TSTP Solution File: RNG039-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : RNG039-1 : 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 : n028.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 0.53s 0.73s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   71
% Syntax   : Number of formulae    :  367 ( 262 unt;  10 typ;   0 def)
%            Number of atoms       : 1851 ( 518 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives : 3899 ( 415   ~; 552   |;   0   &;2932   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   7 con; 0-3 aty)
%            Number of variables   : 1164 (   0   ^1164   !;   0   ?;1164   :)

% 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_additive_inverse,type,
    additive_inverse: $i > $i ).

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

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

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

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,
    ( ( multiply @ b @ a )
    = d ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).

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

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

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

thf(37,axiom,
    ! [A: $i] :
      ( ( 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,
    ! [X: $i,Y: $i,U: $i,V: $i] :
      ( ~ ( product @ X @ Y @ U )
      | ~ ( product @ X @ Y @ V )
      | ( U = V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).

thf(42,axiom,
    ! [X: $i,Y: $i,U: $i,V: $i] :
      ( ~ ( sum @ X @ Y @ U )
      | ~ ( sum @ X @ Y @ V )
      | ( U = V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).

thf(43,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(44,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(45,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(46,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(47,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(48,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(49,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(50,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(51,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(52,axiom,
    ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).

thf(53,axiom,
    ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

thf(54,axiom,
    ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).

thf(55,axiom,
    ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).

thf(56,axiom,
    ! [X: $i] : ( sum @ X @ additive_identity @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).

thf(57,axiom,
    ! [X: $i] : ( sum @ additive_identity @ X @ X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).

thf(58,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(59,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[58]) ).

thf(60,negated_conjecture,
    c != d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).

thf(61,negated_conjecture,
    product @ b @ a @ d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a) ).

thf(62,negated_conjecture,
    product @ a @ b @ c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).

thf(63,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[59]) ).

thf(64,plain,
    ( ( ! [A: $i] : ( product @ A @ A @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(65,plain,
    ( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(66,plain,
    ( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(67,plain,
    ( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(68,plain,
    ( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(69,plain,
    ( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(70,plain,
    ( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(71,plain,
    ( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(72,plain,
    ( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(73,plain,
    ( ( product @ c @ a @ ( multiply @ a @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(74,plain,
    ( ( product @ ( multiply @ d @ b ) @ a @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(75,plain,
    ( ( product @ b @ a @ ( multiply @ b @ d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(76,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(77,plain,
    ( ( product @ d @ b @ ( multiply @ b @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(78,plain,
    ( ( product @ ( multiply @ c @ a ) @ b @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(79,plain,
    ( ( product @ a @ b @ ( multiply @ a @ c ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(80,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(81,plain,
    ( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(82,plain,
    ( ( product @ a @ d @ ( multiply @ c @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(83,plain,
    ( ( product @ b @ c @ ( multiply @ d @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(84,plain,
    ( ( product @ b @ ( multiply @ a @ d ) @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(85,plain,
    ( ( product @ b @ a @ ( multiply @ d @ a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(86,plain,
    ( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(87,plain,
    ( ( product @ a @ ( multiply @ b @ c ) @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(88,plain,
    ( ( product @ a @ b @ ( multiply @ c @ b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(89,plain,
    ( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(90,plain,
    ( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(91,plain,
    ( ( product @ d @ a @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(92,plain,
    ( ( product @ c @ b @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(93,plain,
    ( ( product @ b @ d @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(94,plain,
    ( ( product @ a @ c @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[31]) ).

thf(95,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[32]) ).

thf(96,plain,
    ( ( ( multiply @ b @ a )
      = d )
    = $true ),
    inference(unfold_def,[status(thm)],[33]) ).

thf(97,plain,
    ( ( ( multiply @ a @ b )
      = c )
    = $true ),
    inference(unfold_def,[status(thm)],[34]) ).

thf(98,plain,
    ( ( ! [A: $i] :
          ( ( multiply @ A @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[35]) ).

thf(99,plain,
    ( ( ! [A: $i] :
          ( ( add @ A @ A )
          = additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[36]) ).

thf(100,plain,
    ( ( ! [A: $i] :
          ( ( add @ A @ additive_identity )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[37]) ).

thf(101,plain,
    ( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[38]) ).

thf(102,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[39]) ).

thf(103,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[40]) ).

thf(104,plain,
    ( ( ! [X: $i,Y: $i,U: $i,V: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ X @ Y @ V )
          | ( U = V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[41]) ).

thf(105,plain,
    ( ( ! [X: $i,Y: $i,U: $i,V: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ~ ( sum @ X @ Y @ V )
          | ( U = V ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(106,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)],[43]) ).

thf(107,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)],[44]) ).

thf(108,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)],[45]) ).

thf(109,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)],[46]) ).

thf(110,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)],[47]) ).

thf(111,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)],[48]) ).

thf(112,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ Z )
          | ( sum @ Y @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[49]) ).

thf(113,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)],[50]) ).

thf(114,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)],[51]) ).

thf(115,plain,
    ( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[52]) ).

thf(116,plain,
    ( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[53]) ).

thf(117,plain,
    ( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[54]) ).

thf(118,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[55]) ).

