TSTP Solution File: RNG039-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : RNG039-2 : 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 : n027.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 : Mon Jul 18 20:34:02 EDT 2022

% Result   : Unsatisfiable 0.44s 0.78s
% Output   : CNFRefutation 0.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   85
% Syntax   : Number of formulae    :  513 ( 332 unt;  10 typ;   0 def)
%            Number of atoms       : 2673 ( 684 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives : 5553 ( 605   ~; 802   |;   0   &;4146   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   7 con; 0-3 aty)
%            Number of variables   : 1693 (   0   ^1693   !;   0   ?;1693   :)

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

thf(tp_add,type,
    add: $i > $i > $i ).

thf(tp_additive_identity,type,
    additive_identity: $i ).

thf(tp_b,type,
    b: $i ).

thf(tp_c,type,
    c: $i ).

thf(tp_d,type,
    d: $i ).

thf(tp_equalish,type,
    equalish: $i > $i > $o ).

thf(tp_multiply,type,
    multiply: $i > $i > $i ).

thf(tp_product,type,
    product: $i > $i > $i > $o ).

thf(tp_sum,type,
    sum: $i > $i > $i > $o ).

thf(1,axiom,
    ! [A: $i] : ( product @ A @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).

thf(2,axiom,
    product @ ( add @ a @ b ) @ a @ ( add @ a @ d ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).

thf(3,axiom,
    product @ ( add @ b @ a ) @ a @ ( add @ d @ a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).

thf(4,axiom,
    product @ ( add @ b @ a ) @ b @ ( add @ b @ c ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).

thf(5,axiom,
    product @ ( add @ a @ b ) @ b @ ( add @ c @ b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).

thf(6,axiom,
    product @ b @ ( add @ b @ a ) @ ( add @ b @ d ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).

thf(7,axiom,
    product @ b @ ( add @ a @ b ) @ ( add @ d @ b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).

thf(8,axiom,
    product @ a @ ( add @ a @ b ) @ ( add @ a @ c ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).

thf(9,axiom,
    product @ a @ ( add @ b @ a ) @ ( add @ c @ a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).

thf(10,axiom,
    product @ c @ a @ ( multiply @ a @ d ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).

thf(11,axiom,
    product @ ( multiply @ d @ b ) @ a @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).

thf(12,axiom,
    product @ b @ a @ ( multiply @ b @ d ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).

thf(13,axiom,
    ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).

thf(14,axiom,
    product @ d @ b @ ( multiply @ b @ c ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).

thf(15,axiom,
    product @ ( multiply @ c @ a ) @ b @ c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).

thf(16,axiom,
    product @ a @ b @ ( multiply @ a @ c ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).

thf(17,axiom,
    ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).

thf(18,axiom,
    ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).

thf(19,axiom,
    product @ a @ d @ ( multiply @ c @ a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).

thf(20,axiom,
    product @ b @ c @ ( multiply @ d @ b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).

thf(21,axiom,
    product @ b @ ( multiply @ a @ d ) @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).

thf(22,axiom,
    product @ b @ a @ ( multiply @ d @ a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).

thf(23,axiom,
    ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).

thf(24,axiom,
    product @ a @ ( multiply @ b @ c ) @ c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).

thf(25,axiom,
    product @ a @ b @ ( multiply @ c @ b ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).

thf(26,axiom,
    ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).

thf(27,axiom,
    ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).

thf(28,axiom,
    product @ d @ a @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).

thf(29,axiom,
    product @ c @ b @ c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).

thf(30,axiom,
    product @ b @ d @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).

thf(31,axiom,
    product @ a @ c @ c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).

thf(32,axiom,
    ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).

thf(33,axiom,
    equalish @ ( multiply @ b @ a ) @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).

thf(34,axiom,
    equalish @ ( multiply @ a @ b ) @ c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).

thf(35,axiom,
    ! [A: $i] : ( equalish @ ( multiply @ A @ A ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).

thf(36,axiom,
    ! [A: $i] : ( equalish @ ( add @ A @ A ) @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).

thf(37,axiom,
    ! [A: $i] : ( equalish @ ( add @ A @ additive_identity ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).

thf(38,axiom,
    ! [A: $i] : ( sum @ A @ A @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).

thf(39,axiom,
    ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorbtion2) ).

thf(40,axiom,
    ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorbtion1) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ A @ D @ C )
      | ( equalish @ D @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_right_concellation) ).

thf(42,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ D @ B @ C )
      | ( equalish @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_left_cancellation) ).

thf(43,axiom,
    ! [X: $i,Y: $i,U: $i,V: $i] :
      ( ~ ( product @ X @ Y @ U )
      | ~ ( product @ X @ Y @ V )
      | ( equalish @ U @ V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).

thf(44,axiom,
    ! [X: $i,Y: $i,U: $i,V: $i] :
      ( ~ ( sum @ X @ Y @ U )
      | ~ ( sum @ X @ Y @ V )
      | ( equalish @ U @ V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).

thf(45,axiom,
    ! [X: $i] : ( product @ X @ additive_identity @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).

thf(46,axiom,
    ! [X: $i] : ( product @ additive_identity @ X @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).

thf(47,axiom,
    ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
      ( ~ ( product @ Y @ X @ V1 )
      | ~ ( product @ Z @ X @ V2 )
      | ~ ( sum @ Y @ Z @ V3 )
      | ~ ( sum @ V1 @ V2 @ V4 )
      | ( product @ V3 @ X @ V4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).

thf(48,axiom,
    ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
      ( ~ ( product @ Y @ X @ V1 )
      | ~ ( product @ Z @ X @ V2 )
      | ~ ( sum @ Y @ Z @ V3 )
      | ~ ( product @ V3 @ X @ V4 )
      | ( sum @ V1 @ V2 @ V4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).

thf(49,axiom,
    ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
      ( ~ ( product @ X @ Y @ V1 )
      | ~ ( product @ X @ Z @ V2 )
      | ~ ( sum @ Y @ Z @ V3 )
      | ~ ( sum @ V1 @ V2 @ V4 )
      | ( product @ X @ V3 @ V4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).

thf(50,axiom,
    ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
      ( ~ ( product @ X @ Y @ V1 )
      | ~ ( product @ X @ Z @ V2 )
      | ~ ( sum @ Y @ Z @ V3 )
      | ~ ( product @ X @ V3 @ V4 )
      | ( sum @ V1 @ V2 @ V4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).

thf(51,axiom,
    ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
      ( ~ ( product @ X @ Y @ U )
      | ~ ( product @ Y @ Z @ V )
      | ~ ( product @ X @ V @ W )
      | ( product @ U @ Z @ W ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).

thf(52,axiom,
    ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
      ( ~ ( product @ X @ Y @ U )
      | ~ ( product @ Y @ Z @ V )
      | ~ ( product @ U @ Z @ W )
      | ( product @ X @ V @ W ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication1) ).

thf(53,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( sum @ X @ Y @ Z )
      | ( sum @ Y @ X @ Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).

thf(54,axiom,
    ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
      ( ~ ( sum @ X @ Y @ U )
      | ~ ( sum @ Y @ Z @ V )
      | ~ ( sum @ X @ V @ W )
      | ( sum @ U @ Z @ W ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).

thf(55,axiom,
    ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
      ( ~ ( sum @ X @ Y @ U )
      | ~ ( sum @ Y @ Z @ V )
      | ~ ( sum @ U @ Z @ W )
      | ( sum @ X @ V @ W ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).

thf(56,axiom,
    ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).

thf(57,axiom,
    ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).

thf(58,axiom,
    ! [X: $i] : ( sum @ X @ additive_identity @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).

thf(59,axiom,
    ! [X: $i] : ( sum @ additive_identity @ X @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).

thf(60,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( equalish @ Y @ Z )
      | ( equalish @ X @ Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

thf(61,axiom,
    ! [X: $i] : ( equalish @ X @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

thf(62,axiom,
    ! [X: $i,Y: $i,W: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( product @ W @ Z @ X )
      | ( product @ W @ Z @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).

thf(63,axiom,
    ! [X: $i,Y: $i,W: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( product @ W @ X @ Z )
      | ( product @ W @ Y @ Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).

thf(64,axiom,
    ! [X: $i,Y: $i,W: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( product @ X @ W @ Z )
      | ( product @ Y @ W @ Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).

thf(65,axiom,
    ! [X: $i,Y: $i,W: $i] :
      ( ~ ( equalish @ X @ Y )
      | ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution2) ).

thf(66,axiom,
    ! [X: $i,Y: $i,W: $i] :
      ( ~ ( equalish @ X @ Y )
      | ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).

thf(67,axiom,
    ! [X: $i,Y: $i,W: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( sum @ W @ Z @ X )
      | ( sum @ W @ Z @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).

thf(68,axiom,
    ! [X: $i,Y: $i,W: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( sum @ W @ X @ Z )
      | ( sum @ W @ Y @ Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution2) ).

thf(69,axiom,
    ! [X: $i,Y: $i,W: $i,Z: $i] :
      ( ~ ( equalish @ X @ Y )
      | ~ ( sum @ X @ W @ Z )
      | ( sum @ Y @ W @ Z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution1) ).

thf(70,axiom,
    ! [X: $i,Y: $i,W: $i] :
      ( ~ ( equalish @ X @ Y )
      | ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution2) ).

thf(71,axiom,
    ! [X: $i,Y: $i,W: $i] :
      ( ~ ( equalish @ X @ Y )
      | ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution1) ).

thf(72,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(73,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[72]) ).

thf(74,negated_conjecture,
    ~ ( equalish @ c @ d ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).

thf(75,negated_conjecture,
    product @ b @ a @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a) ).

thf(76,negated_conjecture,
    product @ a @ b @ c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).

thf(77,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[73]) ).

thf(78,plain,
    ( ( ! [A: $i] : ( product @ A @ A @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(79,plain,
    ( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(80,plain,
    ( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(81,plain,
    ( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(82,plain,
    ( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(83,plain,
    ( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(84,plain,
    ( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(85,plain,
    ( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(86,plain,
    ( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(87,plain,
    ( ( product @ c @ a @ ( multiply @ a @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(88,plain,
    ( ( product @ ( multiply @ d @ b ) @ a @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(89,plain,
    ( ( product @ b @ a @ ( multiply @ b @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(90,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(91,plain,
    ( ( product @ d @ b @ ( multiply @ b @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(92,plain,
    ( ( product @ ( multiply @ c @ a ) @ b @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(93,plain,
    ( ( product @ a @ b @ ( multiply @ a @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(94,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(95,plain,
    ( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(96,plain,
    ( ( product @ a @ d @ ( multiply @ c @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(97,plain,
    ( ( product @ b @ c @ ( multiply @ d @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(98,plain,
    ( ( product @ b @ ( multiply @ a @ d ) @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(99,plain,
    ( ( product @ b @ a @ ( multiply @ d @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(100,plain,
    ( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(101,plain,
    ( ( product @ a @ ( multiply @ b @ c ) @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(102,plain,
    ( ( product @ a @ b @ ( multiply @ c @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(103,plain,
    ( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(104,plain,
    ( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(105,plain,
    ( ( product @ d @ a @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(106,plain,
    ( ( product @ c @ b @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(107,plain,
    ( ( product @ b @ d @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(108,plain,
    ( ( product @ a @ c @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(109,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(110,plain,
    ( ( equalish @ ( multiply @ b @ a ) @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(111,plain,
    ( ( equalish @ ( multiply @ a @ b ) @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(112,plain,
    ( ( ! [A: $i] : ( equalish @ ( multiply @ A @ A ) @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(113,plain,
    ( ( ! [A: $i] : ( equalish @ ( add @ A @ A ) @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(114,plain,
    ( ( ! [A: $i] : ( equalish @ ( add @ A @ additive_identity ) @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(115,plain,
    ( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(116,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(117,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(118,plain,
    ( ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ~ ( sum @ A @ B @ C )
          | ~ ( sum @ A @ D @ C )
          | ( equalish @ D @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(119,plain,
    ( ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ~ ( sum @ A @ B @ C )
          | ~ ( sum @ D @ B @ C )
          | ( equalish @ D @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(120,plain,
    ( ( ! [X: $i,Y: $i,U: $i,V: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ X @ Y @ V )
          | ( equalish @ U @ V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[43]) ).

thf(121,plain,
    ( ( ! [X: $i,Y: $i,U: $i,V: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ~ ( sum @ X @ Y @ V )
          | ( equalish @ U @ V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[44]) ).

thf(122,plain,
    ( ( ! [X: $i] : ( product @ X @ additive_identity @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[45]) ).

thf(123,plain,
    ( ( ! [X: $i] : ( product @ additive_identity @ X @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[46]) ).

thf(124,plain,
    ( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
          ( ~ ( product @ Y @ X @ V1 )
          | ~ ( product @ Z @ X @ V2 )
          | ~ ( sum @ Y @ Z @ V3 )
          | ~ ( sum @ V1 @ V2 @ V4 )
          | ( product @ V3 @ X @ V4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[47]) ).

thf(125,plain,
    ( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
          ( ~ ( product @ Y @ X @ V1 )
          | ~ ( product @ Z @ X @ V2 )
          | ~ ( sum @ Y @ Z @ V3 )
          | ~ ( product @ V3 @ X @ V4 )
          | ( sum @ V1 @ V2 @ V4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[48]) ).

thf(126,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
          ( ~ ( product @ X @ Y @ V1 )
          | ~ ( product @ X @ Z @ V2 )
          | ~ ( sum @ Y @ Z @ V3 )
          | ~ ( sum @ V1 @ V2 @ V4 )
          | ( product @ X @ V3 @ V4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[49]) ).

thf(127,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
          ( ~ ( product @ X @ Y @ V1 )
          | ~ ( product @ X @ Z @ V2 )
          | ~ ( sum @ Y @ Z @ V3 )
          | ~ ( product @ X @ V3 @ V4 )
          | ( sum @ V1 @ V2 @ V4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[50]) ).

thf(128,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ X @ V @ W )
          | ( product @ U @ Z @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[51]) ).

thf(129,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ U @ Z @ W )
          | ( product @ X @ V @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[52]) ).

thf(130,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ Z )
          | ( sum @ Y @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[53]) ).

thf(131,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ~ ( sum @ Y @ Z @ V )
          | ~ ( sum @ X @ V @ W )
          | ( sum @ U @ Z @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[54]) ).

thf(132,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ~ ( sum @ Y @ Z @ V )
          | ~ ( sum @ U @ Z @ W )
          | ( sum @ X @ V @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[55]) ).

thf(133,plain,
    ( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[56]) ).

thf(134,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[57]) ).

thf(135,plain,
    ( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[58]) ).

thf(136,plain,
    ( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[59]) ).

thf(137,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( equalish @ Y @ Z )
          | ( equalish @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[60]) ).

thf(138,plain,
    ( ( ! [X: $i] : ( equalish @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[61]) ).

thf(139,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( product @ W @ Z @ X )
          | ( product @ W @ Z @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[62]) ).

thf(140,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( product @ W @ X @ Z )
          | ( product @ W @ Y @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[63]) ).

thf(141,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( product @ X @ W @ Z )
          | ( product @ Y @ W @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[64]) ).

thf(142,plain,
    ( ( ! [X: $i,Y: $i,W: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[65]) ).

thf(143,plain,
    ( ( ! [X: $i,Y: $i,W: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[66]) ).

thf(144,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( sum @ W @ Z @ X )
          | ( sum @ W @ Z @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[67]) ).

thf(145,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( sum @ W @ X @ Z )
          | ( sum @ W @ Y @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[68]) ).

thf(146,plain,
    ( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
          ( ~ ( equalish @ X @ Y )
          | ~ ( sum @ X @ W @ Z )
          | ( sum @ Y @ W @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[69]) ).

