: $i] :
            ( ~ ( less_equal @ SV34 @ SY111 )
            | ! [SY96: $i] :
                ( ~ ( quotient @ SV15 @ SY111 @ SY96 )
                | ( less_equal @ SY96 @ SV27 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(120,plain,
    ! [SV35: $i,SV28: $i,SV16: $i] :
      ( ( ~ ( less_equal @ SV16 @ SV28 )
        | ! [SY113: $i] :
            ( ~ ( quotient @ SV35 @ SV28 @ SY113 )
            | ! [SY114: $i] :
                ( ~ ( quotient @ SV35 @ SV16 @ SY114 )
                | ( less_equal @ SY113 @ SY114 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(121,plain,
    ! [SV36: $i,SV29: $i,SV17: $i] :
      ( ( ~ ( less_equal @ SV17 @ SV29 )
        | ! [SY115: $i] :
            ( ~ ( quotient @ SV17 @ SV36 @ SY115 )
            | ! [SY116: $i] :
                ( ~ ( quotient @ SV29 @ SV36 @ SY116 )
                | ( less_equal @ SY115 @ SY116 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(122,plain,
    ! [SV30: $i,SV18: $i] :
      ( ( ( ~ ( quotient @ identity @ SV18 @ SV30 ) )
        = $true )
      | ( ( ! [SY103: $i] :
              ( ~ ( quotient @ identity @ SV30 @ SY103 )
              | ! [SY104: $i] :
                  ( ~ ( quotient @ identity @ SY103 @ SY104 )
                  | ( SV30 = SY104 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[111]) ).

thf(123,plain,
    ! [SV19: $i,SV1: $i] :
      ( ( ( less_equal @ SV1 @ SV19 )
        = $false )
      | ( ( quotient @ SV1 @ SV19 @ zero )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(124,plain,
    ! [SV20: $i,SV2: $i] :
      ( ( ( quotient @ SV2 @ SV20 @ zero )
        = $false )
      | ( ( less_equal @ SV2 @ SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(125,plain,
    ! [SV31: $i,SV21: $i,SV3: $i] :
      ( ( ( ~ ( quotient @ SV3 @ SV21 @ SV31 ) )
        = $true )
      | ( ( less_equal @ SV31 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[114]) ).

thf(126,plain,
    ! [SV37: $i,SV32: $i,SV22: $i,SV4: $i] :
      ( ( ! [SY117: $i,SY118: $i] :
            ( ~ ( quotient @ SV4 @ SV22 @ SV32 )
            | ~ ( quotient @ SV22 @ SV37 @ SY117 )
            | ~ ( quotient @ SV4 @ SV37 @ SY118 )
            | ! [SY119: $i] :
                ( ~ ( quotient @ SY118 @ SY117 @ SY119 )
                | ! [SY120: $i] :
                    ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                    | ( less_equal @ SY119 @ SY120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(127,plain,
    ! [SV23: $i,SV6: $i] :
      ( ( ( less_equal @ SV6 @ SV23 )
        = $false )
      | ( ( ~ ( less_equal @ SV23 @ SV6 )
          | ( SV6 = SV23 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[116]) ).

thf(128,plain,
    ! [SV33: $i,SV25: $i,SV9: $i] :
      ( ( ( ~ ( quotient @ SV9 @ SV25 @ SV33 ) )
        = $true )
      | ( ( ! [SY110: $i] :
              ( ~ ( quotient @ SV9 @ SV25 @ SY110 )
              | ( SV33 = SY110 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[117]) ).

thf(129,plain,
    ! [SV26: $i,SV14: $i] :
      ( ( ( less_equal @ SV14 @ SV26 )
        = $false )
      | ( ( ! [SY93: $i] :
              ( ~ ( less_equal @ SV26 @ SY93 )
              | ( less_equal @ SV14 @ SY93 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(130,plain,
    ! [SV34: $i,SV27: $i,SV15: $i] :
      ( ( ( ~ ( quotient @ SV15 @ SV27 @ SV34 ) )
        = $true )
      | ( ( ! [SY111: $i] :
              ( ~ ( less_equal @ SV34 @ SY111 )
              | ! [SY96: $i] :
                  ( ~ ( quotient @ SV15 @ SY111 @ SY96 )
                  | ( less_equal @ SY96 @ SV27 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[119]) ).