thf(119,plain,
    ( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[56]) ).

thf(120,plain,
    ( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[57]) ).

thf(121,plain,
    ( ( ( c != d ) )
    = $true ),
    inference(unfold_def,[status(thm)],[60]) ).

thf(122,plain,
    ( ( product @ b @ a @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[61]) ).

thf(123,plain,
    ( ( product @ a @ b @ c )
    = $true ),
    inference(unfold_def,[status(thm)],[62]) ).

thf(124,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[63]) ).

thf(125,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ X @ Y @ V )
              | ( U = V ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[104]) ).

thf(126,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ X @ Y @ V )
              | ( U = V ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[105]) ).

thf(127,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)],[106]) ).

thf(128,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)],[107]) ).

thf(129,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)],[108]) ).

thf(130,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)],[109]) ).

thf(131,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)],[110]) ).

thf(132,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)],[111]) ).

thf(133,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)],[113]) ).

thf(134,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)],[114]) ).

thf(135,plain,
    ( ( ( c != d ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[121]) ).

thf(136,plain,
    ( ( product @ a @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[123]) ).

thf(137,plain,
    ( ( product @ b @ a @ d )
    = $true ),
    inference(copy,[status(thm)],[122]) ).

thf(138,plain,
    ( ( ( c != d ) )
    = $true ),
    inference(copy,[status(thm)],[135]) ).

thf(139,plain,
    ( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[120]) ).

thf(140,plain,
    ( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
    = $true ),
    inference(copy,[status(thm)],[119]) ).

thf(141,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[118]) ).

thf(142,plain,
    ( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[117]) ).

thf(143,plain,
    ( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[116]) ).

thf(144,plain,
    ( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[115]) ).

thf(145,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)],[134]) ).

thf(146,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)],[133]) ).

thf(147,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ Z )
          | ( sum @ Y @ X @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[112]) ).

thf(148,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)],[132]) ).

thf(149,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)],[131]) ).

thf(150,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)],[130]) ).

thf(151,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)],[129]) ).

thf(152,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)],[128]) ).

thf(153,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)],[127]) ).

thf(154,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ X @ Y @ V )
              | ( U = V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[126]) ).

thf(155,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ X @ Y @ V )
              | ( U = V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[125]) ).

thf(156,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(157,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(158,plain,
    ( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(159,plain,
    ( ( ! [A: $i] :
          ( ( add @ A @ additive_identity )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(160,plain,
    ( ( ! [A: $i] :
          ( ( add @ A @ A )
          = additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(161,plain,
    ( ( ! [A: $i] :
          ( ( multiply @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(162,plain,
    ( ( ( multiply @ a @ b )
      = c )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(163,plain,
    ( ( ( multiply @ b @ a )
      = d )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(164,plain,
    ( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(165,plain,
    ( ( product @ a @ c @ c )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(166,plain,
    ( ( product @ b @ d @ d )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(167,plain,
    ( ( product @ c @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(168,plain,
    ( ( product @ d @ a @ d )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(169,plain,
    ( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(170,plain,
    ( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(171,plain,
    ( ( product @ a @ b @ ( multiply @ c @ b ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(172,plain,
    ( ( product @ a @ ( multiply @ b @ c ) @ c )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(173,plain,
    ( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(174,plain,
    ( ( product @ b @ a @ ( multiply @ d @ a ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(175,plain,
    ( ( product @ b @ ( multiply @ a @ d ) @ d )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(176,plain,
    ( ( product @ b @ c @ ( multiply @ d @ b ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(177,plain,
    ( ( product @ a @ d @ ( multiply @ c @ a ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(178,plain,
    ( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(179,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(180,plain,
    ( ( product @ a @ b @ ( multiply @ a @ c ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(181,plain,
    ( ( product @ ( multiply @ c @ a ) @ b @ c )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(182,plain,
    ( ( product @ d @ b @ ( multiply @ b @ c ) )
    = $true ),
    inference(copy,[status(thm)],[77]) ).

thf(183,plain,
    ( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
    = $true ),
    inference(copy,[status(thm)],[76]) ).

thf(184,plain,
    ( ( product @ b @ a @ ( multiply @ b @ d ) )
    = $true ),
    inference(copy,[status(thm)],[75]) ).

thf(185,plain,
    ( ( product @ ( multiply @ d @ b ) @ a @ d )
    = $true ),
    inference(copy,[status(thm)],[74]) ).

thf(186,plain,
    ( ( product @ c @ a @ ( multiply @ a @ d ) )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(187,plain,
    ( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(188,plain,
    ( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(189,plain,
    ( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(190,plain,
    ( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(191,plain,
    ( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(192,plain,
    ( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(193,plain,
    ( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(194,plain,
    ( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(195,plain,
    ( ( ! [A: $i] : ( product @ A @ A @ A ) )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(196,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[124]) ).

thf(197,plain,
    ( ( c = d )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[138]) ).