thf(147,plain,
    ( ( ! [X: $i,Y: $i,W: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[70]) ).

thf(148,plain,
    ( ( ! [X: $i,Y: $i,W: $i] :
          ( ~ ( equalish @ X @ Y )
          | ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[71]) ).

thf(149,plain,
    ( ( ~ ( equalish @ c @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[74]) ).

thf(150,plain,
    ( ( product @ b @ a @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[75]) ).

thf(151,plain,
    ( ( product @ a @ b @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[76]) ).

thf(152,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[77]) ).

thf(153,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( sum @ A @ B @ C )
          | ! [D: $i] :
              ( ~ ( sum @ A @ D @ C )
              | ( equalish @ D @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[118]) ).

thf(154,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( sum @ A @ B @ C )
          | ! [D: $i] :
              ( ~ ( sum @ D @ B @ C )
              | ( equalish @ D @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[119]) ).

thf(155,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ X @ Y @ V )
              | ( equalish @ U @ V ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[120]) ).

thf(156,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ X @ Y @ V )
              | ( equalish @ U @ V ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[121]) ).

thf(157,plain,
    ( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ Y @ X @ V1 )
          | ~ ( product @ Z @ X @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( sum @ V1 @ V2 @ V4 )
                  | ( product @ V3 @ X @ V4 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[124]) ).

thf(158,plain,
    ( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ Y @ X @ V1 )
          | ~ ( product @ Z @ X @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( product @ V3 @ X @ V4 )
                  | ( sum @ V1 @ V2 @ V4 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[125]) ).

thf(159,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ X @ Y @ V1 )
          | ~ ( product @ X @ Z @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( sum @ V1 @ V2 @ V4 )
                  | ( product @ X @ V3 @ V4 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[126]) ).

thf(160,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ X @ Y @ V1 )
          | ~ ( product @ X @ Z @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( product @ X @ V3 @ V4 )
                  | ( sum @ V1 @ V2 @ V4 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[127]) ).

thf(161,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ X @ V @ W )
                  | ( product @ U @ Z @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[128]) ).

thf(162,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ U @ Z @ W )
                  | ( product @ X @ V @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[129]) ).

thf(163,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( sum @ X @ V @ W )
                  | ( sum @ U @ Z @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[131]) ).

thf(164,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( sum @ U @ Z @ W )
                  | ( sum @ X @ V @ W ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[132]) ).

thf(165,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( equalish @ Y @ Z )
              | ( equalish @ X @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[137]) ).

thf(166,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( product @ W @ Z @ X )
              | ( product @ W @ Z @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[139]) ).

thf(167,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( product @ W @ X @ Z )
              | ( product @ W @ Y @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[140]) ).

thf(168,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( product @ X @ W @ Z )
              | ( product @ Y @ W @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[141]) ).

thf(169,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[142]) ).

thf(170,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[143]) ).

thf(171,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( sum @ W @ Z @ X )
              | ( sum @ W @ Z @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[144]) ).

thf(172,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( sum @ W @ X @ Z )
              | ( sum @ W @ Y @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[145]) ).

thf(173,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( sum @ X @ W @ Z )
              | ( sum @ Y @ W @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[146]) ).

thf(174,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[147]) ).

thf(175,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[148]) ).

thf(176,plain,
    ( ( product @ a @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[151]) ).

thf(177,plain,
    ( ( product @ b @ a @ d )
    = $true ),
    inference(copy,[status(thm)],[150]) ).

thf(178,plain,
    ( ( ~ ( equalish @ c @ d ) )
    = $true ),
    inference(copy,[status(thm)],[149]) ).

thf(179,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[175]) ).

thf(180,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[174]) ).

thf(181,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( sum @ X @ W @ Z )
              | ( sum @ Y @ W @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[173]) ).

thf(182,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( sum @ W @ X @ Z )
              | ( sum @ W @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[172]) ).

thf(183,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( sum @ W @ Z @ X )
              | ( sum @ W @ Z @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[171]) ).

thf(184,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[170]) ).

thf(185,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i] : ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[169]) ).

thf(186,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( product @ X @ W @ Z )
              | ( product @ Y @ W @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[168]) ).

thf(187,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( product @ W @ X @ Z )
              | ( product @ W @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[167]) ).

thf(188,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [W: $i,Z: $i] :
              ( ~ ( product @ W @ Z @ X )
              | ( product @ W @ Z @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[166]) ).

thf(189,plain,
    ( ( ! [X: $i] : ( equalish @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[138]) ).

thf(190,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( equalish @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( equalish @ Y @ Z )
              | ( equalish @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[165]) ).

thf(191,plain,
    ( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[136]) ).

thf(192,plain,
    ( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
    = $true ),
    inference(copy,[status(thm)],[135]) ).

thf(193,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[134]) ).

thf(194,plain,
    ( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[133]) ).

thf(195,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( sum @ U @ Z @ W )
                  | ( sum @ X @ V @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[164]) ).

thf(196,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( sum @ X @ V @ W )
                  | ( sum @ U @ Z @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[163]) ).

thf(197,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ Z )
          | ( sum @ Y @ X @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[130]) ).

thf(198,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ U @ Z @ W )
                  | ( product @ X @ V @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[162]) ).

thf(199,plain,
    ( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ Y @ Z @ V )
              | ! [W: $i] :
                  ( ~ ( product @ X @ V @ W )
                  | ( product @ U @ Z @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[161]) ).

thf(200,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ X @ Y @ V1 )
          | ~ ( product @ X @ Z @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( product @ X @ V3 @ V4 )
                  | ( sum @ V1 @ V2 @ V4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[160]) ).

thf(201,plain,
    ( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ X @ Y @ V1 )
          | ~ ( product @ X @ Z @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( sum @ V1 @ V2 @ V4 )
                  | ( product @ X @ V3 @ V4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[159]) ).

thf(202,plain,
    ( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ Y @ X @ V1 )
          | ~ ( product @ Z @ X @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( product @ V3 @ X @ V4 )
                  | ( sum @ V1 @ V2 @ V4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[158]) ).

thf(203,plain,
    ( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
          ( ~ ( product @ Y @ X @ V1 )
          | ~ ( product @ Z @ X @ V2 )
          | ! [V3: $i] :
              ( ~ ( sum @ Y @ Z @ V3 )
              | ! [V4: $i] :
                  ( ~ ( sum @ V1 @ V2 @ V4 )
                  | ( product @ V3 @ X @ V4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[157]) ).

thf(204,plain,
    ( ( ! [X: $i] : ( product @ additive_identity @ X @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[123]) ).

thf(205,plain,
    ( ( ! [X: $i] : ( product @ X @ additive_identity @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[122]) ).

thf(206,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ X @ Y @ V )
              | ( equalish @ U @ V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[156]) ).

thf(207,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ X @ Y @ V )
              | ( equalish @ U @ V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[155]) ).

thf(208,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( sum @ A @ B @ C )
          | ! [D: $i] :
              ( ~ ( sum @ D @ B @ C )
              | ( equalish @ D @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[154]) ).

thf(209,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( sum @ A @ B @ C )
          | ! [D: $i] :
              ( ~ ( sum @ A @ D @ C )
              | ( equalish @ D @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[153]) ).

thf(210,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
    = $true ),
    inference(copy,[status(thm)],[117]) ).

thf(211,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
    = $true ),
    inference(copy,[status(thm)],[116]) ).

thf(212,plain,
    ( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[115]) ).

thf(213,plain,
    ( ( ! [A: $i] : ( equalish @ ( add @ A @ additive_identity ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[114]) ).

thf(214,plain,
    ( ( ! [A: $i] : ( equalish @ ( add @ A @ A ) @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[113]) ).

thf(215,plain,
    ( ( ! [A: $i] : ( equalish @ ( multiply @ A @ A ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[112]) ).

thf(216,plain,
    ( ( equalish @ ( multiply @ a @ b ) @ c )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(217,plain,
    ( ( equalish @ ( multiply @ b @ a ) @ d )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(218,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(219,plain,
    ( ( product @ a @ c @ c )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(220,plain,
    ( ( product @ b @ d @ d )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(221,plain,
    ( ( product @ c @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(222,plain,
    ( ( product @ d @ a @ d )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(223,plain,
    ( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(224,plain,
    ( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(225,plain,
    ( ( product @ a @ b @ ( multiply @ c @ b ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(226,plain,
    ( ( product @ a @ ( multiply @ b @ c ) @ c )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(227,plain,
    ( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(228,plain,
    ( ( product @ b @ a @ ( multiply @ d @ a ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(229,plain,
    ( ( product @ b @ ( multiply @ a @ d ) @ d )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(230,plain,
    ( ( product @ b @ c @ ( multiply @ d @ b ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(231,plain,
    ( ( product @ a @ d @ ( multiply @ c @ a ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(232,plain,
    ( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(233,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(234,plain,
    ( ( product @ a @ b @ ( multiply @ a @ c ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(235,plain,
    ( ( product @ ( multiply @ c @ a ) @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(236,plain,
    ( ( product @ d @ b @ ( multiply @ b @ c ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(237,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(238,plain,
    ( ( product @ b @ a @ ( multiply @ b @ d ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(239,plain,
    ( ( product @ ( multiply @ d @ b ) @ a @ d )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(240,plain,
    ( ( product @ c @ a @ ( multiply @ a @ d ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(241,plain,
    ( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(242,plain,
    ( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(243,plain,
    ( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(244,plain,
    ( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(245,plain,
    ( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(246,plain,
    ( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(247,plain,
    ( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(248,plain,
    ( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(249,plain,
    ( ( ! [A: $i] : ( product @ A @ A @ A ) )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(250,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[152]) ).

thf(251,plain,
    ( ( equalish @ c @ d )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[178]) ).

thf(252,plain,
    ! [SV1: $i] :
      ( ( ! [SY139: $i] :
            ( ~ ( equalish @ SV1 @ SY139 )
            | ! [SY140: $i] : ( equalish @ ( add @ SV1 @ SY140 ) @ ( add @ SY139 @ SY140 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[179]) ).

thf(253,plain,
    ! [SV2: $i] :
      ( ( ! [SY141: $i] :
            ( ~ ( equalish @ SV2 @ SY141 )
            | ! [SY142: $i] : ( equalish @ ( add @ SY142 @ SV2 ) @ ( add @ SY142 @ SY141 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[180]) ).

thf(254,plain,
    ! [SV3: $i] :
      ( ( ! [SY143: $i] :
            ( ~ ( equalish @ SV3 @ SY143 )
            | ! [SY144: $i,SY145: $i] :
                ( ~ ( sum @ SV3 @ SY144 @ SY145 )
                | ( sum @ SY143 @ SY144 @ SY145 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[181]) ).

thf(255,plain,
    ! [SV4: $i] :
      ( ( ! [SY146: $i] :
            ( ~ ( equalish @ SV4 @ SY146 )
            | ! [SY147: $i,SY148: $i] :
                ( ~ ( sum @ SY147 @ SV4 @ SY148 )
                | ( sum @ SY147 @ SY146 @ SY148 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[182]) ).

thf(256,plain,
    ! [SV5: $i] :
      ( ( ! [SY149: $i] :
            ( ~ ( equalish @ SV5 @ SY149 )
            | ! [SY150: $i,SY151: $i] :
                ( ~ ( sum @ SY150 @ SY151 @ SV5 )
                | ( sum @ SY150 @ SY151 @ SY149 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[183]) ).

thf(257,plain,
    ! [SV6: $i] :
      ( ( ! [SY152: $i] :
            ( ~ ( equalish @ SV6 @ SY152 )
            | ! [SY153: $i] : ( equalish @ ( multiply @ SV6 @ SY153 ) @ ( multiply @ SY152 @ SY153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[184]) ).

thf(258,plain,
    ! [SV7: $i] :
      ( ( ! [SY154: $i] :
            ( ~ ( equalish @ SV7 @ SY154 )
            | ! [SY155: $i] : ( equalish @ ( multiply @ SY155 @ SV7 ) @ ( multiply @ SY155 @ SY154 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[185]) ).

thf(259,plain,
    ! [SV8: $i] :
      ( ( ! [SY156: $i] :
            ( ~ ( equalish @ SV8 @ SY156 )
            | ! [SY157: $i,SY158: $i] :
                ( ~ ( product @ SV8 @ SY157 @ SY158 )
                | ( product @ SY156 @ SY157 @ SY158 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[186]) ).

thf(260,plain,
    ! [SV9: $i] :
      ( ( ! [SY159: $i] :
            ( ~ ( equalish @ SV9 @ SY159 )
            | ! [SY160: $i,SY161: $i] :
                ( ~ ( product @ SY160 @ SV9 @ SY161 )
                | ( product @ SY160 @ SY159 @ SY161 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[187]) ).

thf(261,plain,
    ! [SV10: $i] :
      ( ( ! [SY162: $i] :
            ( ~ ( equalish @ SV10 @ SY162 )
            | ! [SY163: $i,SY164: $i] :
                ( ~ ( product @ SY163 @ SY164 @ SV10 )
                | ( product @ SY163 @ SY164 @ SY162 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[188]) ).

thf(262,plain,
    ! [SV11: $i] :
      ( ( equalish @ SV11 @ SV11 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[189]) ).

thf(263,plain,
    ! [SV12: $i] :
      ( ( ! [SY165: $i] :
            ( ~ ( equalish @ SV12 @ SY165 )
            | ! [SY166: $i] :
                ( ~ ( equalish @ SY165 @ SY166 )
                | ( equalish @ SV12 @ SY166 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[190]) ).

thf(264,plain,
    ! [SV13: $i] :
      ( ( sum @ additive_identity @ SV13 @ SV13 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[191]) ).

thf(265,plain,
    ! [SV14: $i] :
      ( ( sum @ SV14 @ additive_identity @ SV14 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[192]) ).

thf(266,plain,
    ! [SV15: $i] :
      ( ( ! [SY167: $i] : ( product @ SV15 @ SY167 @ ( multiply @ SV15 @ SY167 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[193]) ).

thf(267,plain,
    ! [SV16: $i] :
      ( ( ! [SY168: $i] : ( sum @ SV16 @ SY168 @ ( add @ SV16 @ SY168 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[194]) ).

thf(268,plain,
    ! [SV17: $i] :
      ( ( ! [SY169: $i,SY170: $i,SY171: $i] :
            ( ~ ( sum @ SV17 @ SY169 @ SY170 )
            | ! [SY172: $i] :
                ( ~ ( sum @ SY169 @ SY171 @ SY172 )
                | ! [SY173: $i] :
                    ( ~ ( sum @ SY170 @ SY171 @ SY173 )
                    | ( sum @ SV17 @ SY172 @ SY173 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[195]) ).

thf(269,plain,
    ! [SV18: $i] :
      ( ( ! [SY174: $i,SY175: $i,SY176: $i] :
            ( ~ ( sum @ SV18 @ SY174 @ SY175 )
            | ! [SY177: $i] :
                ( ~ ( sum @ SY174 @ SY176 @ SY177 )
                | ! [SY178: $i] :
                    ( ~ ( sum @ SV18 @ SY177 @ SY178 )
                    | ( sum @ SY175 @ SY176 @ SY178 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[196]) ).

thf(270,plain,
    ! [SV19: $i] :
      ( ( ! [SY179: $i,SY180: $i] :
            ( ~ ( sum @ SV19 @ SY179 @ SY180 )
            | ( sum @ SY179 @ SV19 @ SY180 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[197]) ).

thf(271,plain,
    ! [SV20: $i] :
      ( ( ! [SY181: $i,SY182: $i,SY183: $i] :
            ( ~ ( product @ SV20 @ SY181 @ SY182 )
            | ! [SY184: $i] :
                ( ~ ( product @ SY181 @ SY183 @ SY184 )
                | ! [SY185: $i] :
                    ( ~ ( product @ SY182 @ SY183 @ SY185 )
                    | ( product @ SV20 @ SY184 @ SY185 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[198]) ).