thf(131,plain,
    ! [SV35: $i,SV28: $i,SV16: $i] :
      ( ( ( ~ ( less_equal @ SV16 @ SV28 ) )
        = $true )
      | ( ( ! [SY113: $i] :
              ( ~ ( quotient @ SV35 @ SV28 @ SY113 )
              | ! [SY114: $i] :
                  ( ~ ( quotient @ SV35 @ SV16 @ SY114 )
                  | ( less_equal @ SY113 @ SY114 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[120]) ).

thf(132,plain,
    ! [SV36: $i,SV29: $i,SV17: $i] :
      ( ( ( ~ ( less_equal @ SV17 @ SV29 ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ~ ( quotient @ SV17 @ SV36 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( quotient @ SV29 @ SV36 @ SY116 )
                  | ( less_equal @ SY115 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[121]) ).

thf(133,plain,
    ! [SV30: $i,SV18: $i] :
      ( ( ( quotient @ identity @ SV18 @ SV30 )
        = $false )
      | ( ( ! [SY103: $i] :
              ( ~ ( quotient @ identity @ SV30 @ SY103 )
              | ! [SY104: $i] :
                  ( ~ ( quotient @ identity @ SY103 @ SY104 )
                  | ( SV30 = SY104 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[122]) ).

thf(134,plain,
    ! [SV31: $i,SV21: $i,SV3: $i] :
      ( ( ( quotient @ SV3 @ SV21 @ SV31 )
        = $false )
      | ( ( less_equal @ SV31 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(135,plain,
    ! [SV38: $i,SV37: $i,SV32: $i,SV22: $i,SV4: $i] :
      ( ( ! [SY121: $i] :
            ( ~ ( quotient @ SV4 @ SV22 @ SV32 )
            | ~ ( quotient @ SV22 @ SV37 @ SV38 )
            | ~ ( quotient @ SV4 @ SV37 @ SY121 )
            | ! [SY122: $i] :
                ( ~ ( quotient @ SY121 @ SV38 @ SY122 )
                | ! [SY120: $i] :
                    ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                    | ( less_equal @ SY122 @ SY120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(136,plain,
    ! [SV6: $i,SV23: $i] :
      ( ( ( ~ ( less_equal @ SV23 @ SV6 ) )
        = $true )
      | ( ( SV6 = SV23 )
        = $true )
      | ( ( less_equal @ SV6 @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[127]) ).

thf(137,plain,
    ! [SV33: $i,SV25: $i,SV9: $i] :
      ( ( ( quotient @ SV9 @ SV25 @ SV33 )
        = $false )
      | ( ( ! [SY110: $i] :
              ( ~ ( quotient @ SV9 @ SV25 @ SY110 )
              | ( SV33 = SY110 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[128]) ).

thf(138,plain,
    ! [SV14: $i,SV39: $i,SV26: $i] :
      ( ( ( ~ ( less_equal @ SV26 @ SV39 )
          | ( less_equal @ SV14 @ SV39 ) )
        = $true )
      | ( ( less_equal @ SV14 @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(139,plain,
    ! [SV34: $i,SV27: $i,SV15: $i] :
      ( ( ( quotient @ SV15 @ SV27 @ SV34 )
        = $false )
      | ( ( ! [SY111: $i] :
              ( ~ ( less_equal @ SV34 @ SY111 )
              | ! [SY96: $i] :
                  ( ~ ( quotient @ SV15 @ SY111 @ SY96 )
                  | ( less_equal @ SY96 @ SV27 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[130]) ).

thf(140,plain,
    ! [SV35: $i,SV28: $i,SV16: $i] :
      ( ( ( less_equal @ SV16 @ SV28 )
        = $false )
      | ( ( ! [SY113: $i] :
              ( ~ ( quotient @ SV35 @ SV28 @ SY113 )
              | ! [SY114: $i] :
                  ( ~ ( quotient @ SV35 @ SV16 @ SY114 )
                  | ( less_equal @ SY113 @ SY114 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[131]) ).

thf(141,plain,
    ! [SV36: $i,SV29: $i,SV17: $i] :
      ( ( ( less_equal @ SV17 @ SV29 )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ~ ( quotient @ SV17 @ SV36 @ SY115 )
              | ! [SY116: $i] :
                  ( ~ ( quotient @ SV29 @ SV36 @ SY116 )
                  | ( less_equal @ SY115 @ SY116 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[132]) ).