thf(198,plain,
    ! [SV1: $i] :
      ( ( sum @ additive_identity @ SV1 @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(199,plain,
    ! [SV2: $i] :
      ( ( sum @ SV2 @ additive_identity @ SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(200,plain,
    ! [SV3: $i] :
      ( ( ! [SY91: $i] : ( product @ SV3 @ SY91 @ ( multiply @ SV3 @ SY91 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(201,plain,
    ! [SV4: $i] :
      ( ( ! [SY92: $i] : ( sum @ SV4 @ SY92 @ ( add @ SV4 @ SY92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(202,plain,
    ! [SV5: $i] :
      ( ( sum @ ( additive_inverse @ SV5 ) @ SV5 @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(203,plain,
    ! [SV6: $i] :
      ( ( sum @ SV6 @ ( additive_inverse @ SV6 ) @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(204,plain,
    ! [SV7: $i] :
      ( ( ! [SY93: $i,SY94: $i,SY95: $i] :
            ( ~ ( sum @ SV7 @ SY93 @ SY94 )
            | ! [SY96: $i] :
                ( ~ ( sum @ SY93 @ SY95 @ SY96 )
                | ! [SY97: $i] :
                    ( ~ ( sum @ SY94 @ SY95 @ SY97 )
                    | ( sum @ SV7 @ SY96 @ SY97 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(205,plain,
    ! [SV8: $i] :
      ( ( ! [SY98: $i,SY99: $i,SY100: $i] :
            ( ~ ( sum @ SV8 @ SY98 @ SY99 )
            | ! [SY101: $i] :
                ( ~ ( sum @ SY98 @ SY100 @ SY101 )
                | ! [SY102: $i] :
                    ( ~ ( sum @ SV8 @ SY101 @ SY102 )
                    | ( sum @ SY99 @ SY100 @ SY102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[146]) ).

thf(206,plain,
    ! [SV9: $i] :
      ( ( ! [SY103: $i,SY104: $i] :
            ( ~ ( sum @ SV9 @ SY103 @ SY104 )
            | ( sum @ SY103 @ SV9 @ SY104 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[147]) ).

thf(207,plain,
    ! [SV10: $i] :
      ( ( ! [SY105: $i,SY106: $i,SY107: $i] :
            ( ~ ( product @ SV10 @ SY105 @ SY106 )
            | ! [SY108: $i] :
                ( ~ ( product @ SY105 @ SY107 @ SY108 )
                | ! [SY109: $i] :
                    ( ~ ( product @ SY106 @ SY107 @ SY109 )
                    | ( product @ SV10 @ SY108 @ SY109 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[148]) ).

thf(208,plain,
    ! [SV11: $i] :
      ( ( ! [SY110: $i,SY111: $i,SY112: $i] :
            ( ~ ( product @ SV11 @ SY110 @ SY111 )
            | ! [SY113: $i] :
                ( ~ ( product @ SY110 @ SY112 @ SY113 )
                | ! [SY114: $i] :
                    ( ~ ( product @ SV11 @ SY113 @ SY114 )
                    | ( product @ SY111 @ SY112 @ SY114 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[149]) ).

thf(209,plain,
    ! [SV12: $i] :
      ( ( ! [SY115: $i,SY116: $i,SY117: $i,SY118: $i] :
            ( ~ ( product @ SV12 @ SY115 @ SY116 )
            | ~ ( product @ SV12 @ SY117 @ SY118 )
            | ! [SY119: $i] :
                ( ~ ( sum @ SY115 @ SY117 @ SY119 )
                | ! [SY120: $i] :
                    ( ~ ( product @ SV12 @ SY119 @ SY120 )
                    | ( sum @ SY116 @ SY118 @ SY120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[150]) ).

thf(210,plain,
    ! [SV13: $i] :
      ( ( ! [SY121: $i,SY122: $i,SY123: $i,SY124: $i] :
            ( ~ ( product @ SV13 @ SY121 @ SY122 )
            | ~ ( product @ SV13 @ SY123 @ SY124 )
            | ! [SY125: $i] :
                ( ~ ( sum @ SY121 @ SY123 @ SY125 )
                | ! [SY126: $i] :
                    ( ~ ( sum @ SY122 @ SY124 @ SY126 )
                    | ( product @ SV13 @ SY125 @ SY126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[151]) ).

thf(211,plain,
    ! [SV14: $i] :
      ( ( ! [SY127: $i,SY128: $i,SY129: $i,SY130: $i] :
            ( ~ ( product @ SV14 @ SY127 @ SY128 )
            | ~ ( product @ SY129 @ SY127 @ SY130 )
            | ! [SY131: $i] :
                ( ~ ( sum @ SV14 @ SY129 @ SY131 )
                | ! [V4: $i] :
                    ( ~ ( product @ SY131 @ SY127 @ V4 )
                    | ( sum @ SY128 @ SY130 @ V4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[152]) ).

thf(212,plain,
    ! [SV15: $i] :
      ( ( ! [SY133: $i,SY134: $i,SY135: $i,SY136: $i] :
            ( ~ ( product @ SV15 @ SY133 @ SY134 )
            | ~ ( product @ SY135 @ SY133 @ SY136 )
            | ! [SY137: $i] :
                ( ~ ( sum @ SV15 @ SY135 @ SY137 )
                | ! [V4: $i] :
                    ( ~ ( sum @ SY134 @ SY136 @ V4 )
                    | ( product @ SY137 @ SY133 @ V4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[153]) ).