thf(272,plain,
    ! [SV21: $i] :
      ( ( ! [SY186: $i,SY187: $i,SY188: $i] :
            ( ~ ( product @ SV21 @ SY186 @ SY187 )
            | ! [SY189: $i] :
                ( ~ ( product @ SY186 @ SY188 @ SY189 )
                | ! [SY190: $i] :
                    ( ~ ( product @ SV21 @ SY189 @ SY190 )
                    | ( product @ SY187 @ SY188 @ SY190 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[199]) ).

thf(273,plain,
    ! [SV22: $i] :
      ( ( ! [SY191: $i,SY192: $i,SY193: $i,SY194: $i] :
            ( ~ ( product @ SV22 @ SY191 @ SY192 )
            | ~ ( product @ SV22 @ SY193 @ SY194 )
            | ! [SY195: $i] :
                ( ~ ( sum @ SY191 @ SY193 @ SY195 )
                | ! [SY196: $i] :
                    ( ~ ( product @ SV22 @ SY195 @ SY196 )
                    | ( sum @ SY192 @ SY194 @ SY196 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[200]) ).

thf(274,plain,
    ! [SV23: $i] :
      ( ( ! [SY197: $i,SY198: $i,SY199: $i,SY200: $i] :
            ( ~ ( product @ SV23 @ SY197 @ SY198 )
            | ~ ( product @ SV23 @ SY199 @ SY200 )
            | ! [SY201: $i] :
                ( ~ ( sum @ SY197 @ SY199 @ SY201 )
                | ! [SY202: $i] :
                    ( ~ ( sum @ SY198 @ SY200 @ SY202 )
                    | ( product @ SV23 @ SY201 @ SY202 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(275,plain,
    ! [SV24: $i] :
      ( ( ! [SY203: $i,SY204: $i,SY205: $i,SY206: $i] :
            ( ~ ( product @ SV24 @ SY203 @ SY204 )
            | ~ ( product @ SY205 @ SY203 @ SY206 )
            | ! [SY207: $i] :
                ( ~ ( sum @ SV24 @ SY205 @ SY207 )
                | ! [V4: $i] :
                    ( ~ ( product @ SY207 @ SY203 @ V4 )
                    | ( sum @ SY204 @ SY206 @ V4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[202]) ).

thf(276,plain,
    ! [SV25: $i] :
      ( ( ! [SY209: $i,SY210: $i,SY211: $i,SY212: $i] :
            ( ~ ( product @ SV25 @ SY209 @ SY210 )
            | ~ ( product @ SY211 @ SY209 @ SY212 )
            | ! [SY213: $i] :
                ( ~ ( sum @ SV25 @ SY211 @ SY213 )
                | ! [V4: $i] :
                    ( ~ ( sum @ SY210 @ SY212 @ V4 )
                    | ( product @ SY213 @ SY209 @ V4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[203]) ).

thf(277,plain,
    ! [SV26: $i] :
      ( ( product @ additive_identity @ SV26 @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[204]) ).

thf(278,plain,
    ! [SV27: $i] :
      ( ( product @ SV27 @ additive_identity @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[205]) ).

thf(279,plain,
    ! [SV28: $i] :
      ( ( ! [SY215: $i,SY216: $i] :
            ( ~ ( sum @ SV28 @ SY215 @ SY216 )
            | ! [SY217: $i] :
                ( ~ ( sum @ SV28 @ SY215 @ SY217 )
                | ( equalish @ SY216 @ SY217 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[206]) ).

thf(280,plain,
    ! [SV29: $i] :
      ( ( ! [SY218: $i,SY219: $i] :
            ( ~ ( product @ SV29 @ SY218 @ SY219 )
            | ! [SY220: $i] :
                ( ~ ( product @ SV29 @ SY218 @ SY220 )
                | ( equalish @ SY219 @ SY220 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[207]) ).

thf(281,plain,
    ! [SV30: $i] :
      ( ( ! [SY221: $i,SY222: $i] :
            ( ~ ( sum @ SV30 @ SY221 @ SY222 )
            | ! [SY223: $i] :
                ( ~ ( sum @ SY223 @ SY221 @ SY222 )
                | ( equalish @ SY223 @ SV30 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[208]) ).

thf(282,plain,
    ! [SV31: $i] :
      ( ( ! [SY224: $i,SY225: $i] :
            ( ~ ( sum @ SV31 @ SY224 @ SY225 )
            | ! [SY226: $i] :
                ( ~ ( sum @ SV31 @ SY226 @ SY225 )
                | ( equalish @ SY226 @ SY224 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[209]) ).

thf(283,plain,
    ! [SV32: $i] :
      ( ( ! [SY227: $i] : ( sum @ SV32 @ ( add @ SV32 @ SY227 ) @ SY227 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[210]) ).

thf(284,plain,
    ! [SV33: $i] :
      ( ( ! [SY228: $i] : ( sum @ ( add @ SV33 @ SY228 ) @ SY228 @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[211]) ).

thf(285,plain,
    ! [SV34: $i] :
      ( ( sum @ SV34 @ SV34 @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[212]) ).

thf(286,plain,
    ! [SV35: $i] :
      ( ( equalish @ ( add @ SV35 @ additive_identity ) @ SV35 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[213]) ).

thf(287,plain,
    ! [SV36: $i] :
      ( ( equalish @ ( add @ SV36 @ SV36 ) @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[214]) ).

thf(288,plain,
    ! [SV37: $i] :
      ( ( equalish @ ( multiply @ SV37 @ SV37 ) @ SV37 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[215]) ).

thf(289,plain,
    ! [SV38: $i] :
      ( ( ! [SY229: $i] : ( sum @ SV38 @ SY229 @ ( add @ SY229 @ SV38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[218]) ).

thf(290,plain,
    ! [SV39: $i] :
      ( ( ! [SY230: $i] : ( product @ SV39 @ ( multiply @ SV39 @ SY230 ) @ ( multiply @ SV39 @ SY230 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[223]) ).

thf(291,plain,
    ! [SV40: $i] :
      ( ( ! [SY231: $i] : ( product @ a @ ( multiply @ b @ SV40 ) @ ( multiply @ SY231 @ SV40 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[224]) ).

thf(292,plain,
    ! [SV41: $i] :
      ( ( product @ b @ ( multiply @ a @ SV41 ) @ ( multiply @ d @ SV41 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[227]) ).

thf(293,plain,
    ! [SV42: $i] :
      ( ( ! [SY232: $i] : ( product @ ( multiply @ SV42 @ SY232 ) @ SY232 @ ( multiply @ SV42 @ SY232 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[232]) ).

thf(294,plain,
    ! [SV43: $i] :
      ( ( product @ ( multiply @ SV43 @ a ) @ b @ ( multiply @ SV43 @ c ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[233]) ).

thf(295,plain,
    ! [SV44: $i] :
      ( ( product @ ( multiply @ SV44 @ b ) @ a @ ( multiply @ SV44 @ d ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[237]) ).

thf(296,plain,
    ! [SV45: $i] :
      ( ( product @ SV45 @ SV45 @ SV45 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[249]) ).

thf(297,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[250]) ).

thf(298,plain,
    ! [SV46: $i,SV1: $i] :
      ( ( ~ ( equalish @ SV1 @ SV46 )
        | ! [SY233: $i] : ( equalish @ ( add @ SV1 @ SY233 ) @ ( add @ SV46 @ SY233 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[252]) ).

thf(299,plain,
    ! [SV47: $i,SV2: $i] :
      ( ( ~ ( equalish @ SV2 @ SV47 )
        | ! [SY234: $i] : ( equalish @ ( add @ SY234 @ SV2 ) @ ( add @ SY234 @ SV47 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[253]) ).

thf(300,plain,
    ! [SV48: $i,SV3: $i] :
      ( ( ~ ( equalish @ SV3 @ SV48 )
        | ! [SY235: $i,SY236: $i] :
            ( ~ ( sum @ SV3 @ SY235 @ SY236 )
            | ( sum @ SV48 @ SY235 @ SY236 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[254]) ).

thf(301,plain,
    ! [SV49: $i,SV4: $i] :
      ( ( ~ ( equalish @ SV4 @ SV49 )
        | ! [SY237: $i,SY238: $i] :
            ( ~ ( sum @ SY237 @ SV4 @ SY238 )
            | ( sum @ SY237 @ SV49 @ SY238 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[255]) ).

thf(302,plain,
    ! [SV50: $i,SV5: $i] :
      ( ( ~ ( equalish @ SV5 @ SV50 )
        | ! [SY239: $i,SY240: $i] :
            ( ~ ( sum @ SY239 @ SY240 @ SV5 )
            | ( sum @ SY239 @ SY240 @ SV50 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[256]) ).

thf(303,plain,
    ! [SV51: $i,SV6: $i] :
      ( ( ~ ( equalish @ SV6 @ SV51 )
        | ! [SY241: $i] : ( equalish @ ( multiply @ SV6 @ SY241 ) @ ( multiply @ SV51 @ SY241 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[257]) ).

thf(304,plain,
    ! [SV52: $i,SV7: $i] :
      ( ( ~ ( equalish @ SV7 @ SV52 )
        | ! [SY242: $i] : ( equalish @ ( multiply @ SY242 @ SV7 ) @ ( multiply @ SY242 @ SV52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[258]) ).

thf(305,plain,
    ! [SV53: $i,SV8: $i] :
      ( ( ~ ( equalish @ SV8 @ SV53 )
        | ! [SY243: $i,SY244: $i] :
            ( ~ ( product @ SV8 @ SY243 @ SY244 )
            | ( product @ SV53 @ SY243 @ SY244 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[259]) ).

thf(306,plain,
    ! [SV54: $i,SV9: $i] :
      ( ( ~ ( equalish @ SV9 @ SV54 )
        | ! [SY245: $i,SY246: $i] :
            ( ~ ( product @ SY245 @ SV9 @ SY246 )
            | ( product @ SY245 @ SV54 @ SY246 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[260]) ).

thf(307,plain,
    ! [SV55: $i,SV10: $i] :
      ( ( ~ ( equalish @ SV10 @ SV55 )
        | ! [SY247: $i,SY248: $i] :
            ( ~ ( product @ SY247 @ SY248 @ SV10 )
            | ( product @ SY247 @ SY248 @ SV55 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[261]) ).

thf(308,plain,
    ! [SV56: $i,SV12: $i] :
      ( ( ~ ( equalish @ SV12 @ SV56 )
        | ! [SY249: $i] :
            ( ~ ( equalish @ SV56 @ SY249 )
            | ( equalish @ SV12 @ SY249 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[263]) ).

thf(309,plain,
    ! [SV57: $i,SV15: $i] :
      ( ( product @ SV15 @ SV57 @ ( multiply @ SV15 @ SV57 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[266]) ).

thf(310,plain,
    ! [SV58: $i,SV16: $i] :
      ( ( sum @ SV16 @ SV58 @ ( add @ SV16 @ SV58 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[267]) ).

thf(311,plain,
    ! [SV59: $i,SV17: $i] :
      ( ( ! [SY250: $i,SY251: $i] :
            ( ~ ( sum @ SV17 @ SV59 @ SY250 )
            | ! [SY252: $i] :
                ( ~ ( sum @ SV59 @ SY251 @ SY252 )
                | ! [SY173: $i] :
                    ( ~ ( sum @ SY250 @ SY251 @ SY173 )
                    | ( sum @ SV17 @ SY252 @ SY173 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[268]) ).

thf(312,plain,
    ! [SV60: $i,SV18: $i] :
      ( ( ! [SY254: $i,SY255: $i] :
            ( ~ ( sum @ SV18 @ SV60 @ SY254 )
            | ! [SY256: $i] :
                ( ~ ( sum @ SV60 @ SY255 @ SY256 )
                | ! [SY178: $i] :
                    ( ~ ( sum @ SV18 @ SY256 @ SY178 )
                    | ( sum @ SY254 @ SY255 @ SY178 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[269]) ).

thf(313,plain,
    ! [SV61: $i,SV19: $i] :
      ( ( ! [SY258: $i] :
            ( ~ ( sum @ SV19 @ SV61 @ SY258 )
            | ( sum @ SV61 @ SV19 @ SY258 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[270]) ).

thf(314,plain,
    ! [SV62: $i,SV20: $i] :
      ( ( ! [SY259: $i,SY260: $i] :
            ( ~ ( product @ SV20 @ SV62 @ SY259 )
            | ! [SY261: $i] :
                ( ~ ( product @ SV62 @ SY260 @ SY261 )
                | ! [SY185: $i] :
                    ( ~ ( product @ SY259 @ SY260 @ SY185 )
                    | ( product @ SV20 @ SY261 @ SY185 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[271]) ).

thf(315,plain,
    ! [SV63: $i,SV21: $i] :
      ( ( ! [SY263: $i,SY264: $i] :
            ( ~ ( product @ SV21 @ SV63 @ SY263 )
            | ! [SY265: $i] :
                ( ~ ( product @ SV63 @ SY264 @ SY265 )
                | ! [SY190: $i] :
                    ( ~ ( product @ SV21 @ SY265 @ SY190 )
                    | ( product @ SY263 @ SY264 @ SY190 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[272]) ).

thf(316,plain,
    ! [SV64: $i,SV22: $i] :
      ( ( ! [SY267: $i,SY268: $i,SY269: $i] :
            ( ~ ( product @ SV22 @ SV64 @ SY267 )
            | ~ ( product @ SV22 @ SY268 @ SY269 )
            | ! [SY270: $i] :
                ( ~ ( sum @ SV64 @ SY268 @ SY270 )
                | ! [SY196: $i] :
                    ( ~ ( product @ SV22 @ SY270 @ SY196 )
                    | ( sum @ SY267 @ SY269 @ SY196 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[273]) ).

thf(317,plain,
    ! [SV65: $i,SV23: $i] :
      ( ( ! [SY272: $i,SY273: $i,SY274: $i] :
            ( ~ ( product @ SV23 @ SV65 @ SY272 )
            | ~ ( product @ SV23 @ SY273 @ SY274 )
            | ! [SY275: $i] :
                ( ~ ( sum @ SV65 @ SY273 @ SY275 )
                | ! [SY202: $i] :
                    ( ~ ( sum @ SY272 @ SY274 @ SY202 )
                    | ( product @ SV23 @ SY275 @ SY202 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[274]) ).

thf(318,plain,
    ! [SV66: $i,SV24: $i] :
      ( ( ! [SY277: $i,SY278: $i,SY279: $i] :
            ( ~ ( product @ SV24 @ SV66 @ SY277 )
            | ~ ( product @ SY278 @ SV66 @ SY279 )
            | ! [SY280: $i] :
                ( ~ ( sum @ SV24 @ SY278 @ SY280 )
                | ! [SY281: $i] :
                    ( ~ ( product @ SY280 @ SV66 @ SY281 )
                    | ( sum @ SY277 @ SY279 @ SY281 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[275]) ).

thf(319,plain,
    ! [SV67: $i,SV25: $i] :
      ( ( ! [SY282: $i,SY283: $i,SY284: $i] :
            ( ~ ( product @ SV25 @ SV67 @ SY282 )
            | ~ ( product @ SY283 @ SV67 @ SY284 )
            | ! [SY285: $i] :
                ( ~ ( sum @ SV25 @ SY283 @ SY285 )
                | ! [SY286: $i] :
                    ( ~ ( sum @ SY282 @ SY284 @ SY286 )
                    | ( product @ SY285 @ SV67 @ SY286 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[276]) ).