thf(142,plain,
    ! [SV18: $i,SV40: $i,SV30: $i] :
      ( ( ( ~ ( quotient @ identity @ SV30 @ SV40 )
          | ! [SY124: $i] :
              ( ~ ( quotient @ identity @ SV40 @ SY124 )
              | ( SV30 = SY124 ) ) )
        = $true )
      | ( ( quotient @ identity @ SV18 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(143,plain,
    ! [SV41: $i,SV38: $i,SV37: $i,SV32: $i,SV22: $i,SV4: $i] :
      ( ( ~ ( quotient @ SV4 @ SV22 @ SV32 )
        | ~ ( quotient @ SV22 @ SV37 @ SV38 )
        | ~ ( quotient @ SV4 @ SV37 @ SV41 )
        | ! [SY125: $i] :
            ( ~ ( quotient @ SV41 @ SV38 @ SY125 )
            | ! [SY120: $i] :
                ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                | ( less_equal @ SY125 @ SY120 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[135]) ).

thf(144,plain,
    ! [SV6: $i,SV23: $i] :
      ( ( ( less_equal @ SV23 @ SV6 )
        = $false )
      | ( ( SV6 = SV23 )
        = $true )
      | ( ( less_equal @ SV6 @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[136]) ).

thf(145,plain,
    ! [SV33: $i,SV42: $i,SV25: $i,SV9: $i] :
      ( ( ( ~ ( quotient @ SV9 @ SV25 @ SV42 )
          | ( SV33 = SV42 ) )
        = $true )
      | ( ( quotient @ SV9 @ SV25 @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(146,plain,
    ! [SV14: $i,SV39: $i,SV26: $i] :
      ( ( ( ~ ( less_equal @ SV26 @ SV39 ) )
        = $true )
      | ( ( less_equal @ SV14 @ SV39 )
        = $true )
      | ( ( less_equal @ SV14 @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[138]) ).

thf(147,plain,
    ! [SV27: $i,SV15: $i,SV43: $i,SV34: $i] :
      ( ( ( ~ ( less_equal @ SV34 @ SV43 )
          | ! [SY127: $i] :
              ( ~ ( quotient @ SV15 @ SV43 @ SY127 )
              | ( less_equal @ SY127 @ SV27 ) ) )
        = $true )
      | ( ( quotient @ SV15 @ SV27 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(148,plain,
    ! [SV16: $i,SV44: $i,SV28: $i,SV35: $i] :
      ( ( ( ~ ( quotient @ SV35 @ SV28 @ SV44 )
          | ! [SY128: $i] :
              ( ~ ( quotient @ SV35 @ SV16 @ SY128 )
              | ( less_equal @ SV44 @ SY128 ) ) )
        = $true )
      | ( ( less_equal @ SV16 @ SV28 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(149,plain,
    ! [SV29: $i,SV45: $i,SV36: $i,SV17: $i] :
      ( ( ( ~ ( quotient @ SV17 @ SV36 @ SV45 )
          | ! [SY129: $i] :
              ( ~ ( quotient @ SV29 @ SV36 @ SY129 )
              | ( less_equal @ SV45 @ SY129 ) ) )
        = $true )
      | ( ( less_equal @ SV17 @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(150,plain,
    ! [SV18: $i,SV40: $i,SV30: $i] :
      ( ( ( ~ ( quotient @ identity @ SV30 @ SV40 ) )
        = $true )
      | ( ( ! [SY124: $i] :
              ( ~ ( quotient @ identity @ SV40 @ SY124 )
              | ( SV30 = SY124 ) ) )
        = $true )
      | ( ( quotient @ identity @ SV18 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[142]) ).

thf(151,plain,
    ! [SV41: $i,SV38: $i,SV37: $i,SV32: $i,SV22: $i,SV4: $i] :
      ( ( ( ~ ( quotient @ SV4 @ SV22 @ SV32 ) )
        = $true )
      | ( ( ~ ( quotient @ SV22 @ SV37 @ SV38 )
          | ~ ( quotient @ SV4 @ SV37 @ SV41 )
          | ! [SY125: $i] :
              ( ~ ( quotient @ SV41 @ SV38 @ SY125 )
              | ! [SY120: $i] :
                  ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                  | ( less_equal @ SY125 @ SY120 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[143]) ).