thf(213,plain,
    ! [SV16: $i] :
      ( ( ! [SY139: $i,SY140: $i] :
            ( ~ ( sum @ SV16 @ SY139 @ SY140 )
            | ! [SY141: $i] :
                ( ~ ( sum @ SV16 @ SY139 @ SY141 )
                | ( SY140 = SY141 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(214,plain,
    ! [SV17: $i] :
      ( ( ! [SY142: $i,SY143: $i] :
            ( ~ ( product @ SV17 @ SY142 @ SY143 )
            | ! [SY144: $i] :
                ( ~ ( product @ SV17 @ SY142 @ SY144 )
                | ( SY143 = SY144 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(215,plain,
    ! [SV18: $i] :
      ( ( ! [SY145: $i] : ( sum @ SV18 @ ( add @ SV18 @ SY145 ) @ SY145 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[156]) ).

thf(216,plain,
    ! [SV19: $i] :
      ( ( ! [SY146: $i] : ( sum @ ( add @ SV19 @ SY146 ) @ SY146 @ SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[157]) ).

thf(217,plain,
    ! [SV20: $i] :
      ( ( sum @ SV20 @ SV20 @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[158]) ).

thf(218,plain,
    ! [SV21: $i] :
      ( ( ( add @ SV21 @ additive_identity )
        = SV21 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[159]) ).

thf(219,plain,
    ! [SV22: $i] :
      ( ( ( add @ SV22 @ SV22 )
        = additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[160]) ).

thf(220,plain,
    ! [SV23: $i] :
      ( ( ( multiply @ SV23 @ SV23 )
        = SV23 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[161]) ).

thf(221,plain,
    ! [SV24: $i] :
      ( ( ! [SY147: $i] : ( sum @ SV24 @ SY147 @ ( add @ SY147 @ SV24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(222,plain,
    ! [SV25: $i] :
      ( ( ! [SY148: $i] : ( product @ SV25 @ ( multiply @ SV25 @ SY148 ) @ ( multiply @ SV25 @ SY148 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[169]) ).

thf(223,plain,
    ! [SV26: $i] :
      ( ( ! [SY149: $i] : ( product @ a @ ( multiply @ b @ SV26 ) @ ( multiply @ SY149 @ SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[170]) ).

thf(224,plain,
    ! [SV27: $i] :
      ( ( product @ b @ ( multiply @ a @ SV27 ) @ ( multiply @ d @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[173]) ).

thf(225,plain,
    ! [SV28: $i] :
      ( ( ! [SY150: $i] : ( product @ ( multiply @ SV28 @ SY150 ) @ SY150 @ ( multiply @ SV28 @ SY150 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[178]) ).

thf(226,plain,
    ! [SV29: $i] :
      ( ( product @ ( multiply @ SV29 @ a ) @ b @ ( multiply @ SV29 @ c ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[179]) ).

thf(227,plain,
    ! [SV30: $i] :
      ( ( product @ ( multiply @ SV30 @ b ) @ a @ ( multiply @ SV30 @ d ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[183]) ).

thf(228,plain,
    ! [SV31: $i] :
      ( ( product @ SV31 @ SV31 @ SV31 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[195]) ).

thf(229,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[196]) ).

thf(230,plain,
    ! [SV32: $i,SV3: $i] :
      ( ( product @ SV3 @ SV32 @ ( multiply @ SV3 @ SV32 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[200]) ).

thf(231,plain,
    ! [SV33: $i,SV4: $i] :
      ( ( sum @ SV4 @ SV33 @ ( add @ SV4 @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(232,plain,
    ! [SV34: $i,SV7: $i] :
      ( ( ! [SY151: $i,SY152: $i] :
            ( ~ ( sum @ SV7 @ SV34 @ SY151 )
            | ! [SY153: $i] :
                ( ~ ( sum @ SV34 @ SY152 @ SY153 )
                | ! [SY97: $i] :
                    ( ~ ( sum @ SY151 @ SY152 @ SY97 )
                    | ( sum @ SV7 @ SY153 @ SY97 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[204]) ).

thf(233,plain,
    ! [SV35: $i,SV8: $i] :
      ( ( ! [SY155: $i,SY156: $i] :
            ( ~ ( sum @ SV8 @ SV35 @ SY155 )
            | ! [SY157: $i] :
                ( ~ ( sum @ SV35 @ SY156 @ SY157 )
                | ! [SY102: $i] :
                    ( ~ ( sum @ SV8 @ SY157 @ SY102 )
                    | ( sum @ SY155 @ SY156 @ SY102 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[205]) ).

thf(234,plain,
    ! [SV36: $i,SV9: $i] :
      ( ( ! [SY159: $i] :
            ( ~ ( sum @ SV9 @ SV36 @ SY159 )
            | ( sum @ SV36 @ SV9 @ SY159 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[206]) ).