thf(320,plain,
    ! [SV68: $i,SV28: $i] :
      ( ( ! [SY287: $i] :
            ( ~ ( sum @ SV28 @ SV68 @ SY287 )
            | ! [SY288: $i] :
                ( ~ ( sum @ SV28 @ SV68 @ SY288 )
                | ( equalish @ SY287 @ SY288 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[279]) ).

thf(321,plain,
    ! [SV69: $i,SV29: $i] :
      ( ( ! [SY289: $i] :
            ( ~ ( product @ SV29 @ SV69 @ SY289 )
            | ! [SY290: $i] :
                ( ~ ( product @ SV29 @ SV69 @ SY290 )
                | ( equalish @ SY289 @ SY290 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[280]) ).

thf(322,plain,
    ! [SV70: $i,SV30: $i] :
      ( ( ! [SY291: $i] :
            ( ~ ( sum @ SV30 @ SV70 @ SY291 )
            | ! [SY292: $i] :
                ( ~ ( sum @ SY292 @ SV70 @ SY291 )
                | ( equalish @ SY292 @ SV30 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[281]) ).

thf(323,plain,
    ! [SV71: $i,SV31: $i] :
      ( ( ! [SY293: $i] :
            ( ~ ( sum @ SV31 @ SV71 @ SY293 )
            | ! [SY294: $i] :
                ( ~ ( sum @ SV31 @ SY294 @ SY293 )
                | ( equalish @ SY294 @ SV71 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[282]) ).

thf(324,plain,
    ! [SV72: $i,SV32: $i] :
      ( ( sum @ SV32 @ ( add @ SV32 @ SV72 ) @ SV72 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[283]) ).

thf(325,plain,
    ! [SV73: $i,SV33: $i] :
      ( ( sum @ ( add @ SV33 @ SV73 ) @ SV73 @ SV33 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[284]) ).

thf(326,plain,
    ! [SV74: $i,SV38: $i] :
      ( ( sum @ SV38 @ SV74 @ ( add @ SV74 @ SV38 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[289]) ).

thf(327,plain,
    ! [SV75: $i,SV39: $i] :
      ( ( product @ SV39 @ ( multiply @ SV39 @ SV75 ) @ ( multiply @ SV39 @ SV75 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[290]) ).

thf(328,plain,
    ! [SV76: $i,SV40: $i] :
      ( ( product @ a @ ( multiply @ b @ SV40 ) @ ( multiply @ SV76 @ SV40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[291]) ).

thf(329,plain,
    ! [SV77: $i,SV42: $i] :
      ( ( product @ ( multiply @ SV42 @ SV77 ) @ SV77 @ ( multiply @ SV42 @ SV77 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[293]) ).

thf(330,plain,
    ! [SV46: $i,SV1: $i] :
      ( ( ( ~ ( equalish @ SV1 @ SV46 ) )
        = $true )
      | ( ( ! [SY233: $i] : ( equalish @ ( add @ SV1 @ SY233 ) @ ( add @ SV46 @ SY233 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[298]) ).

thf(331,plain,
    ! [SV47: $i,SV2: $i] :
      ( ( ( ~ ( equalish @ SV2 @ SV47 ) )
        = $true )
      | ( ( ! [SY234: $i] : ( equalish @ ( add @ SY234 @ SV2 ) @ ( add @ SY234 @ SV47 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[299]) ).

thf(332,plain,
    ! [SV48: $i,SV3: $i] :
      ( ( ( ~ ( equalish @ SV3 @ SV48 ) )
        = $true )
      | ( ( ! [SY235: $i,SY236: $i] :
              ( ~ ( sum @ SV3 @ SY235 @ SY236 )
              | ( sum @ SV48 @ SY235 @ SY236 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[300]) ).

thf(333,plain,
    ! [SV49: $i,SV4: $i] :
      ( ( ( ~ ( equalish @ SV4 @ SV49 ) )
        = $true )
      | ( ( ! [SY237: $i,SY238: $i] :
              ( ~ ( sum @ SY237 @ SV4 @ SY238 )
              | ( sum @ SY237 @ SV49 @ SY238 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[301]) ).

thf(334,plain,
    ! [SV50: $i,SV5: $i] :
      ( ( ( ~ ( equalish @ SV5 @ SV50 ) )
        = $true )
      | ( ( ! [SY239: $i,SY240: $i] :
              ( ~ ( sum @ SY239 @ SY240 @ SV5 )
              | ( sum @ SY239 @ SY240 @ SV50 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[302]) ).

thf(335,plain,
    ! [SV51: $i,SV6: $i] :
      ( ( ( ~ ( equalish @ SV6 @ SV51 ) )
        = $true )
      | ( ( ! [SY241: $i] : ( equalish @ ( multiply @ SV6 @ SY241 ) @ ( multiply @ SV51 @ SY241 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[303]) ).

thf(336,plain,
    ! [SV52: $i,SV7: $i] :
      ( ( ( ~ ( equalish @ SV7 @ SV52 ) )
        = $true )
      | ( ( ! [SY242: $i] : ( equalish @ ( multiply @ SY242 @ SV7 ) @ ( multiply @ SY242 @ SV52 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[304]) ).

thf(337,plain,
    ! [SV53: $i,SV8: $i] :
      ( ( ( ~ ( equalish @ SV8 @ SV53 ) )
        = $true )
      | ( ( ! [SY243: $i,SY244: $i] :
              ( ~ ( product @ SV8 @ SY243 @ SY244 )
              | ( product @ SV53 @ SY243 @ SY244 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[305]) ).

thf(338,plain,
    ! [SV54: $i,SV9: $i] :
      ( ( ( ~ ( equalish @ SV9 @ SV54 ) )
        = $true )
      | ( ( ! [SY245: $i,SY246: $i] :
              ( ~ ( product @ SY245 @ SV9 @ SY246 )
              | ( product @ SY245 @ SV54 @ SY246 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[306]) ).

thf(339,plain,
    ! [SV55: $i,SV10: $i] :
      ( ( ( ~ ( equalish @ SV10 @ SV55 ) )
        = $true )
      | ( ( ! [SY247: $i,SY248: $i] :
              ( ~ ( product @ SY247 @ SY248 @ SV10 )
              | ( product @ SY247 @ SY248 @ SV55 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[307]) ).

thf(340,plain,
    ! [SV56: $i,SV12: $i] :
      ( ( ( ~ ( equalish @ SV12 @ SV56 ) )
        = $true )
      | ( ( ! [SY249: $i] :
              ( ~ ( equalish @ SV56 @ SY249 )
              | ( equalish @ SV12 @ SY249 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[308]) ).

thf(341,plain,
    ! [SV78: $i,SV59: $i,SV17: $i] :
      ( ( ! [SY295: $i] :
            ( ~ ( sum @ SV17 @ SV59 @ SV78 )
            | ! [SY296: $i] :
                ( ~ ( sum @ SV59 @ SY295 @ SY296 )
                | ! [SY297: $i] :
                    ( ~ ( sum @ SV78 @ SY295 @ SY297 )
                    | ( sum @ SV17 @ SY296 @ SY297 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[311]) ).

thf(342,plain,
    ! [SV79: $i,SV60: $i,SV18: $i] :
      ( ( ! [SY298: $i] :
            ( ~ ( sum @ SV18 @ SV60 @ SV79 )
            | ! [SY299: $i] :
                ( ~ ( sum @ SV60 @ SY298 @ SY299 )
                | ! [SY300: $i] :
                    ( ~ ( sum @ SV18 @ SY299 @ SY300 )
                    | ( sum @ SV79 @ SY298 @ SY300 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[312]) ).

thf(343,plain,
    ! [SV80: $i,SV61: $i,SV19: $i] :
      ( ( ~ ( sum @ SV19 @ SV61 @ SV80 )
        | ( sum @ SV61 @ SV19 @ SV80 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[313]) ).

thf(344,plain,
    ! [SV81: $i,SV62: $i,SV20: $i] :
      ( ( ! [SY301: $i] :
            ( ~ ( product @ SV20 @ SV62 @ SV81 )
            | ! [SY302: $i] :
                ( ~ ( product @ SV62 @ SY301 @ SY302 )
                | ! [SY303: $i] :
                    ( ~ ( product @ SV81 @ SY301 @ SY303 )
                    | ( product @ SV20 @ SY302 @ SY303 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[314]) ).

thf(345,plain,
    ! [SV82: $i,SV63: $i,SV21: $i] :
      ( ( ! [SY304: $i] :
            ( ~ ( product @ SV21 @ SV63 @ SV82 )
            | ! [SY305: $i] :
                ( ~ ( product @ SV63 @ SY304 @ SY305 )
                | ! [SY306: $i] :
                    ( ~ ( product @ SV21 @ SY305 @ SY306 )
                    | ( product @ SV82 @ SY304 @ SY306 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[315]) ).

thf(346,plain,
    ! [SV83: $i,SV64: $i,SV22: $i] :
      ( ( ! [SY307: $i,SY308: $i] :
            ( ~ ( product @ SV22 @ SV64 @ SV83 )
            | ~ ( product @ SV22 @ SY307 @ SY308 )
            | ! [SY309: $i] :
                ( ~ ( sum @ SV64 @ SY307 @ SY309 )
                | ! [SY310: $i] :
                    ( ~ ( product @ SV22 @ SY309 @ SY310 )
                    | ( sum @ SV83 @ SY308 @ SY310 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[316]) ).

thf(347,plain,
    ! [SV84: $i,SV65: $i,SV23: $i] :
      ( ( ! [SY311: $i,SY312: $i] :
            ( ~ ( product @ SV23 @ SV65 @ SV84 )
            | ~ ( product @ SV23 @ SY311 @ SY312 )
            | ! [SY313: $i] :
                ( ~ ( sum @ SV65 @ SY311 @ SY313 )
                | ! [SY314: $i] :
                    ( ~ ( sum @ SV84 @ SY312 @ SY314 )
                    | ( product @ SV23 @ SY313 @ SY314 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[317]) ).

thf(348,plain,
    ! [SV85: $i,SV66: $i,SV24: $i] :
      ( ( ! [SY315: $i,SY316: $i] :
            ( ~ ( product @ SV24 @ SV66 @ SV85 )
            | ~ ( product @ SY315 @ SV66 @ SY316 )
            | ! [SY317: $i] :
                ( ~ ( sum @ SV24 @ SY315 @ SY317 )
                | ! [SY318: $i] :
                    ( ~ ( product @ SY317 @ SV66 @ SY318 )
                    | ( sum @ SV85 @ SY316 @ SY318 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[318]) ).

thf(349,plain,
    ! [SV86: $i,SV67: $i,SV25: $i] :
      ( ( ! [SY319: $i,SY320: $i] :
            ( ~ ( product @ SV25 @ SV67 @ SV86 )
            | ~ ( product @ SY319 @ SV67 @ SY320 )
            | ! [SY321: $i] :
                ( ~ ( sum @ SV25 @ SY319 @ SY321 )
                | ! [SY322: $i] :
                    ( ~ ( sum @ SV86 @ SY320 @ SY322 )
                    | ( product @ SY321 @ SV67 @ SY322 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[319]) ).

thf(350,plain,
    ! [SV87: $i,SV68: $i,SV28: $i] :
      ( ( ~ ( sum @ SV28 @ SV68 @ SV87 )
        | ! [SY323: $i] :
            ( ~ ( sum @ SV28 @ SV68 @ SY323 )
            | ( equalish @ SV87 @ SY323 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[320]) ).

thf(351,plain,
    ! [SV88: $i,SV69: $i,SV29: $i] :
      ( ( ~ ( product @ SV29 @ SV69 @ SV88 )
        | ! [SY324: $i] :
            ( ~ ( product @ SV29 @ SV69 @ SY324 )
            | ( equalish @ SV88 @ SY324 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[321]) ).

thf(352,plain,
    ! [SV89: $i,SV70: $i,SV30: $i] :
      ( ( ~ ( sum @ SV30 @ SV70 @ SV89 )
        | ! [SY325: $i] :
            ( ~ ( sum @ SY325 @ SV70 @ SV89 )
            | ( equalish @ SY325 @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[322]) ).

thf(353,plain,
    ! [SV90: $i,SV71: $i,SV31: $i] :
      ( ( ~ ( sum @ SV31 @ SV71 @ SV90 )
        | ! [SY326: $i] :
            ( ~ ( sum @ SV31 @ SY326 @ SV90 )
            | ( equalish @ SY326 @ SV71 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[323]) ).

thf(354,plain,
    ! [SV46: $i,SV1: $i] :
      ( ( ( equalish @ SV1 @ SV46 )
        = $false )
      | ( ( ! [SY233: $i] : ( equalish @ ( add @ SV1 @ SY233 ) @ ( add @ SV46 @ SY233 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[330]) ).

thf(355,plain,
    ! [SV47: $i,SV2: $i] :
      ( ( ( equalish @ SV2 @ SV47 )
        = $false )
      | ( ( ! [SY234: $i] : ( equalish @ ( add @ SY234 @ SV2 ) @ ( add @ SY234 @ SV47 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[331]) ).

thf(356,plain,
    ! [SV48: $i,SV3: $i] :
      ( ( ( equalish @ SV3 @ SV48 )
        = $false )
      | ( ( ! [SY235: $i,SY236: $i] :
              ( ~ ( sum @ SV3 @ SY235 @ SY236 )
              | ( sum @ SV48 @ SY235 @ SY236 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[332]) ).

thf(357,plain,
    ! [SV49: $i,SV4: $i] :
      ( ( ( equalish @ SV4 @ SV49 )
        = $false )
      | ( ( ! [SY237: $i,SY238: $i] :
              ( ~ ( sum @ SY237 @ SV4 @ SY238 )
              | ( sum @ SY237 @ SV49 @ SY238 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[333]) ).

thf(358,plain,
    ! [SV50: $i,SV5: $i] :
      ( ( ( equalish @ SV5 @ SV50 )
        = $false )
      | ( ( ! [SY239: $i,SY240: $i] :
              ( ~ ( sum @ SY239 @ SY240 @ SV5 )
              | ( sum @ SY239 @ SY240 @ SV50 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[334]) ).

thf(359,plain,
    ! [SV51: $i,SV6: $i] :
      ( ( ( equalish @ SV6 @ SV51 )
        = $false )
      | ( ( ! [SY241: $i] : ( equalish @ ( multiply @ SV6 @ SY241 ) @ ( multiply @ SV51 @ SY241 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[335]) ).

thf(360,plain,
    ! [SV52: $i,SV7: $i] :
      ( ( ( equalish @ SV7 @ SV52 )
        = $false )
      | ( ( ! [SY242: $i] : ( equalish @ ( multiply @ SY242 @ SV7 ) @ ( multiply @ SY242 @ SV52 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[336]) ).

thf(361,plain,
    ! [SV53: $i,SV8: $i] :
      ( ( ( equalish @ SV8 @ SV53 )
        = $false )
      | ( ( ! [SY243: $i,SY244: $i] :
              ( ~ ( product @ SV8 @ SY243 @ SY244 )
              | ( product @ SV53 @ SY243 @ SY244 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[337]) ).

thf(362,plain,
    ! [SV54: $i,SV9: $i] :
      ( ( ( equalish @ SV9 @ SV54 )
        = $false )
      | ( ( ! [SY245: $i,SY246: $i] :
              ( ~ ( product @ SY245 @ SV9 @ SY246 )
              | ( product @ SY245 @ SV54 @ SY246 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[338]) ).