thf(152,plain,
    ! [SV33: $i,SV42: $i,SV25: $i,SV9: $i] :
      ( ( ( ~ ( quotient @ SV9 @ SV25 @ SV42 ) )
        = $true )
      | ( ( SV33 = SV42 )
        = $true )
      | ( ( quotient @ SV9 @ SV25 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[145]) ).

thf(153,plain,
    ! [SV14: $i,SV39: $i,SV26: $i] :
      ( ( ( less_equal @ SV26 @ SV39 )
        = $false )
      | ( ( less_equal @ SV14 @ SV39 )
        = $true )
      | ( ( less_equal @ SV14 @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(154,plain,
    ! [SV27: $i,SV15: $i,SV43: $i,SV34: $i] :
      ( ( ( ~ ( less_equal @ SV34 @ SV43 ) )
        = $true )
      | ( ( ! [SY127: $i] :
              ( ~ ( quotient @ SV15 @ SV43 @ SY127 )
              | ( less_equal @ SY127 @ SV27 ) ) )
        = $true )
      | ( ( quotient @ SV15 @ SV27 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[147]) ).

thf(155,plain,
    ! [SV16: $i,SV44: $i,SV28: $i,SV35: $i] :
      ( ( ( ~ ( quotient @ SV35 @ SV28 @ SV44 ) )
        = $true )
      | ( ( ! [SY128: $i] :
              ( ~ ( quotient @ SV35 @ SV16 @ SY128 )
              | ( less_equal @ SV44 @ SY128 ) ) )
        = $true )
      | ( ( less_equal @ SV16 @ SV28 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[148]) ).

thf(156,plain,
    ! [SV29: $i,SV45: $i,SV36: $i,SV17: $i] :
      ( ( ( ~ ( quotient @ SV17 @ SV36 @ SV45 ) )
        = $true )
      | ( ( ! [SY129: $i] :
              ( ~ ( quotient @ SV29 @ SV36 @ SY129 )
              | ( less_equal @ SV45 @ SY129 ) ) )
        = $true )
      | ( ( less_equal @ SV17 @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[149]) ).

thf(157,plain,
    ! [SV18: $i,SV40: $i,SV30: $i] :
      ( ( ( quotient @ identity @ SV30 @ SV40 )
        = $false )
      | ( ( ! [SY124: $i] :
              ( ~ ( quotient @ identity @ SV40 @ SY124 )
              | ( SV30 = SY124 ) ) )
        = $true )
      | ( ( quotient @ identity @ SV18 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(158,plain,
    ! [SV41: $i,SV38: $i,SV37: $i,SV32: $i,SV22: $i,SV4: $i] :
      ( ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false )
      | ( ( ~ ( quotient @ SV22 @ SV37 @ SV38 )
          | ~ ( quotient @ SV4 @ SV37 @ SV41 )
          | ! [SY125: $i] :
              ( ~ ( quotient @ SV41 @ SV38 @ SY125 )
              | ! [SY120: $i] :
                  ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                  | ( less_equal @ SY125 @ SY120 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[151]) ).

thf(159,plain,
    ! [SV33: $i,SV42: $i,SV25: $i,SV9: $i] :
      ( ( ( quotient @ SV9 @ SV25 @ SV42 )
        = $false )
      | ( ( SV33 = SV42 )
        = $true )
      | ( ( quotient @ SV9 @ SV25 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(160,plain,
    ! [SV27: $i,SV15: $i,SV43: $i,SV34: $i] :
      ( ( ( less_equal @ SV34 @ SV43 )
        = $false )
      | ( ( ! [SY127: $i] :
              ( ~ ( quotient @ SV15 @ SV43 @ SY127 )
              | ( less_equal @ SY127 @ SV27 ) ) )
        = $true )
      | ( ( quotient @ SV15 @ SV27 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[154]) ).