thf(235,plain,
    ! [SV37: $i,SV10: $i] :
      ( ( ! [SY160: $i,SY161: $i] :
            ( ~ ( product @ SV10 @ SV37 @ SY160 )
            | ! [SY162: $i] :
                ( ~ ( product @ SV37 @ SY161 @ SY162 )
                | ! [SY109: $i] :
                    ( ~ ( product @ SY160 @ SY161 @ SY109 )
                    | ( product @ SV10 @ SY162 @ SY109 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[207]) ).

thf(236,plain,
    ! [SV38: $i,SV11: $i] :
      ( ( ! [SY164: $i,SY165: $i] :
            ( ~ ( product @ SV11 @ SV38 @ SY164 )
            | ! [SY166: $i] :
                ( ~ ( product @ SV38 @ SY165 @ SY166 )
                | ! [SY114: $i] :
                    ( ~ ( product @ SV11 @ SY166 @ SY114 )
                    | ( product @ SY164 @ SY165 @ SY114 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[208]) ).

thf(237,plain,
    ! [SV39: $i,SV12: $i] :
      ( ( ! [SY168: $i,SY169: $i,SY170: $i] :
            ( ~ ( product @ SV12 @ SV39 @ SY168 )
            | ~ ( product @ SV12 @ SY169 @ SY170 )
            | ! [SY171: $i] :
                ( ~ ( sum @ SV39 @ SY169 @ SY171 )
                | ! [SY120: $i] :
                    ( ~ ( product @ SV12 @ SY171 @ SY120 )
                    | ( sum @ SY168 @ SY170 @ SY120 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[209]) ).

thf(238,plain,
    ! [SV40: $i,SV13: $i] :
      ( ( ! [SY173: $i,SY174: $i,SY175: $i] :
            ( ~ ( product @ SV13 @ SV40 @ SY173 )
            | ~ ( product @ SV13 @ SY174 @ SY175 )
            | ! [SY176: $i] :
                ( ~ ( sum @ SV40 @ SY174 @ SY176 )
                | ! [SY126: $i] :
                    ( ~ ( sum @ SY173 @ SY175 @ SY126 )
                    | ( product @ SV13 @ SY176 @ SY126 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[210]) ).

thf(239,plain,
    ! [SV41: $i,SV14: $i] :
      ( ( ! [SY178: $i,SY179: $i,SY180: $i] :
            ( ~ ( product @ SV14 @ SV41 @ SY178 )
            | ~ ( product @ SY179 @ SV41 @ SY180 )
            | ! [SY181: $i] :
                ( ~ ( sum @ SV14 @ SY179 @ SY181 )
                | ! [SY182: $i] :
                    ( ~ ( product @ SY181 @ SV41 @ SY182 )
                    | ( sum @ SY178 @ SY180 @ SY182 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[211]) ).

thf(240,plain,
    ! [SV42: $i,SV15: $i] :
      ( ( ! [SY183: $i,SY184: $i,SY185: $i] :
            ( ~ ( product @ SV15 @ SV42 @ SY183 )
            | ~ ( product @ SY184 @ SV42 @ SY185 )
            | ! [SY186: $i] :
                ( ~ ( sum @ SV15 @ SY184 @ SY186 )
                | ! [SY187: $i] :
                    ( ~ ( sum @ SY183 @ SY185 @ SY187 )
                    | ( product @ SY186 @ SV42 @ SY187 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[212]) ).

thf(241,plain,
    ! [SV43: $i,SV16: $i] :
      ( ( ! [SY188: $i] :
            ( ~ ( sum @ SV16 @ SV43 @ SY188 )
            | ! [SY189: $i] :
                ( ~ ( sum @ SV16 @ SV43 @ SY189 )
                | ( SY188 = SY189 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[213]) ).

thf(242,plain,
    ! [SV44: $i,SV17: $i] :
      ( ( ! [SY190: $i] :
            ( ~ ( product @ SV17 @ SV44 @ SY190 )
            | ! [SY191: $i] :
                ( ~ ( product @ SV17 @ SV44 @ SY191 )
                | ( SY190 = SY191 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[214]) ).

thf(243,plain,
    ! [SV45: $i,SV18: $i] :
      ( ( sum @ SV18 @ ( add @ SV18 @ SV45 ) @ SV45 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[215]) ).

thf(244,plain,
    ! [SV46: $i,SV19: $i] :
      ( ( sum @ ( add @ SV19 @ SV46 ) @ SV46 @ SV19 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[216]) ).

thf(245,plain,
    ! [SV47: $i,SV24: $i] :
      ( ( sum @ SV24 @ SV47 @ ( add @ SV47 @ SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[221]) ).

thf(246,plain,
    ! [SV48: $i,SV25: $i] :
      ( ( product @ SV25 @ ( multiply @ SV25 @ SV48 ) @ ( multiply @ SV25 @ SV48 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[222]) ).

thf(247,plain,
    ! [SV49: $i,SV26: $i] :
      ( ( product @ a @ ( multiply @ b @ SV26 ) @ ( multiply @ SV49 @ SV26 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[223]) ).

thf(248,plain,
    ! [SV50: $i,SV28: $i] :
      ( ( product @ ( multiply @ SV28 @ SV50 ) @ SV50 @ ( multiply @ SV28 @ SV50 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[225]) ).