thf(363,plain,
    ! [SV55: $i,SV10: $i] :
      ( ( ( equalish @ SV10 @ SV55 )
        = $false )
      | ( ( ! [SY247: $i,SY248: $i] :
              ( ~ ( product @ SY247 @ SY248 @ SV10 )
              | ( product @ SY247 @ SY248 @ SV55 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[339]) ).

thf(364,plain,
    ! [SV56: $i,SV12: $i] :
      ( ( ( equalish @ SV12 @ SV56 )
        = $false )
      | ( ( ! [SY249: $i] :
              ( ~ ( equalish @ SV56 @ SY249 )
              | ( equalish @ SV12 @ SY249 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[340]) ).

thf(365,plain,
    ! [SV91: $i,SV78: $i,SV59: $i,SV17: $i] :
      ( ( ~ ( sum @ SV17 @ SV59 @ SV78 )
        | ! [SY327: $i] :
            ( ~ ( sum @ SV59 @ SV91 @ SY327 )
            | ! [SY328: $i] :
                ( ~ ( sum @ SV78 @ SV91 @ SY328 )
                | ( sum @ SV17 @ SY327 @ SY328 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[341]) ).

thf(366,plain,
    ! [SV92: $i,SV79: $i,SV60: $i,SV18: $i] :
      ( ( ~ ( sum @ SV18 @ SV60 @ SV79 )
        | ! [SY329: $i] :
            ( ~ ( sum @ SV60 @ SV92 @ SY329 )
            | ! [SY330: $i] :
                ( ~ ( sum @ SV18 @ SY329 @ SY330 )
                | ( sum @ SV79 @ SV92 @ SY330 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[342]) ).

thf(367,plain,
    ! [SV80: $i,SV61: $i,SV19: $i] :
      ( ( ( ~ ( sum @ SV19 @ SV61 @ SV80 ) )
        = $true )
      | ( ( sum @ SV61 @ SV19 @ SV80 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[343]) ).

thf(368,plain,
    ! [SV93: $i,SV81: $i,SV62: $i,SV20: $i] :
      ( ( ~ ( product @ SV20 @ SV62 @ SV81 )
        | ! [SY331: $i] :
            ( ~ ( product @ SV62 @ SV93 @ SY331 )
            | ! [SY332: $i] :
                ( ~ ( product @ SV81 @ SV93 @ SY332 )
                | ( product @ SV20 @ SY331 @ SY332 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[344]) ).

thf(369,plain,
    ! [SV94: $i,SV82: $i,SV63: $i,SV21: $i] :
      ( ( ~ ( product @ SV21 @ SV63 @ SV82 )
        | ! [SY333: $i] :
            ( ~ ( product @ SV63 @ SV94 @ SY333 )
            | ! [SY334: $i] :
                ( ~ ( product @ SV21 @ SY333 @ SY334 )
                | ( product @ SV82 @ SV94 @ SY334 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[345]) ).

thf(370,plain,
    ! [SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
      ( ( ! [SY335: $i] :
            ( ~ ( product @ SV22 @ SV64 @ SV83 )
            | ~ ( product @ SV22 @ SV95 @ SY335 )
            | ! [SY336: $i] :
                ( ~ ( sum @ SV64 @ SV95 @ SY336 )
                | ! [SY310: $i] :
                    ( ~ ( product @ SV22 @ SY336 @ SY310 )
                    | ( sum @ SV83 @ SY335 @ SY310 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[346]) ).

thf(371,plain,
    ! [SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
      ( ( ! [SY338: $i] :
            ( ~ ( product @ SV23 @ SV65 @ SV84 )
            | ~ ( product @ SV23 @ SV96 @ SY338 )
            | ! [SY339: $i] :
                ( ~ ( sum @ SV65 @ SV96 @ SY339 )
                | ! [SY314: $i] :
                    ( ~ ( sum @ SV84 @ SY338 @ SY314 )
                    | ( product @ SV23 @ SY339 @ SY314 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[347]) ).

thf(372,plain,
    ! [SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
      ( ( ! [SY341: $i] :
            ( ~ ( product @ SV24 @ SV66 @ SV85 )
            | ~ ( product @ SV97 @ SV66 @ SY341 )
            | ! [SY342: $i] :
                ( ~ ( sum @ SV24 @ SV97 @ SY342 )
                | ! [SY318: $i] :
                    ( ~ ( product @ SY342 @ SV66 @ SY318 )
                    | ( sum @ SV85 @ SY341 @ SY318 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[348]) ).

thf(373,plain,
    ! [SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
      ( ( ! [SY344: $i] :
            ( ~ ( product @ SV25 @ SV67 @ SV86 )
            | ~ ( product @ SV98 @ SV67 @ SY344 )
            | ! [SY345: $i] :
                ( ~ ( sum @ SV25 @ SV98 @ SY345 )
                | ! [SY322: $i] :
                    ( ~ ( sum @ SV86 @ SY344 @ SY322 )
                    | ( product @ SY345 @ SV67 @ SY322 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[349]) ).

thf(374,plain,
    ! [SV87: $i,SV68: $i,SV28: $i] :
      ( ( ( ~ ( sum @ SV28 @ SV68 @ SV87 ) )
        = $true )
      | ( ( ! [SY323: $i] :
              ( ~ ( sum @ SV28 @ SV68 @ SY323 )
              | ( equalish @ SV87 @ SY323 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[350]) ).

thf(375,plain,
    ! [SV88: $i,SV69: $i,SV29: $i] :
      ( ( ( ~ ( product @ SV29 @ SV69 @ SV88 ) )
        = $true )
      | ( ( ! [SY324: $i] :
              ( ~ ( product @ SV29 @ SV69 @ SY324 )
              | ( equalish @ SV88 @ SY324 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[351]) ).

thf(376,plain,
    ! [SV89: $i,SV70: $i,SV30: $i] :
      ( ( ( ~ ( sum @ SV30 @ SV70 @ SV89 ) )
        = $true )
      | ( ( ! [SY325: $i] :
              ( ~ ( sum @ SY325 @ SV70 @ SV89 )
              | ( equalish @ SY325 @ SV30 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[352]) ).

thf(377,plain,
    ! [SV90: $i,SV71: $i,SV31: $i] :
      ( ( ( ~ ( sum @ SV31 @ SV71 @ SV90 ) )
        = $true )
      | ( ( ! [SY326: $i] :
              ( ~ ( sum @ SV31 @ SY326 @ SV90 )
              | ( equalish @ SY326 @ SV71 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[353]) ).

thf(378,plain,
    ! [SV46: $i,SV99: $i,SV1: $i] :
      ( ( ( equalish @ ( add @ SV1 @ SV99 ) @ ( add @ SV46 @ SV99 ) )
        = $true )
      | ( ( equalish @ SV1 @ SV46 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[354]) ).

thf(379,plain,
    ! [SV47: $i,SV2: $i,SV100: $i] :
      ( ( ( equalish @ ( add @ SV100 @ SV2 ) @ ( add @ SV100 @ SV47 ) )
        = $true )
      | ( ( equalish @ SV2 @ SV47 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[355]) ).

thf(380,plain,
    ! [SV48: $i,SV101: $i,SV3: $i] :
      ( ( ( ! [SY347: $i] :
              ( ~ ( sum @ SV3 @ SV101 @ SY347 )
              | ( sum @ SV48 @ SV101 @ SY347 ) ) )
        = $true )
      | ( ( equalish @ SV3 @ SV48 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[356]) ).

thf(381,plain,
    ! [SV49: $i,SV4: $i,SV102: $i] :
      ( ( ( ! [SY348: $i] :
              ( ~ ( sum @ SV102 @ SV4 @ SY348 )
              | ( sum @ SV102 @ SV49 @ SY348 ) ) )
        = $true )
      | ( ( equalish @ SV4 @ SV49 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[357]) ).

thf(382,plain,
    ! [SV50: $i,SV5: $i,SV103: $i] :
      ( ( ( ! [SY349: $i] :
              ( ~ ( sum @ SV103 @ SY349 @ SV5 )
              | ( sum @ SV103 @ SY349 @ SV50 ) ) )
        = $true )
      | ( ( equalish @ SV5 @ SV50 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[358]) ).

thf(383,plain,
    ! [SV51: $i,SV104: $i,SV6: $i] :
      ( ( ( equalish @ ( multiply @ SV6 @ SV104 ) @ ( multiply @ SV51 @ SV104 ) )
        = $true )
      | ( ( equalish @ SV6 @ SV51 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[359]) ).

thf(384,plain,
    ! [SV52: $i,SV7: $i,SV105: $i] :
      ( ( ( equalish @ ( multiply @ SV105 @ SV7 ) @ ( multiply @ SV105 @ SV52 ) )
        = $true )
      | ( ( equalish @ SV7 @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[360]) ).

thf(385,plain,
    ! [SV53: $i,SV106: $i,SV8: $i] :
      ( ( ( ! [SY350: $i] :
              ( ~ ( product @ SV8 @ SV106 @ SY350 )
              | ( product @ SV53 @ SV106 @ SY350 ) ) )
        = $true )
      | ( ( equalish @ SV8 @ SV53 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[361]) ).

thf(386,plain,
    ! [SV54: $i,SV9: $i,SV107: $i] :
      ( ( ( ! [SY351: $i] :
              ( ~ ( product @ SV107 @ SV9 @ SY351 )
              | ( product @ SV107 @ SV54 @ SY351 ) ) )
        = $true )
      | ( ( equalish @ SV9 @ SV54 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[362]) ).

thf(387,plain,
    ! [SV55: $i,SV10: $i,SV108: $i] :
      ( ( ( ! [SY352: $i] :
              ( ~ ( product @ SV108 @ SY352 @ SV10 )
              | ( product @ SV108 @ SY352 @ SV55 ) ) )
        = $true )
      | ( ( equalish @ SV10 @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[363]) ).

thf(388,plain,
    ! [SV12: $i,SV109: $i,SV56: $i] :
      ( ( ( ~ ( equalish @ SV56 @ SV109 )
          | ( equalish @ SV12 @ SV109 ) )
        = $true )
      | ( ( equalish @ SV12 @ SV56 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[364]) ).

thf(389,plain,
    ! [SV91: $i,SV78: $i,SV59: $i,SV17: $i] :
      ( ( ( ~ ( sum @ SV17 @ SV59 @ SV78 ) )
        = $true )
      | ( ( ! [SY327: $i] :
              ( ~ ( sum @ SV59 @ SV91 @ SY327 )
              | ! [SY328: $i] :
                  ( ~ ( sum @ SV78 @ SV91 @ SY328 )
                  | ( sum @ SV17 @ SY327 @ SY328 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[365]) ).

thf(390,plain,
    ! [SV92: $i,SV79: $i,SV60: $i,SV18: $i] :
      ( ( ( ~ ( sum @ SV18 @ SV60 @ SV79 ) )
        = $true )
      | ( ( ! [SY329: $i] :
              ( ~ ( sum @ SV60 @ SV92 @ SY329 )
              | ! [SY330: $i] :
                  ( ~ ( sum @ SV18 @ SY329 @ SY330 )
                  | ( sum @ SV79 @ SV92 @ SY330 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[366]) ).

thf(391,plain,
    ! [SV80: $i,SV61: $i,SV19: $i] :
      ( ( ( sum @ SV19 @ SV61 @ SV80 )
        = $false )
      | ( ( sum @ SV61 @ SV19 @ SV80 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[367]) ).

thf(392,plain,
    ! [SV93: $i,SV81: $i,SV62: $i,SV20: $i] :
      ( ( ( ~ ( product @ SV20 @ SV62 @ SV81 ) )
        = $true )
      | ( ( ! [SY331: $i] :
              ( ~ ( product @ SV62 @ SV93 @ SY331 )
              | ! [SY332: $i] :
                  ( ~ ( product @ SV81 @ SV93 @ SY332 )
                  | ( product @ SV20 @ SY331 @ SY332 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[368]) ).

thf(393,plain,
    ! [SV94: $i,SV82: $i,SV63: $i,SV21: $i] :
      ( ( ( ~ ( product @ SV21 @ SV63 @ SV82 ) )
        = $true )
      | ( ( ! [SY333: $i] :
              ( ~ ( product @ SV63 @ SV94 @ SY333 )
              | ! [SY334: $i] :
                  ( ~ ( product @ SV21 @ SY333 @ SY334 )
                  | ( product @ SV82 @ SV94 @ SY334 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[369]) ).

thf(394,plain,
    ! [SV110: $i,SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
      ( ( ~ ( product @ SV22 @ SV64 @ SV83 )
        | ~ ( product @ SV22 @ SV95 @ SV110 )
        | ! [SY353: $i] :
            ( ~ ( sum @ SV64 @ SV95 @ SY353 )
            | ! [SY354: $i] :
                ( ~ ( product @ SV22 @ SY353 @ SY354 )
                | ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[370]) ).

thf(395,plain,
    ! [SV111: $i,SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
      ( ( ~ ( product @ SV23 @ SV65 @ SV84 )
        | ~ ( product @ SV23 @ SV96 @ SV111 )
        | ! [SY355: $i] :
            ( ~ ( sum @ SV65 @ SV96 @ SY355 )
            | ! [SY356: $i] :
                ( ~ ( sum @ SV84 @ SV111 @ SY356 )
                | ( product @ SV23 @ SY355 @ SY356 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[371]) ).

thf(396,plain,
    ! [SV112: $i,SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
      ( ( ~ ( product @ SV24 @ SV66 @ SV85 )
        | ~ ( product @ SV97 @ SV66 @ SV112 )
        | ! [SY357: $i] :
            ( ~ ( sum @ SV24 @ SV97 @ SY357 )
            | ! [SY358: $i] :
                ( ~ ( product @ SY357 @ SV66 @ SY358 )
                | ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[372]) ).

thf(397,plain,
    ! [SV113: $i,SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
      ( ( ~ ( product @ SV25 @ SV67 @ SV86 )
        | ~ ( product @ SV98 @ SV67 @ SV113 )
        | ! [SY359: $i] :
            ( ~ ( sum @ SV25 @ SV98 @ SY359 )
            | ! [SY360: $i] :
                ( ~ ( sum @ SV86 @ SV113 @ SY360 )
                | ( product @ SY359 @ SV67 @ SY360 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[373]) ).

thf(398,plain,
    ! [SV87: $i,SV68: $i,SV28: $i] :
      ( ( ( sum @ SV28 @ SV68 @ SV87 )
        = $false )
      | ( ( ! [SY323: $i] :
              ( ~ ( sum @ SV28 @ SV68 @ SY323 )
              | ( equalish @ SV87 @ SY323 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[374]) ).

thf(399,plain,
    ! [SV88: $i,SV69: $i,SV29: $i] :
      ( ( ( product @ SV29 @ SV69 @ SV88 )
        = $false )
      | ( ( ! [SY324: $i] :
              ( ~ ( product @ SV29 @ SV69 @ SY324 )
              | ( equalish @ SV88 @ SY324 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[375]) ).

thf(400,plain,
    ! [SV89: $i,SV70: $i,SV30: $i] :
      ( ( ( sum @ SV30 @ SV70 @ SV89 )
        = $false )
      | ( ( ! [SY325: $i] :
              ( ~ ( sum @ SY325 @ SV70 @ SV89 )
              | ( equalish @ SY325 @ SV30 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[376]) ).

thf(401,plain,
    ! [SV90: $i,SV71: $i,SV31: $i] :
      ( ( ( sum @ SV31 @ SV71 @ SV90 )
        = $false )
      | ( ( ! [SY326: $i] :
              ( ~ ( sum @ SV31 @ SY326 @ SV90 )
              | ( equalish @ SY326 @ SV71 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[377]) ).