thf(161,plain,
    ! [SV16: $i,SV44: $i,SV28: $i,SV35: $i] :
      ( ( ( quotient @ SV35 @ SV28 @ SV44 )
        = $false )
      | ( ( ! [SY128: $i] :
              ( ~ ( quotient @ SV35 @ SV16 @ SY128 )
              | ( less_equal @ SV44 @ SY128 ) ) )
        = $true )
      | ( ( less_equal @ SV16 @ SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(162,plain,
    ! [SV29: $i,SV45: $i,SV36: $i,SV17: $i] :
      ( ( ( quotient @ SV17 @ SV36 @ SV45 )
        = $false )
      | ( ( ! [SY129: $i] :
              ( ~ ( quotient @ SV29 @ SV36 @ SY129 )
              | ( less_equal @ SV45 @ SY129 ) ) )
        = $true )
      | ( ( less_equal @ SV17 @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(163,plain,
    ! [SV18: $i,SV30: $i,SV46: $i,SV40: $i] :
      ( ( ( ~ ( quotient @ identity @ SV40 @ SV46 )
          | ( SV30 = SV46 ) )
        = $true )
      | ( ( quotient @ identity @ SV30 @ SV40 )
        = $false )
      | ( ( quotient @ identity @ SV18 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[157]) ).

thf(164,plain,
    ! [SV32: $i,SV41: $i,SV4: $i,SV38: $i,SV37: $i,SV22: $i] :
      ( ( ( ~ ( quotient @ SV22 @ SV37 @ SV38 ) )
        = $true )
      | ( ( ~ ( quotient @ SV4 @ SV37 @ SV41 )
          | ! [SY125: $i] :
              ( ~ ( quotient @ SV41 @ SV38 @ SY125 )
              | ! [SY120: $i] :
                  ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                  | ( less_equal @ SY125 @ SY120 ) ) ) )
        = $true )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[158]) ).

thf(165,plain,
    ! [SV34: $i,SV27: $i,SV47: $i,SV43: $i,SV15: $i] :
      ( ( ( ~ ( quotient @ SV15 @ SV43 @ SV47 )
          | ( less_equal @ SV47 @ SV27 ) )
        = $true )
      | ( ( less_equal @ SV34 @ SV43 )
        = $false )
      | ( ( quotient @ SV15 @ SV27 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(166,plain,
    ! [SV28: $i,SV44: $i,SV48: $i,SV16: $i,SV35: $i] :
      ( ( ( ~ ( quotient @ SV35 @ SV16 @ SV48 )
          | ( less_equal @ SV44 @ SV48 ) )
        = $true )
      | ( ( quotient @ SV35 @ SV28 @ SV44 )
        = $false )
      | ( ( less_equal @ SV16 @ SV28 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[161]) ).

thf(167,plain,
    ! [SV17: $i,SV45: $i,SV49: $i,SV36: $i,SV29: $i] :
      ( ( ( ~ ( quotient @ SV29 @ SV36 @ SV49 )
          | ( less_equal @ SV45 @ SV49 ) )
        = $true )
      | ( ( quotient @ SV17 @ SV36 @ SV45 )
        = $false )
      | ( ( less_equal @ SV17 @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[162]) ).

thf(168,plain,
    ! [SV18: $i,SV30: $i,SV46: $i,SV40: $i] :
      ( ( ( ~ ( quotient @ identity @ SV40 @ SV46 ) )
        = $true )
      | ( ( SV30 = SV46 )
        = $true )
      | ( ( quotient @ identity @ SV30 @ SV40 )
        = $false )
      | ( ( quotient @ identity @ SV18 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[163]) ).

thf(169,plain,
    ! [SV32: $i,SV41: $i,SV4: $i,SV38: $i,SV37: $i,SV22: $i] :
      ( ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( ~ ( quotient @ SV4 @ SV37 @ SV41 )
          | ! [SY125: $i] :
              ( ~ ( quotient @ SV41 @ SV38 @ SY125 )
              | ! [SY120: $i] :
                  ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                  | ( less_equal @ SY125 @ SY120 ) ) ) )
        = $true )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[164]) ).

thf(170,plain,
    ! [SV34: $i,SV27: $i,SV47: $i,SV43: $i,SV15: $i] :
      ( ( ( ~ ( quotient @ SV15 @ SV43 @ SV47 ) )
        = $true )
      | ( ( less_equal @ SV47 @ SV27 )
        = $true )
      | ( ( less_equal @ SV34 @ SV43 )
        = $false )
      | ( ( quotient @ SV15 @ SV27 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[165]) ).