thf(249,plain,
    ! [SV51: $i,SV34: $i,SV7: $i] :
      ( ( ! [SY192: $i] :
            ( ~ ( sum @ SV7 @ SV34 @ SV51 )
            | ! [SY193: $i] :
                ( ~ ( sum @ SV34 @ SY192 @ SY193 )
                | ! [SY194: $i] :
                    ( ~ ( sum @ SV51 @ SY192 @ SY194 )
                    | ( sum @ SV7 @ SY193 @ SY194 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[232]) ).

thf(250,plain,
    ! [SV52: $i,SV35: $i,SV8: $i] :
      ( ( ! [SY195: $i] :
            ( ~ ( sum @ SV8 @ SV35 @ SV52 )
            | ! [SY196: $i] :
                ( ~ ( sum @ SV35 @ SY195 @ SY196 )
                | ! [SY197: $i] :
                    ( ~ ( sum @ SV8 @ SY196 @ SY197 )
                    | ( sum @ SV52 @ SY195 @ SY197 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[233]) ).

thf(251,plain,
    ! [SV53: $i,SV36: $i,SV9: $i] :
      ( ( ~ ( sum @ SV9 @ SV36 @ SV53 )
        | ( sum @ SV36 @ SV9 @ SV53 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[234]) ).

thf(252,plain,
    ! [SV54: $i,SV37: $i,SV10: $i] :
      ( ( ! [SY198: $i] :
            ( ~ ( product @ SV10 @ SV37 @ SV54 )
            | ! [SY199: $i] :
                ( ~ ( product @ SV37 @ SY198 @ SY199 )
                | ! [SY200: $i] :
                    ( ~ ( product @ SV54 @ SY198 @ SY200 )
                    | ( product @ SV10 @ SY199 @ SY200 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[235]) ).

thf(253,plain,
    ! [SV55: $i,SV38: $i,SV11: $i] :
      ( ( ! [SY201: $i] :
            ( ~ ( product @ SV11 @ SV38 @ SV55 )
            | ! [SY202: $i] :
                ( ~ ( product @ SV38 @ SY201 @ SY202 )
                | ! [SY203: $i] :
                    ( ~ ( product @ SV11 @ SY202 @ SY203 )
                    | ( product @ SV55 @ SY201 @ SY203 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[236]) ).

thf(254,plain,
    ! [SV56: $i,SV39: $i,SV12: $i] :
      ( ( ! [SY204: $i,SY205: $i] :
            ( ~ ( product @ SV12 @ SV39 @ SV56 )
            | ~ ( product @ SV12 @ SY204 @ SY205 )
            | ! [SY206: $i] :
                ( ~ ( sum @ SV39 @ SY204 @ SY206 )
                | ! [SY207: $i] :
                    ( ~ ( product @ SV12 @ SY206 @ SY207 )
                    | ( sum @ SV56 @ SY205 @ SY207 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[237]) ).

thf(255,plain,
    ! [SV57: $i,SV40: $i,SV13: $i] :
      ( ( ! [SY208: $i,SY209: $i] :
            ( ~ ( product @ SV13 @ SV40 @ SV57 )
            | ~ ( product @ SV13 @ SY208 @ SY209 )
            | ! [SY210: $i] :
                ( ~ ( sum @ SV40 @ SY208 @ SY210 )
                | ! [SY211: $i] :
                    ( ~ ( sum @ SV57 @ SY209 @ SY211 )
                    | ( product @ SV13 @ SY210 @ SY211 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[238]) ).

thf(256,plain,
    ! [SV58: $i,SV41: $i,SV14: $i] :
      ( ( ! [SY212: $i,SY213: $i] :
            ( ~ ( product @ SV14 @ SV41 @ SV58 )
            | ~ ( product @ SY212 @ SV41 @ SY213 )
            | ! [SY214: $i] :
                ( ~ ( sum @ SV14 @ SY212 @ SY214 )
                | ! [SY215: $i] :
                    ( ~ ( product @ SY214 @ SV41 @ SY215 )
                    | ( sum @ SV58 @ SY213 @ SY215 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[239]) ).

thf(257,plain,
    ! [SV59: $i,SV42: $i,SV15: $i] :
      ( ( ! [SY216: $i,SY217: $i] :
            ( ~ ( product @ SV15 @ SV42 @ SV59 )
            | ~ ( product @ SY216 @ SV42 @ SY217 )
            | ! [SY218: $i] :
                ( ~ ( sum @ SV15 @ SY216 @ SY218 )
                | ! [SY219: $i] :
                    ( ~ ( sum @ SV59 @ SY217 @ SY219 )
                    | ( product @ SY218 @ SV42 @ SY219 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[240]) ).

thf(258,plain,
    ! [SV60: $i,SV43: $i,SV16: $i] :
      ( ( ~ ( sum @ SV16 @ SV43 @ SV60 )
        | ! [SY220: $i] :
            ( ~ ( sum @ SV16 @ SV43 @ SY220 )
            | ( SV60 = SY220 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[241]) ).