thf(402,plain,
    ! [SV48: $i,SV114: $i,SV101: $i,SV3: $i] :
      ( ( ( ~ ( sum @ SV3 @ SV101 @ SV114 )
          | ( sum @ SV48 @ SV101 @ SV114 ) )
        = $true )
      | ( ( equalish @ SV3 @ SV48 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[380]) ).

thf(403,plain,
    ! [SV49: $i,SV115: $i,SV4: $i,SV102: $i] :
      ( ( ( ~ ( sum @ SV102 @ SV4 @ SV115 )
          | ( sum @ SV102 @ SV49 @ SV115 ) )
        = $true )
      | ( ( equalish @ SV4 @ SV49 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[381]) ).

thf(404,plain,
    ! [SV50: $i,SV5: $i,SV116: $i,SV103: $i] :
      ( ( ( ~ ( sum @ SV103 @ SV116 @ SV5 )
          | ( sum @ SV103 @ SV116 @ SV50 ) )
        = $true )
      | ( ( equalish @ SV5 @ SV50 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[382]) ).

thf(405,plain,
    ! [SV53: $i,SV117: $i,SV106: $i,SV8: $i] :
      ( ( ( ~ ( product @ SV8 @ SV106 @ SV117 )
          | ( product @ SV53 @ SV106 @ SV117 ) )
        = $true )
      | ( ( equalish @ SV8 @ SV53 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[385]) ).

thf(406,plain,
    ! [SV54: $i,SV118: $i,SV9: $i,SV107: $i] :
      ( ( ( ~ ( product @ SV107 @ SV9 @ SV118 )
          | ( product @ SV107 @ SV54 @ SV118 ) )
        = $true )
      | ( ( equalish @ SV9 @ SV54 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[386]) ).

thf(407,plain,
    ! [SV55: $i,SV10: $i,SV119: $i,SV108: $i] :
      ( ( ( ~ ( product @ SV108 @ SV119 @ SV10 )
          | ( product @ SV108 @ SV119 @ SV55 ) )
        = $true )
      | ( ( equalish @ SV10 @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[387]) ).

thf(408,plain,
    ! [SV12: $i,SV109: $i,SV56: $i] :
      ( ( ( ~ ( equalish @ SV56 @ SV109 ) )
        = $true )
      | ( ( equalish @ SV12 @ SV109 )
        = $true )
      | ( ( equalish @ SV12 @ SV56 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[388]) ).

thf(409,plain,
    ! [SV91: $i,SV78: $i,SV59: $i,SV17: $i] :
      ( ( ( sum @ SV17 @ SV59 @ SV78 )
        = $false )
      | ( ( ! [SY327: $i] :
              ( ~ ( sum @ SV59 @ SV91 @ SY327 )
              | ! [SY328: $i] :
                  ( ~ ( sum @ SV78 @ SV91 @ SY328 )
                  | ( sum @ SV17 @ SY327 @ SY328 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[389]) ).

thf(410,plain,
    ! [SV92: $i,SV79: $i,SV60: $i,SV18: $i] :
      ( ( ( sum @ SV18 @ SV60 @ SV79 )
        = $false )
      | ( ( ! [SY329: $i] :
              ( ~ ( sum @ SV60 @ SV92 @ SY329 )
              | ! [SY330: $i] :
                  ( ~ ( sum @ SV18 @ SY329 @ SY330 )
                  | ( sum @ SV79 @ SV92 @ SY330 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[390]) ).

thf(411,plain,
    ! [SV93: $i,SV81: $i,SV62: $i,SV20: $i] :
      ( ( ( product @ SV20 @ SV62 @ SV81 )
        = $false )
      | ( ( ! [SY331: $i] :
              ( ~ ( product @ SV62 @ SV93 @ SY331 )
              | ! [SY332: $i] :
                  ( ~ ( product @ SV81 @ SV93 @ SY332 )
                  | ( product @ SV20 @ SY331 @ SY332 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[392]) ).

thf(412,plain,
    ! [SV94: $i,SV82: $i,SV63: $i,SV21: $i] :
      ( ( ( product @ SV21 @ SV63 @ SV82 )
        = $false )
      | ( ( ! [SY333: $i] :
              ( ~ ( product @ SV63 @ SV94 @ SY333 )
              | ! [SY334: $i] :
                  ( ~ ( product @ SV21 @ SY333 @ SY334 )
                  | ( product @ SV82 @ SV94 @ SY334 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[393]) ).

thf(413,plain,
    ! [SV110: $i,SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
      ( ( ( ~ ( product @ SV22 @ SV64 @ SV83 ) )
        = $true )
      | ( ( ~ ( product @ SV22 @ SV95 @ SV110 )
          | ! [SY353: $i] :
              ( ~ ( sum @ SV64 @ SV95 @ SY353 )
              | ! [SY354: $i] :
                  ( ~ ( product @ SV22 @ SY353 @ SY354 )
                  | ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[394]) ).

thf(414,plain,
    ! [SV111: $i,SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
      ( ( ( ~ ( product @ SV23 @ SV65 @ SV84 ) )
        = $true )
      | ( ( ~ ( product @ SV23 @ SV96 @ SV111 )
          | ! [SY355: $i] :
              ( ~ ( sum @ SV65 @ SV96 @ SY355 )
              | ! [SY356: $i] :
                  ( ~ ( sum @ SV84 @ SV111 @ SY356 )
                  | ( product @ SV23 @ SY355 @ SY356 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[395]) ).

thf(415,plain,
    ! [SV112: $i,SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
      ( ( ( ~ ( product @ SV24 @ SV66 @ SV85 ) )
        = $true )
      | ( ( ~ ( product @ SV97 @ SV66 @ SV112 )
          | ! [SY357: $i] :
              ( ~ ( sum @ SV24 @ SV97 @ SY357 )
              | ! [SY358: $i] :
                  ( ~ ( product @ SY357 @ SV66 @ SY358 )
                  | ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[396]) ).

thf(416,plain,
    ! [SV113: $i,SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
      ( ( ( ~ ( product @ SV25 @ SV67 @ SV86 ) )
        = $true )
      | ( ( ~ ( product @ SV98 @ SV67 @ SV113 )
          | ! [SY359: $i] :
              ( ~ ( sum @ SV25 @ SV98 @ SY359 )
              | ! [SY360: $i] :
                  ( ~ ( sum @ SV86 @ SV113 @ SY360 )
                  | ( product @ SY359 @ SV67 @ SY360 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[397]) ).

thf(417,plain,
    ! [SV87: $i,SV120: $i,SV68: $i,SV28: $i] :
      ( ( ( ~ ( sum @ SV28 @ SV68 @ SV120 )
          | ( equalish @ SV87 @ SV120 ) )
        = $true )
      | ( ( sum @ SV28 @ SV68 @ SV87 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[398]) ).

thf(418,plain,
    ! [SV88: $i,SV121: $i,SV69: $i,SV29: $i] :
      ( ( ( ~ ( product @ SV29 @ SV69 @ SV121 )
          | ( equalish @ SV88 @ SV121 ) )
        = $true )
      | ( ( product @ SV29 @ SV69 @ SV88 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[399]) ).

thf(419,plain,
    ! [SV30: $i,SV89: $i,SV70: $i,SV122: $i] :
      ( ( ( ~ ( sum @ SV122 @ SV70 @ SV89 )
          | ( equalish @ SV122 @ SV30 ) )
        = $true )
      | ( ( sum @ SV30 @ SV70 @ SV89 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[400]) ).

thf(420,plain,
    ! [SV71: $i,SV90: $i,SV123: $i,SV31: $i] :
      ( ( ( ~ ( sum @ SV31 @ SV123 @ SV90 )
          | ( equalish @ SV123 @ SV71 ) )
        = $true )
      | ( ( sum @ SV31 @ SV71 @ SV90 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[401]) ).

thf(421,plain,
    ! [SV48: $i,SV114: $i,SV101: $i,SV3: $i] :
      ( ( ( ~ ( sum @ SV3 @ SV101 @ SV114 ) )
        = $true )
      | ( ( sum @ SV48 @ SV101 @ SV114 )
        = $true )
      | ( ( equalish @ SV3 @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[402]) ).

thf(422,plain,
    ! [SV49: $i,SV115: $i,SV4: $i,SV102: $i] :
      ( ( ( ~ ( sum @ SV102 @ SV4 @ SV115 ) )
        = $true )
      | ( ( sum @ SV102 @ SV49 @ SV115 )
        = $true )
      | ( ( equalish @ SV4 @ SV49 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[403]) ).

thf(423,plain,
    ! [SV50: $i,SV5: $i,SV116: $i,SV103: $i] :
      ( ( ( ~ ( sum @ SV103 @ SV116 @ SV5 ) )
        = $true )
      | ( ( sum @ SV103 @ SV116 @ SV50 )
        = $true )
      | ( ( equalish @ SV5 @ SV50 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[404]) ).

thf(424,plain,
    ! [SV53: $i,SV117: $i,SV106: $i,SV8: $i] :
      ( ( ( ~ ( product @ SV8 @ SV106 @ SV117 ) )
        = $true )
      | ( ( product @ SV53 @ SV106 @ SV117 )
        = $true )
      | ( ( equalish @ SV8 @ SV53 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[405]) ).

thf(425,plain,
    ! [SV54: $i,SV118: $i,SV9: $i,SV107: $i] :
      ( ( ( ~ ( product @ SV107 @ SV9 @ SV118 ) )
        = $true )
      | ( ( product @ SV107 @ SV54 @ SV118 )
        = $true )
      | ( ( equalish @ SV9 @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[406]) ).

thf(426,plain,
    ! [SV55: $i,SV10: $i,SV119: $i,SV108: $i] :
      ( ( ( ~ ( product @ SV108 @ SV119 @ SV10 ) )
        = $true )
      | ( ( product @ SV108 @ SV119 @ SV55 )
        = $true )
      | ( ( equalish @ SV10 @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[407]) ).

thf(427,plain,
    ! [SV12: $i,SV109: $i,SV56: $i] :
      ( ( ( equalish @ SV56 @ SV109 )
        = $false )
      | ( ( equalish @ SV12 @ SV109 )
        = $true )
      | ( ( equalish @ SV12 @ SV56 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[408]) ).

thf(428,plain,
    ! [SV17: $i,SV78: $i,SV124: $i,SV91: $i,SV59: $i] :
      ( ( ( ~ ( sum @ SV59 @ SV91 @ SV124 )
          | ! [SY361: $i] :
              ( ~ ( sum @ SV78 @ SV91 @ SY361 )
              | ( sum @ SV17 @ SV124 @ SY361 ) ) )
        = $true )
      | ( ( sum @ SV17 @ SV59 @ SV78 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[409]) ).

thf(429,plain,
    ! [SV79: $i,SV18: $i,SV125: $i,SV92: $i,SV60: $i] :
      ( ( ( ~ ( sum @ SV60 @ SV92 @ SV125 )
          | ! [SY362: $i] :
              ( ~ ( sum @ SV18 @ SV125 @ SY362 )
              | ( sum @ SV79 @ SV92 @ SY362 ) ) )
        = $true )
      | ( ( sum @ SV18 @ SV60 @ SV79 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[410]) ).

thf(430,plain,
    ! [SV20: $i,SV81: $i,SV126: $i,SV93: $i,SV62: $i] :
      ( ( ( ~ ( product @ SV62 @ SV93 @ SV126 )
          | ! [SY363: $i] :
              ( ~ ( product @ SV81 @ SV93 @ SY363 )
              | ( product @ SV20 @ SV126 @ SY363 ) ) )
        = $true )
      | ( ( product @ SV20 @ SV62 @ SV81 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[411]) ).

thf(431,plain,
    ! [SV82: $i,SV21: $i,SV127: $i,SV94: $i,SV63: $i] :
      ( ( ( ~ ( product @ SV63 @ SV94 @ SV127 )
          | ! [SY364: $i] :
              ( ~ ( product @ SV21 @ SV127 @ SY364 )
              | ( product @ SV82 @ SV94 @ SY364 ) ) )
        = $true )
      | ( ( product @ SV21 @ SV63 @ SV82 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[412]) ).

thf(432,plain,
    ! [SV110: $i,SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
      ( ( ( product @ SV22 @ SV64 @ SV83 )
        = $false )
      | ( ( ~ ( product @ SV22 @ SV95 @ SV110 )
          | ! [SY353: $i] :
              ( ~ ( sum @ SV64 @ SV95 @ SY353 )
              | ! [SY354: $i] :
                  ( ~ ( product @ SV22 @ SY353 @ SY354 )
                  | ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[413]) ).

thf(433,plain,
    ! [SV111: $i,SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
      ( ( ( product @ SV23 @ SV65 @ SV84 )
        = $false )
      | ( ( ~ ( product @ SV23 @ SV96 @ SV111 )
          | ! [SY355: $i] :
              ( ~ ( sum @ SV65 @ SV96 @ SY355 )
              | ! [SY356: $i] :
                  ( ~ ( sum @ SV84 @ SV111 @ SY356 )
                  | ( product @ SV23 @ SY355 @ SY356 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[414]) ).

thf(434,plain,
    ! [SV112: $i,SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
      ( ( ( product @ SV24 @ SV66 @ SV85 )
        = $false )
      | ( ( ~ ( product @ SV97 @ SV66 @ SV112 )
          | ! [SY357: $i] :
              ( ~ ( sum @ SV24 @ SV97 @ SY357 )
              | ! [SY358: $i] :
                  ( ~ ( product @ SY357 @ SV66 @ SY358 )
                  | ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[415]) ).

thf(435,plain,
    ! [SV113: $i,SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
      ( ( ( product @ SV25 @ SV67 @ SV86 )
        = $false )
      | ( ( ~ ( product @ SV98 @ SV67 @ SV113 )
          | ! [SY359: $i] :
              ( ~ ( sum @ SV25 @ SV98 @ SY359 )
              | ! [SY360: $i] :
                  ( ~ ( sum @ SV86 @ SV113 @ SY360 )
                  | ( product @ SY359 @ SV67 @ SY360 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[416]) ).

thf(436,plain,
    ! [SV87: $i,SV120: $i,SV68: $i,SV28: $i] :
      ( ( ( ~ ( sum @ SV28 @ SV68 @ SV120 ) )
        = $true )
      | ( ( equalish @ SV87 @ SV120 )
        = $true )
      | ( ( sum @ SV28 @ SV68 @ SV87 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[417]) ).

thf(437,plain,
    ! [SV88: $i,SV121: $i,SV69: $i,SV29: $i] :
      ( ( ( ~ ( product @ SV29 @ SV69 @ SV121 ) )
        = $true )
      | ( ( equalish @ SV88 @ SV121 )
        = $true )
      | ( ( product @ SV29 @ SV69 @ SV88 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[418]) ).

thf(438,plain,
    ! [SV30: $i,SV89: $i,SV70: $i,SV122: $i] :
      ( ( ( ~ ( sum @ SV122 @ SV70 @ SV89 ) )
        = $true )
      | ( ( equalish @ SV122 @ SV30 )
        = $true )
      | ( ( sum @ SV30 @ SV70 @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[419]) ).

thf(439,plain,
    ! [SV71: $i,SV90: $i,SV123: $i,SV31: $i] :
      ( ( ( ~ ( sum @ SV31 @ SV123 @ SV90 ) )
        = $true )
      | ( ( equalish @ SV123 @ SV71 )
        = $true )
      | ( ( sum @ SV31 @ SV71 @ SV90 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[420]) ).

thf(440,plain,
    ! [SV48: $i,SV114: $i,SV101: $i,SV3: $i] :
      ( ( ( sum @ SV3 @ SV101 @ SV114 )
        = $false )
      | ( ( sum @ SV48 @ SV101 @ SV114 )
        = $true )
      | ( ( equalish @ SV3 @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[421]) ).