thf(171,plain,
    ! [SV28: $i,SV44: $i,SV48: $i,SV16: $i,SV35: $i] :
      ( ( ( ~ ( quotient @ SV35 @ SV16 @ SV48 ) )
        = $true )
      | ( ( less_equal @ SV44 @ SV48 )
        = $true )
      | ( ( quotient @ SV35 @ SV28 @ SV44 )
        = $false )
      | ( ( less_equal @ SV16 @ SV28 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[166]) ).

thf(172,plain,
    ! [SV17: $i,SV45: $i,SV49: $i,SV36: $i,SV29: $i] :
      ( ( ( ~ ( quotient @ SV29 @ SV36 @ SV49 ) )
        = $true )
      | ( ( less_equal @ SV45 @ SV49 )
        = $true )
      | ( ( quotient @ SV17 @ SV36 @ SV45 )
        = $false )
      | ( ( less_equal @ SV17 @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[167]) ).

thf(173,plain,
    ! [SV18: $i,SV30: $i,SV46: $i,SV40: $i] :
      ( ( ( quotient @ identity @ SV40 @ SV46 )
        = $false )
      | ( ( SV30 = SV46 )
        = $true )
      | ( ( quotient @ identity @ SV30 @ SV40 )
        = $false )
      | ( ( quotient @ identity @ SV18 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[168]) ).

thf(174,plain,
    ! [SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV37: $i,SV4: $i] :
      ( ( ( ~ ( quotient @ SV4 @ SV37 @ SV41 ) )
        = $true )
      | ( ( ! [SY125: $i] :
              ( ~ ( quotient @ SV41 @ SV38 @ SY125 )
              | ! [SY120: $i] :
                  ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                  | ( less_equal @ SY125 @ SY120 ) ) ) )
        = $true )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[169]) ).

thf(175,plain,
    ! [SV34: $i,SV27: $i,SV47: $i,SV43: $i,SV15: $i] :
      ( ( ( quotient @ SV15 @ SV43 @ SV47 )
        = $false )
      | ( ( less_equal @ SV47 @ SV27 )
        = $true )
      | ( ( less_equal @ SV34 @ SV43 )
        = $false )
      | ( ( quotient @ SV15 @ SV27 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[170]) ).

thf(176,plain,
    ! [SV28: $i,SV44: $i,SV48: $i,SV16: $i,SV35: $i] :
      ( ( ( quotient @ SV35 @ SV16 @ SV48 )
        = $false )
      | ( ( less_equal @ SV44 @ SV48 )
        = $true )
      | ( ( quotient @ SV35 @ SV28 @ SV44 )
        = $false )
      | ( ( less_equal @ SV16 @ SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[171]) ).

thf(177,plain,
    ! [SV17: $i,SV45: $i,SV49: $i,SV36: $i,SV29: $i] :
      ( ( ( quotient @ SV29 @ SV36 @ SV49 )
        = $false )
      | ( ( less_equal @ SV45 @ SV49 )
        = $true )
      | ( ( quotient @ SV17 @ SV36 @ SV45 )
        = $false )
      | ( ( less_equal @ SV17 @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[172]) ).

thf(178,plain,
    ! [SV22: $i,SV32: $i,SV38: $i,SV41: $i,SV37: $i,SV4: $i] :
      ( ( ( quotient @ SV4 @ SV37 @ SV41 )
        = $false )
      | ( ( ! [SY125: $i] :
              ( ~ ( quotient @ SV41 @ SV38 @ SY125 )
              | ! [SY120: $i] :
                  ( ~ ( quotient @ SV32 @ SV37 @ SY120 )
                  | ( less_equal @ SY125 @ SY120 ) ) ) )
        = $true )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[174]) ).

thf(179,plain,
    ! [SV22: $i,SV4: $i,SV37: $i,SV32: $i,SV50: $i,SV38: $i,SV41: $i] :
      ( ( ( ~ ( quotient @ SV41 @ SV38 @ SV50 )
          | ! [SY130: $i] :
              ( ~ ( quotient @ SV32 @ SV37 @ SY130 )
              | ( less_equal @ SV50 @ SY130 ) ) )
        = $true )
      | ( ( quotient @ SV4 @ SV37 @ SV41 )
        = $false )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[178]) ).