thf(259,plain,
    ! [SV61: $i,SV44: $i,SV17: $i] :
      ( ( ~ ( product @ SV17 @ SV44 @ SV61 )
        | ! [SY221: $i] :
            ( ~ ( product @ SV17 @ SV44 @ SY221 )
            | ( SV61 = SY221 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[242]) ).

thf(260,plain,
    ! [SV62: $i,SV51: $i,SV34: $i,SV7: $i] :
      ( ( ~ ( sum @ SV7 @ SV34 @ SV51 )
        | ! [SY222: $i] :
            ( ~ ( sum @ SV34 @ SV62 @ SY222 )
            | ! [SY223: $i] :
                ( ~ ( sum @ SV51 @ SV62 @ SY223 )
                | ( sum @ SV7 @ SY222 @ SY223 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[249]) ).

thf(261,plain,
    ! [SV63: $i,SV52: $i,SV35: $i,SV8: $i] :
      ( ( ~ ( sum @ SV8 @ SV35 @ SV52 )
        | ! [SY224: $i] :
            ( ~ ( sum @ SV35 @ SV63 @ SY224 )
            | ! [SY225: $i] :
                ( ~ ( sum @ SV8 @ SY224 @ SY225 )
                | ( sum @ SV52 @ SV63 @ SY225 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[250]) ).

thf(262,plain,
    ! [SV53: $i,SV36: $i,SV9: $i] :
      ( ( ( ~ ( sum @ SV9 @ SV36 @ SV53 ) )
        = $true )
      | ( ( sum @ SV36 @ SV9 @ SV53 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[251]) ).

thf(263,plain,
    ! [SV64: $i,SV54: $i,SV37: $i,SV10: $i] :
      ( ( ~ ( product @ SV10 @ SV37 @ SV54 )
        | ! [SY226: $i] :
            ( ~ ( product @ SV37 @ SV64 @ SY226 )
            | ! [SY227: $i] :
                ( ~ ( product @ SV54 @ SV64 @ SY227 )
                | ( product @ SV10 @ SY226 @ SY227 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[252]) ).

thf(264,plain,
    ! [SV65: $i,SV55: $i,SV38: $i,SV11: $i] :
      ( ( ~ ( product @ SV11 @ SV38 @ SV55 )
        | ! [SY228: $i] :
            ( ~ ( product @ SV38 @ SV65 @ SY228 )
            | ! [SY229: $i] :
                ( ~ ( product @ SV11 @ SY228 @ SY229 )
                | ( product @ SV55 @ SV65 @ SY229 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[253]) ).

thf(265,plain,
    ! [SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
      ( ( ! [SY230: $i] :
            ( ~ ( product @ SV12 @ SV39 @ SV56 )
            | ~ ( product @ SV12 @ SV66 @ SY230 )
            | ! [SY231: $i] :
                ( ~ ( sum @ SV39 @ SV66 @ SY231 )
                | ! [SY207: $i] :
                    ( ~ ( product @ SV12 @ SY231 @ SY207 )
                    | ( sum @ SV56 @ SY230 @ SY207 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[254]) ).

thf(266,plain,
    ! [SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
      ( ( ! [SY233: $i] :
            ( ~ ( product @ SV13 @ SV40 @ SV57 )
            | ~ ( product @ SV13 @ SV67 @ SY233 )
            | ! [SY234: $i] :
                ( ~ ( sum @ SV40 @ SV67 @ SY234 )
                | ! [SY211: $i] :
                    ( ~ ( sum @ SV57 @ SY233 @ SY211 )
                    | ( product @ SV13 @ SY234 @ SY211 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[255]) ).

thf(267,plain,
    ! [SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
      ( ( ! [SY236: $i] :
            ( ~ ( product @ SV14 @ SV41 @ SV58 )
            | ~ ( product @ SV68 @ SV41 @ SY236 )
            | ! [SY237: $i] :
                ( ~ ( sum @ SV14 @ SV68 @ SY237 )
                | ! [SY215: $i] :
                    ( ~ ( product @ SY237 @ SV41 @ SY215 )
                    | ( sum @ SV58 @ SY236 @ SY215 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[256]) ).

thf(268,plain,
    ! [SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
      ( ( ! [SY239: $i] :
            ( ~ ( product @ SV15 @ SV42 @ SV59 )
            | ~ ( product @ SV69 @ SV42 @ SY239 )
            | ! [SY240: $i] :
                ( ~ ( sum @ SV15 @ SV69 @ SY240 )
                | ! [SY219: $i] :
                    ( ~ ( sum @ SV59 @ SY239 @ SY219 )
                    | ( product @ SY240 @ SV42 @ SY219 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[257]) ).

thf(269,plain,
    ! [SV60: $i,SV43: $i,SV16: $i] :
      ( ( ( ~ ( sum @ SV16 @ SV43 @ SV60 ) )
        = $true )
      | ( ( ! [SY220: $i] :
              ( ~ ( sum @ SV16 @ SV43 @ SY220 )
              | ( SV60 = SY220 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[258]) ).

thf(270,plain,
    ! [SV61: $i,SV44: $i,SV17: $i] :
      ( ( ( ~ ( product @ SV17 @ SV44 @ SV61 ) )
        = $true )
      | ( ( ! [SY221: $i] :
              ( ~ ( product @ SV17 @ SV44 @ SY221 )
              | ( SV61 = SY221 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[259]) ).