thf(441,plain,
    ! [SV49: $i,SV115: $i,SV4: $i,SV102: $i] :
      ( ( ( sum @ SV102 @ SV4 @ SV115 )
        = $false )
      | ( ( sum @ SV102 @ SV49 @ SV115 )
        = $true )
      | ( ( equalish @ SV4 @ SV49 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[422]) ).

thf(442,plain,
    ! [SV50: $i,SV5: $i,SV116: $i,SV103: $i] :
      ( ( ( sum @ SV103 @ SV116 @ SV5 )
        = $false )
      | ( ( sum @ SV103 @ SV116 @ SV50 )
        = $true )
      | ( ( equalish @ SV5 @ SV50 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[423]) ).

thf(443,plain,
    ! [SV53: $i,SV117: $i,SV106: $i,SV8: $i] :
      ( ( ( product @ SV8 @ SV106 @ SV117 )
        = $false )
      | ( ( product @ SV53 @ SV106 @ SV117 )
        = $true )
      | ( ( equalish @ SV8 @ SV53 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[424]) ).

thf(444,plain,
    ! [SV54: $i,SV118: $i,SV9: $i,SV107: $i] :
      ( ( ( product @ SV107 @ SV9 @ SV118 )
        = $false )
      | ( ( product @ SV107 @ SV54 @ SV118 )
        = $true )
      | ( ( equalish @ SV9 @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[425]) ).

thf(445,plain,
    ! [SV55: $i,SV10: $i,SV119: $i,SV108: $i] :
      ( ( ( product @ SV108 @ SV119 @ SV10 )
        = $false )
      | ( ( product @ SV108 @ SV119 @ SV55 )
        = $true )
      | ( ( equalish @ SV10 @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[426]) ).

thf(446,plain,
    ! [SV17: $i,SV78: $i,SV124: $i,SV91: $i,SV59: $i] :
      ( ( ( ~ ( sum @ SV59 @ SV91 @ SV124 ) )
        = $true )
      | ( ( ! [SY361: $i] :
              ( ~ ( sum @ SV78 @ SV91 @ SY361 )
              | ( sum @ SV17 @ SV124 @ SY361 ) ) )
        = $true )
      | ( ( sum @ SV17 @ SV59 @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[428]) ).

thf(447,plain,
    ! [SV79: $i,SV18: $i,SV125: $i,SV92: $i,SV60: $i] :
      ( ( ( ~ ( sum @ SV60 @ SV92 @ SV125 ) )
        = $true )
      | ( ( ! [SY362: $i] :
              ( ~ ( sum @ SV18 @ SV125 @ SY362 )
              | ( sum @ SV79 @ SV92 @ SY362 ) ) )
        = $true )
      | ( ( sum @ SV18 @ SV60 @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[429]) ).

thf(448,plain,
    ! [SV20: $i,SV81: $i,SV126: $i,SV93: $i,SV62: $i] :
      ( ( ( ~ ( product @ SV62 @ SV93 @ SV126 ) )
        = $true )
      | ( ( ! [SY363: $i] :
              ( ~ ( product @ SV81 @ SV93 @ SY363 )
              | ( product @ SV20 @ SV126 @ SY363 ) ) )
        = $true )
      | ( ( product @ SV20 @ SV62 @ SV81 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[430]) ).

thf(449,plain,
    ! [SV82: $i,SV21: $i,SV127: $i,SV94: $i,SV63: $i] :
      ( ( ( ~ ( product @ SV63 @ SV94 @ SV127 ) )
        = $true )
      | ( ( ! [SY364: $i] :
              ( ~ ( product @ SV21 @ SV127 @ SY364 )
              | ( product @ SV82 @ SV94 @ SY364 ) ) )
        = $true )
      | ( ( product @ SV21 @ SV63 @ SV82 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[431]) ).

thf(450,plain,
    ! [SV83: $i,SV64: $i,SV110: $i,SV95: $i,SV22: $i] :
      ( ( ( ~ ( product @ SV22 @ SV95 @ SV110 ) )
        = $true )
      | ( ( ! [SY353: $i] :
              ( ~ ( sum @ SV64 @ SV95 @ SY353 )
              | ! [SY354: $i] :
                  ( ~ ( product @ SV22 @ SY353 @ SY354 )
                  | ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
        = $true )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[432]) ).

thf(451,plain,
    ! [SV84: $i,SV65: $i,SV111: $i,SV96: $i,SV23: $i] :
      ( ( ( ~ ( product @ SV23 @ SV96 @ SV111 ) )
        = $true )
      | ( ( ! [SY355: $i] :
              ( ~ ( sum @ SV65 @ SV96 @ SY355 )
              | ! [SY356: $i] :
                  ( ~ ( sum @ SV84 @ SV111 @ SY356 )
                  | ( product @ SV23 @ SY355 @ SY356 ) ) ) )
        = $true )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[433]) ).

thf(452,plain,
    ! [SV85: $i,SV24: $i,SV112: $i,SV66: $i,SV97: $i] :
      ( ( ( ~ ( product @ SV97 @ SV66 @ SV112 ) )
        = $true )
      | ( ( ! [SY357: $i] :
              ( ~ ( sum @ SV24 @ SV97 @ SY357 )
              | ! [SY358: $i] :
                  ( ~ ( product @ SY357 @ SV66 @ SY358 )
                  | ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
        = $true )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[434]) ).

thf(453,plain,
    ! [SV86: $i,SV25: $i,SV113: $i,SV67: $i,SV98: $i] :
      ( ( ( ~ ( product @ SV98 @ SV67 @ SV113 ) )
        = $true )
      | ( ( ! [SY359: $i] :
              ( ~ ( sum @ SV25 @ SV98 @ SY359 )
              | ! [SY360: $i] :
                  ( ~ ( sum @ SV86 @ SV113 @ SY360 )
                  | ( product @ SY359 @ SV67 @ SY360 ) ) ) )
        = $true )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[435]) ).

thf(454,plain,
    ! [SV87: $i,SV120: $i,SV68: $i,SV28: $i] :
      ( ( ( sum @ SV28 @ SV68 @ SV120 )
        = $false )
      | ( ( equalish @ SV87 @ SV120 )
        = $true )
      | ( ( sum @ SV28 @ SV68 @ SV87 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[436]) ).

thf(455,plain,
    ! [SV88: $i,SV121: $i,SV69: $i,SV29: $i] :
      ( ( ( product @ SV29 @ SV69 @ SV121 )
        = $false )
      | ( ( equalish @ SV88 @ SV121 )
        = $true )
      | ( ( product @ SV29 @ SV69 @ SV88 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[437]) ).

thf(456,plain,
    ! [SV30: $i,SV89: $i,SV70: $i,SV122: $i] :
      ( ( ( sum @ SV122 @ SV70 @ SV89 )
        = $false )
      | ( ( equalish @ SV122 @ SV30 )
        = $true )
      | ( ( sum @ SV30 @ SV70 @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[438]) ).

thf(457,plain,
    ! [SV71: $i,SV90: $i,SV123: $i,SV31: $i] :
      ( ( ( sum @ SV31 @ SV123 @ SV90 )
        = $false )
      | ( ( equalish @ SV123 @ SV71 )
        = $true )
      | ( ( sum @ SV31 @ SV71 @ SV90 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[439]) ).

thf(458,plain,
    ! [SV17: $i,SV78: $i,SV124: $i,SV91: $i,SV59: $i] :
      ( ( ( sum @ SV59 @ SV91 @ SV124 )
        = $false )
      | ( ( ! [SY361: $i] :
              ( ~ ( sum @ SV78 @ SV91 @ SY361 )
              | ( sum @ SV17 @ SV124 @ SY361 ) ) )
        = $true )
      | ( ( sum @ SV17 @ SV59 @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[446]) ).

thf(459,plain,
    ! [SV79: $i,SV18: $i,SV125: $i,SV92: $i,SV60: $i] :
      ( ( ( sum @ SV60 @ SV92 @ SV125 )
        = $false )
      | ( ( ! [SY362: $i] :
              ( ~ ( sum @ SV18 @ SV125 @ SY362 )
              | ( sum @ SV79 @ SV92 @ SY362 ) ) )
        = $true )
      | ( ( sum @ SV18 @ SV60 @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[447]) ).

thf(460,plain,
    ! [SV20: $i,SV81: $i,SV126: $i,SV93: $i,SV62: $i] :
      ( ( ( product @ SV62 @ SV93 @ SV126 )
        = $false )
      | ( ( ! [SY363: $i] :
              ( ~ ( product @ SV81 @ SV93 @ SY363 )
              | ( product @ SV20 @ SV126 @ SY363 ) ) )
        = $true )
      | ( ( product @ SV20 @ SV62 @ SV81 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[448]) ).

thf(461,plain,
    ! [SV82: $i,SV21: $i,SV127: $i,SV94: $i,SV63: $i] :
      ( ( ( product @ SV63 @ SV94 @ SV127 )
        = $false )
      | ( ( ! [SY364: $i] :
              ( ~ ( product @ SV21 @ SV127 @ SY364 )
              | ( product @ SV82 @ SV94 @ SY364 ) ) )
        = $true )
      | ( ( product @ SV21 @ SV63 @ SV82 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[449]) ).

thf(462,plain,
    ! [SV83: $i,SV64: $i,SV110: $i,SV95: $i,SV22: $i] :
      ( ( ( product @ SV22 @ SV95 @ SV110 )
        = $false )
      | ( ( ! [SY353: $i] :
              ( ~ ( sum @ SV64 @ SV95 @ SY353 )
              | ! [SY354: $i] :
                  ( ~ ( product @ SV22 @ SY353 @ SY354 )
                  | ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
        = $true )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[450]) ).

thf(463,plain,
    ! [SV84: $i,SV65: $i,SV111: $i,SV96: $i,SV23: $i] :
      ( ( ( product @ SV23 @ SV96 @ SV111 )
        = $false )
      | ( ( ! [SY355: $i] :
              ( ~ ( sum @ SV65 @ SV96 @ SY355 )
              | ! [SY356: $i] :
                  ( ~ ( sum @ SV84 @ SV111 @ SY356 )
                  | ( product @ SV23 @ SY355 @ SY356 ) ) ) )
        = $true )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[451]) ).

thf(464,plain,
    ! [SV85: $i,SV24: $i,SV112: $i,SV66: $i,SV97: $i] :
      ( ( ( product @ SV97 @ SV66 @ SV112 )
        = $false )
      | ( ( ! [SY357: $i] :
              ( ~ ( sum @ SV24 @ SV97 @ SY357 )
              | ! [SY358: $i] :
                  ( ~ ( product @ SY357 @ SV66 @ SY358 )
                  | ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
        = $true )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[452]) ).

thf(465,plain,
    ! [SV86: $i,SV25: $i,SV113: $i,SV67: $i,SV98: $i] :
      ( ( ( product @ SV98 @ SV67 @ SV113 )
        = $false )
      | ( ( ! [SY359: $i] :
              ( ~ ( sum @ SV25 @ SV98 @ SY359 )
              | ! [SY360: $i] :
                  ( ~ ( sum @ SV86 @ SV113 @ SY360 )
                  | ( product @ SY359 @ SV67 @ SY360 ) ) ) )
        = $true )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[453]) ).

thf(466,plain,
    ! [SV59: $i,SV124: $i,SV17: $i,SV128: $i,SV91: $i,SV78: $i] :
      ( ( ( ~ ( sum @ SV78 @ SV91 @ SV128 )
          | ( sum @ SV17 @ SV124 @ SV128 ) )
        = $true )
      | ( ( sum @ SV59 @ SV91 @ SV124 )
        = $false )
      | ( ( sum @ SV17 @ SV59 @ SV78 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[458]) ).

thf(467,plain,
    ! [SV60: $i,SV92: $i,SV79: $i,SV129: $i,SV125: $i,SV18: $i] :
      ( ( ( ~ ( sum @ SV18 @ SV125 @ SV129 )
          | ( sum @ SV79 @ SV92 @ SV129 ) )
        = $true )
      | ( ( sum @ SV60 @ SV92 @ SV125 )
        = $false )
      | ( ( sum @ SV18 @ SV60 @ SV79 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[459]) ).

thf(468,plain,
    ! [SV62: $i,SV126: $i,SV20: $i,SV130: $i,SV93: $i,SV81: $i] :
      ( ( ( ~ ( product @ SV81 @ SV93 @ SV130 )
          | ( product @ SV20 @ SV126 @ SV130 ) )
        = $true )
      | ( ( product @ SV62 @ SV93 @ SV126 )
        = $false )
      | ( ( product @ SV20 @ SV62 @ SV81 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[460]) ).

thf(469,plain,
    ! [SV63: $i,SV94: $i,SV82: $i,SV131: $i,SV127: $i,SV21: $i] :
      ( ( ( ~ ( product @ SV21 @ SV127 @ SV131 )
          | ( product @ SV82 @ SV94 @ SV131 ) )
        = $true )
      | ( ( product @ SV63 @ SV94 @ SV127 )
        = $false )
      | ( ( product @ SV21 @ SV63 @ SV82 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[461]) ).

thf(470,plain,
    ! [SV110: $i,SV83: $i,SV22: $i,SV132: $i,SV95: $i,SV64: $i] :
      ( ( ( ~ ( sum @ SV64 @ SV95 @ SV132 )
          | ! [SY365: $i] :
              ( ~ ( product @ SV22 @ SV132 @ SY365 )
              | ( sum @ SV83 @ SV110 @ SY365 ) ) )
        = $true )
      | ( ( product @ SV22 @ SV95 @ SV110 )
        = $false )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[462]) ).

thf(471,plain,
    ! [SV23: $i,SV111: $i,SV84: $i,SV133: $i,SV96: $i,SV65: $i] :
      ( ( ( ~ ( sum @ SV65 @ SV96 @ SV133 )
          | ! [SY366: $i] :
              ( ~ ( sum @ SV84 @ SV111 @ SY366 )
              | ( product @ SV23 @ SV133 @ SY366 ) ) )
        = $true )
      | ( ( product @ SV23 @ SV96 @ SV111 )
        = $false )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[463]) ).

thf(472,plain,
    ! [SV112: $i,SV85: $i,SV66: $i,SV134: $i,SV97: $i,SV24: $i] :
      ( ( ( ~ ( sum @ SV24 @ SV97 @ SV134 )
          | ! [SY367: $i] :
              ( ~ ( product @ SV134 @ SV66 @ SY367 )
              | ( sum @ SV85 @ SV112 @ SY367 ) ) )
        = $true )
      | ( ( product @ SV97 @ SV66 @ SV112 )
        = $false )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[464]) ).

thf(473,plain,
    ! [SV67: $i,SV113: $i,SV86: $i,SV135: $i,SV98: $i,SV25: $i] :
      ( ( ( ~ ( sum @ SV25 @ SV98 @ SV135 )
          | ! [SY368: $i] :
              ( ~ ( sum @ SV86 @ SV113 @ SY368 )
              | ( product @ SV135 @ SV67 @ SY368 ) ) )
        = $true )
      | ( ( product @ SV98 @ SV67 @ SV113 )
        = $false )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[465]) ).

thf(474,plain,
    ! [SV59: $i,SV124: $i,SV17: $i,SV128: $i,SV91: $i,SV78: $i] :
      ( ( ( ~ ( sum @ SV78 @ SV91 @ SV128 ) )
        = $true )
      | ( ( sum @ SV17 @ SV124 @ SV128 )
        = $true )
      | ( ( sum @ SV59 @ SV91 @ SV124 )
        = $false )
      | ( ( sum @ SV17 @ SV59 @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[466]) ).