thf(180,plain,
    ! [SV22: $i,SV4: $i,SV37: $i,SV32: $i,SV50: $i,SV38: $i,SV41: $i] :
      ( ( ( ~ ( quotient @ SV41 @ SV38 @ SV50 ) )
        = $true )
      | ( ( ! [SY130: $i] :
              ( ~ ( quotient @ SV32 @ SV37 @ SY130 )
              | ( less_equal @ SV50 @ SY130 ) ) )
        = $true )
      | ( ( quotient @ SV4 @ SV37 @ SV41 )
        = $false )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(181,plain,
    ! [SV22: $i,SV4: $i,SV37: $i,SV32: $i,SV50: $i,SV38: $i,SV41: $i] :
      ( ( ( quotient @ SV41 @ SV38 @ SV50 )
        = $false )
      | ( ( ! [SY130: $i] :
              ( ~ ( quotient @ SV32 @ SV37 @ SY130 )
              | ( less_equal @ SV50 @ SY130 ) ) )
        = $true )
      | ( ( quotient @ SV4 @ SV37 @ SV41 )
        = $false )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[180]) ).

thf(182,plain,
    ! [SV22: $i,SV4: $i,SV38: $i,SV41: $i,SV50: $i,SV51: $i,SV37: $i,SV32: $i] :
      ( ( ( ~ ( quotient @ SV32 @ SV37 @ SV51 )
          | ( less_equal @ SV50 @ SV51 ) )
        = $true )
      | ( ( quotient @ SV41 @ SV38 @ SV50 )
        = $false )
      | ( ( quotient @ SV4 @ SV37 @ SV41 )
        = $false )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[181]) ).

thf(183,plain,
    ! [SV22: $i,SV4: $i,SV38: $i,SV41: $i,SV50: $i,SV51: $i,SV37: $i,SV32: $i] :
      ( ( ( ~ ( quotient @ SV32 @ SV37 @ SV51 ) )
        = $true )
      | ( ( less_equal @ SV50 @ SV51 )
        = $true )
      | ( ( quotient @ SV41 @ SV38 @ SV50 )
        = $false )
      | ( ( quotient @ SV4 @ SV37 @ SV41 )
        = $false )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[182]) ).

thf(184,plain,
    ! [SV22: $i,SV4: $i,SV38: $i,SV41: $i,SV50: $i,SV51: $i,SV37: $i,SV32: $i] :
      ( ( ( quotient @ SV32 @ SV37 @ SV51 )
        = $false )
      | ( ( less_equal @ SV50 @ SV51 )
        = $true )
      | ( ( quotient @ SV41 @ SV38 @ SV50 )
        = $false )
      | ( ( quotient @ SV4 @ SV37 @ SV41 )
        = $false )
      | ( ( quotient @ SV22 @ SV37 @ SV38 )
        = $false )
      | ( ( quotient @ SV4 @ SV22 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[183]) ).

thf(185,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[58,184,177,176,175,173,159,153,144,134,124,123,105,99,93,92,91,90,87,85,80,60,59]) ).

thf(186,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[185]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HEN010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Fri Jul  1 14:43:14 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.36  
% 0.14/0.36   No.of.Axioms: 22
% 0.14/0.36  
% 0.14/0.36   Length.of.Defs: 0
% 0.14/0.36  
% 0.14/0.36   Contains.Choice.Funs: false
% 0.14/0.38  (rf:0,axioms:22,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:24,loop_count:0,foatp_calls:0,translation:fof_full)............
% 3.05/3.21  
% 3.05/3.21  ********************************
% 3.05/3.21  *   All subproblems solved!    *
% 3.05/3.21  ********************************
% 3.05/3.21  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,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:185,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.05/3.22  
% 3.05/3.22  %**** Beginning of derivation protocol ****
% 3.05/3.22  % SZS output start CNFRefutation
% See solution above
% 3.05/3.22  
% 3.05/3.22  %**** End of derivation protocol ****
% 3.05/3.22  %**** no. of clauses in derivation: 186 ****
% 3.05/3.22  %**** clause counter: 185 ****
% 3.05/3.22  
% 3.05/3.22  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,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:185,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------