thf(475,plain,
    ! [SV60: $i,SV92: $i,SV79: $i,SV129: $i,SV125: $i,SV18: $i] :
      ( ( ( ~ ( sum @ SV18 @ SV125 @ SV129 ) )
        = $true )
      | ( ( sum @ SV79 @ SV92 @ SV129 )
        = $true )
      | ( ( sum @ SV60 @ SV92 @ SV125 )
        = $false )
      | ( ( sum @ SV18 @ SV60 @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[467]) ).

thf(476,plain,
    ! [SV62: $i,SV126: $i,SV20: $i,SV130: $i,SV93: $i,SV81: $i] :
      ( ( ( ~ ( product @ SV81 @ SV93 @ SV130 ) )
        = $true )
      | ( ( product @ SV20 @ SV126 @ SV130 )
        = $true )
      | ( ( product @ SV62 @ SV93 @ SV126 )
        = $false )
      | ( ( product @ SV20 @ SV62 @ SV81 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[468]) ).

thf(477,plain,
    ! [SV63: $i,SV94: $i,SV82: $i,SV131: $i,SV127: $i,SV21: $i] :
      ( ( ( ~ ( product @ SV21 @ SV127 @ SV131 ) )
        = $true )
      | ( ( product @ SV82 @ SV94 @ SV131 )
        = $true )
      | ( ( product @ SV63 @ SV94 @ SV127 )
        = $false )
      | ( ( product @ SV21 @ SV63 @ SV82 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[469]) ).

thf(478,plain,
    ! [SV110: $i,SV83: $i,SV22: $i,SV132: $i,SV95: $i,SV64: $i] :
      ( ( ( ~ ( sum @ SV64 @ SV95 @ SV132 ) )
        = $true )
      | ( ( ! [SY365: $i] :
              ( ~ ( product @ SV22 @ SV132 @ SY365 )
              | ( sum @ SV83 @ SV110 @ SY365 ) ) )
        = $true )
      | ( ( product @ SV22 @ SV95 @ SV110 )
        = $false )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[470]) ).

thf(479,plain,
    ! [SV23: $i,SV111: $i,SV84: $i,SV133: $i,SV96: $i,SV65: $i] :
      ( ( ( ~ ( sum @ SV65 @ SV96 @ SV133 ) )
        = $true )
      | ( ( ! [SY366: $i] :
              ( ~ ( sum @ SV84 @ SV111 @ SY366 )
              | ( product @ SV23 @ SV133 @ SY366 ) ) )
        = $true )
      | ( ( product @ SV23 @ SV96 @ SV111 )
        = $false )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[471]) ).

thf(480,plain,
    ! [SV112: $i,SV85: $i,SV66: $i,SV134: $i,SV97: $i,SV24: $i] :
      ( ( ( ~ ( sum @ SV24 @ SV97 @ SV134 ) )
        = $true )
      | ( ( ! [SY367: $i] :
              ( ~ ( product @ SV134 @ SV66 @ SY367 )
              | ( sum @ SV85 @ SV112 @ SY367 ) ) )
        = $true )
      | ( ( product @ SV97 @ SV66 @ SV112 )
        = $false )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[472]) ).

thf(481,plain,
    ! [SV67: $i,SV113: $i,SV86: $i,SV135: $i,SV98: $i,SV25: $i] :
      ( ( ( ~ ( sum @ SV25 @ SV98 @ SV135 ) )
        = $true )
      | ( ( ! [SY368: $i] :
              ( ~ ( sum @ SV86 @ SV113 @ SY368 )
              | ( product @ SV135 @ SV67 @ SY368 ) ) )
        = $true )
      | ( ( product @ SV98 @ SV67 @ SV113 )
        = $false )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[473]) ).

thf(482,plain,
    ! [SV59: $i,SV124: $i,SV17: $i,SV128: $i,SV91: $i,SV78: $i] :
      ( ( ( sum @ SV78 @ SV91 @ SV128 )
        = $false )
      | ( ( sum @ SV17 @ SV124 @ SV128 )
        = $true )
      | ( ( sum @ SV59 @ SV91 @ SV124 )
        = $false )
      | ( ( sum @ SV17 @ SV59 @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[474]) ).

thf(483,plain,
    ! [SV60: $i,SV92: $i,SV79: $i,SV129: $i,SV125: $i,SV18: $i] :
      ( ( ( sum @ SV18 @ SV125 @ SV129 )
        = $false )
      | ( ( sum @ SV79 @ SV92 @ SV129 )
        = $true )
      | ( ( sum @ SV60 @ SV92 @ SV125 )
        = $false )
      | ( ( sum @ SV18 @ SV60 @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[475]) ).

thf(484,plain,
    ! [SV62: $i,SV126: $i,SV20: $i,SV130: $i,SV93: $i,SV81: $i] :
      ( ( ( product @ SV81 @ SV93 @ SV130 )
        = $false )
      | ( ( product @ SV20 @ SV126 @ SV130 )
        = $true )
      | ( ( product @ SV62 @ SV93 @ SV126 )
        = $false )
      | ( ( product @ SV20 @ SV62 @ SV81 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[476]) ).

thf(485,plain,
    ! [SV63: $i,SV94: $i,SV82: $i,SV131: $i,SV127: $i,SV21: $i] :
      ( ( ( product @ SV21 @ SV127 @ SV131 )
        = $false )
      | ( ( product @ SV82 @ SV94 @ SV131 )
        = $true )
      | ( ( product @ SV63 @ SV94 @ SV127 )
        = $false )
      | ( ( product @ SV21 @ SV63 @ SV82 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[477]) ).

thf(486,plain,
    ! [SV110: $i,SV83: $i,SV22: $i,SV132: $i,SV95: $i,SV64: $i] :
      ( ( ( sum @ SV64 @ SV95 @ SV132 )
        = $false )
      | ( ( ! [SY365: $i] :
              ( ~ ( product @ SV22 @ SV132 @ SY365 )
              | ( sum @ SV83 @ SV110 @ SY365 ) ) )
        = $true )
      | ( ( product @ SV22 @ SV95 @ SV110 )
        = $false )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[478]) ).

thf(487,plain,
    ! [SV23: $i,SV111: $i,SV84: $i,SV133: $i,SV96: $i,SV65: $i] :
      ( ( ( sum @ SV65 @ SV96 @ SV133 )
        = $false )
      | ( ( ! [SY366: $i] :
              ( ~ ( sum @ SV84 @ SV111 @ SY366 )
              | ( product @ SV23 @ SV133 @ SY366 ) ) )
        = $true )
      | ( ( product @ SV23 @ SV96 @ SV111 )
        = $false )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[479]) ).

thf(488,plain,
    ! [SV112: $i,SV85: $i,SV66: $i,SV134: $i,SV97: $i,SV24: $i] :
      ( ( ( sum @ SV24 @ SV97 @ SV134 )
        = $false )
      | ( ( ! [SY367: $i] :
              ( ~ ( product @ SV134 @ SV66 @ SY367 )
              | ( sum @ SV85 @ SV112 @ SY367 ) ) )
        = $true )
      | ( ( product @ SV97 @ SV66 @ SV112 )
        = $false )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[480]) ).

thf(489,plain,
    ! [SV67: $i,SV113: $i,SV86: $i,SV135: $i,SV98: $i,SV25: $i] :
      ( ( ( sum @ SV25 @ SV98 @ SV135 )
        = $false )
      | ( ( ! [SY368: $i] :
              ( ~ ( sum @ SV86 @ SV113 @ SY368 )
              | ( product @ SV135 @ SV67 @ SY368 ) ) )
        = $true )
      | ( ( product @ SV98 @ SV67 @ SV113 )
        = $false )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[481]) ).

thf(490,plain,
    ! [SV95: $i,SV64: $i,SV110: $i,SV83: $i,SV136: $i,SV132: $i,SV22: $i] :
      ( ( ( ~ ( product @ SV22 @ SV132 @ SV136 )
          | ( sum @ SV83 @ SV110 @ SV136 ) )
        = $true )
      | ( ( sum @ SV64 @ SV95 @ SV132 )
        = $false )
      | ( ( product @ SV22 @ SV95 @ SV110 )
        = $false )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[486]) ).

thf(491,plain,
    ! [SV96: $i,SV65: $i,SV133: $i,SV23: $i,SV137: $i,SV111: $i,SV84: $i] :
      ( ( ( ~ ( sum @ SV84 @ SV111 @ SV137 )
          | ( product @ SV23 @ SV133 @ SV137 ) )
        = $true )
      | ( ( sum @ SV65 @ SV96 @ SV133 )
        = $false )
      | ( ( product @ SV23 @ SV96 @ SV111 )
        = $false )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[487]) ).

thf(492,plain,
    ! [SV97: $i,SV24: $i,SV112: $i,SV85: $i,SV138: $i,SV66: $i,SV134: $i] :
      ( ( ( ~ ( product @ SV134 @ SV66 @ SV138 )
          | ( sum @ SV85 @ SV112 @ SV138 ) )
        = $true )
      | ( ( sum @ SV24 @ SV97 @ SV134 )
        = $false )
      | ( ( product @ SV97 @ SV66 @ SV112 )
        = $false )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[488]) ).

thf(493,plain,
    ! [SV98: $i,SV25: $i,SV67: $i,SV135: $i,SV139: $i,SV113: $i,SV86: $i] :
      ( ( ( ~ ( sum @ SV86 @ SV113 @ SV139 )
          | ( product @ SV135 @ SV67 @ SV139 ) )
        = $true )
      | ( ( sum @ SV25 @ SV98 @ SV135 )
        = $false )
      | ( ( product @ SV98 @ SV67 @ SV113 )
        = $false )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[489]) ).

thf(494,plain,
    ! [SV95: $i,SV64: $i,SV110: $i,SV83: $i,SV136: $i,SV132: $i,SV22: $i] :
      ( ( ( ~ ( product @ SV22 @ SV132 @ SV136 ) )
        = $true )
      | ( ( sum @ SV83 @ SV110 @ SV136 )
        = $true )
      | ( ( sum @ SV64 @ SV95 @ SV132 )
        = $false )
      | ( ( product @ SV22 @ SV95 @ SV110 )
        = $false )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[490]) ).

thf(495,plain,
    ! [SV96: $i,SV65: $i,SV133: $i,SV23: $i,SV137: $i,SV111: $i,SV84: $i] :
      ( ( ( ~ ( sum @ SV84 @ SV111 @ SV137 ) )
        = $true )
      | ( ( product @ SV23 @ SV133 @ SV137 )
        = $true )
      | ( ( sum @ SV65 @ SV96 @ SV133 )
        = $false )
      | ( ( product @ SV23 @ SV96 @ SV111 )
        = $false )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[491]) ).

thf(496,plain,
    ! [SV97: $i,SV24: $i,SV112: $i,SV85: $i,SV138: $i,SV66: $i,SV134: $i] :
      ( ( ( ~ ( product @ SV134 @ SV66 @ SV138 ) )
        = $true )
      | ( ( sum @ SV85 @ SV112 @ SV138 )
        = $true )
      | ( ( sum @ SV24 @ SV97 @ SV134 )
        = $false )
      | ( ( product @ SV97 @ SV66 @ SV112 )
        = $false )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[492]) ).

thf(497,plain,
    ! [SV98: $i,SV25: $i,SV67: $i,SV135: $i,SV139: $i,SV113: $i,SV86: $i] :
      ( ( ( ~ ( sum @ SV86 @ SV113 @ SV139 ) )
        = $true )
      | ( ( product @ SV135 @ SV67 @ SV139 )
        = $true )
      | ( ( sum @ SV25 @ SV98 @ SV135 )
        = $false )
      | ( ( product @ SV98 @ SV67 @ SV113 )
        = $false )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[493]) ).

thf(498,plain,
    ! [SV95: $i,SV64: $i,SV110: $i,SV83: $i,SV136: $i,SV132: $i,SV22: $i] :
      ( ( ( product @ SV22 @ SV132 @ SV136 )
        = $false )
      | ( ( sum @ SV83 @ SV110 @ SV136 )
        = $true )
      | ( ( sum @ SV64 @ SV95 @ SV132 )
        = $false )
      | ( ( product @ SV22 @ SV95 @ SV110 )
        = $false )
      | ( ( product @ SV22 @ SV64 @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[494]) ).

thf(499,plain,
    ! [SV96: $i,SV65: $i,SV133: $i,SV23: $i,SV137: $i,SV111: $i,SV84: $i] :
      ( ( ( sum @ SV84 @ SV111 @ SV137 )
        = $false )
      | ( ( product @ SV23 @ SV133 @ SV137 )
        = $true )
      | ( ( sum @ SV65 @ SV96 @ SV133 )
        = $false )
      | ( ( product @ SV23 @ SV96 @ SV111 )
        = $false )
      | ( ( product @ SV23 @ SV65 @ SV84 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[495]) ).

thf(500,plain,
    ! [SV97: $i,SV24: $i,SV112: $i,SV85: $i,SV138: $i,SV66: $i,SV134: $i] :
      ( ( ( product @ SV134 @ SV66 @ SV138 )
        = $false )
      | ( ( sum @ SV85 @ SV112 @ SV138 )
        = $true )
      | ( ( sum @ SV24 @ SV97 @ SV134 )
        = $false )
      | ( ( product @ SV97 @ SV66 @ SV112 )
        = $false )
      | ( ( product @ SV24 @ SV66 @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[496]) ).

thf(501,plain,
    ! [SV98: $i,SV25: $i,SV67: $i,SV135: $i,SV139: $i,SV113: $i,SV86: $i] :
      ( ( ( sum @ SV86 @ SV113 @ SV139 )
        = $false )
      | ( ( product @ SV135 @ SV67 @ SV139 )
        = $true )
      | ( ( sum @ SV25 @ SV98 @ SV135 )
        = $false )
      | ( ( product @ SV98 @ SV67 @ SV113 )
        = $false )
      | ( ( product @ SV25 @ SV67 @ SV86 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[497]) ).

thf(502,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[176,501,500,499,498,485,484,483,482,457,456,455,454,445,444,443,442,441,440,427,391,384,383,379,378,329,328,327,326,325,324,310,309,297,296,295,294,292,288,287,286,285,278,277,265,264,262,251,248,247,246,245,244,243,242,241,240,239,238,236,235,234,231,230,229,228,226,225,222,221,220,219,217,216,177]) ).

thf(503,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[502]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : RNG039-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon May 30 17:10:46 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.40  .
% 0.13/0.40  
% 0.13/0.40   No.of.Axioms: 74
% 0.13/0.40  
% 0.13/0.40   Length.of.Defs: 0
% 0.13/0.40  
% 0.13/0.40   Contains.Choice.Funs: false
% 0.19/0.43  .
% 0.19/0.46  (rf:0,axioms:74,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:76,loop_count:0,foatp_calls:0,translation:fof_full)..............................
% 0.44/0.78  
% 0.44/0.78  ********************************
% 0.44/0.78  *   All subproblems solved!    *
% 0.44/0.78  ********************************
% 0.44/0.78  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:74,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:502,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.68/0.87  
% 0.68/0.87  %**** Beginning of derivation protocol ****
% 0.68/0.87  % SZS output start CNFRefutation
% See solution above
% 0.68/0.88  
% 0.68/0.88  %**** End of derivation protocol ****
% 0.68/0.88  %**** no. of clauses in derivation: 503 ****
% 0.68/0.88  %**** clause counter: 502 ****
% 0.68/0.88  
% 0.68/0.88  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:74,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:502,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------