thf(271,plain,
    ! [SV62: $i,SV51: $i,SV34: $i,SV7: $i] :
      ( ( ( ~ ( sum @ SV7 @ SV34 @ SV51 ) )
        = $true )
      | ( ( ! [SY222: $i] :
              ( ~ ( sum @ SV34 @ SV62 @ SY222 )
              | ! [SY223: $i] :
                  ( ~ ( sum @ SV51 @ SV62 @ SY223 )
                  | ( sum @ SV7 @ SY222 @ SY223 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[260]) ).

thf(272,plain,
    ! [SV63: $i,SV52: $i,SV35: $i,SV8: $i] :
      ( ( ( ~ ( sum @ SV8 @ SV35 @ SV52 ) )
        = $true )
      | ( ( ! [SY224: $i] :
              ( ~ ( sum @ SV35 @ SV63 @ SY224 )
              | ! [SY225: $i] :
                  ( ~ ( sum @ SV8 @ SY224 @ SY225 )
                  | ( sum @ SV52 @ SV63 @ SY225 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[261]) ).

thf(273,plain,
    ! [SV53: $i,SV36: $i,SV9: $i] :
      ( ( ( sum @ SV9 @ SV36 @ SV53 )
        = $false )
      | ( ( sum @ SV36 @ SV9 @ SV53 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[262]) ).

thf(274,plain,
    ! [SV64: $i,SV54: $i,SV37: $i,SV10: $i] :
      ( ( ( ~ ( product @ SV10 @ SV37 @ SV54 ) )
        = $true )
      | ( ( ! [SY226: $i] :
              ( ~ ( product @ SV37 @ SV64 @ SY226 )
              | ! [SY227: $i] :
                  ( ~ ( product @ SV54 @ SV64 @ SY227 )
                  | ( product @ SV10 @ SY226 @ SY227 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[263]) ).

thf(275,plain,
    ! [SV65: $i,SV55: $i,SV38: $i,SV11: $i] :
      ( ( ( ~ ( product @ SV11 @ SV38 @ SV55 ) )
        = $true )
      | ( ( ! [SY228: $i] :
              ( ~ ( product @ SV38 @ SV65 @ SY228 )
              | ! [SY229: $i] :
                  ( ~ ( product @ SV11 @ SY228 @ SY229 )
                  | ( product @ SV55 @ SV65 @ SY229 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[264]) ).

thf(276,plain,
    ! [SV70: $i,SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
      ( ( ~ ( product @ SV12 @ SV39 @ SV56 )
        | ~ ( product @ SV12 @ SV66 @ SV70 )
        | ! [SY242: $i] :
            ( ~ ( sum @ SV39 @ SV66 @ SY242 )
            | ! [SY243: $i] :
                ( ~ ( product @ SV12 @ SY242 @ SY243 )
                | ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[265]) ).

thf(277,plain,
    ! [SV71: $i,SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
      ( ( ~ ( product @ SV13 @ SV40 @ SV57 )
        | ~ ( product @ SV13 @ SV67 @ SV71 )
        | ! [SY244: $i] :
            ( ~ ( sum @ SV40 @ SV67 @ SY244 )
            | ! [SY245: $i] :
                ( ~ ( sum @ SV57 @ SV71 @ SY245 )
                | ( product @ SV13 @ SY244 @ SY245 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[266]) ).

thf(278,plain,
    ! [SV72: $i,SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
      ( ( ~ ( product @ SV14 @ SV41 @ SV58 )
        | ~ ( product @ SV68 @ SV41 @ SV72 )
        | ! [SY246: $i] :
            ( ~ ( sum @ SV14 @ SV68 @ SY246 )
            | ! [SY247: $i] :
                ( ~ ( product @ SY246 @ SV41 @ SY247 )
                | ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[267]) ).

thf(279,plain,
    ! [SV73: $i,SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
      ( ( ~ ( product @ SV15 @ SV42 @ SV59 )
        | ~ ( product @ SV69 @ SV42 @ SV73 )
        | ! [SY248: $i] :
            ( ~ ( sum @ SV15 @ SV69 @ SY248 )
            | ! [SY249: $i] :
                ( ~ ( sum @ SV59 @ SV73 @ SY249 )
                | ( product @ SY248 @ SV42 @ SY249 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[268]) ).

thf(280,plain,
    ! [SV60: $i,SV43: $i,SV16: $i] :
      ( ( ( sum @ SV16 @ SV43 @ SV60 )
        = $false )
      | ( ( ! [SY220: $i] :
              ( ~ ( sum @ SV16 @ SV43 @ SY220 )
              | ( SV60 = SY220 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[269]) ).

thf(281,plain,
    ! [SV61: $i,SV44: $i,SV17: $i] :
      ( ( ( product @ SV17 @ SV44 @ SV61 )
        = $false )
      | ( ( ! [SY221: $i] :
              ( ~ ( product @ SV17 @ SV44 @ SY221 )
              | ( SV61 = SY221 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[270]) ).

thf(282,plain,
    ! [SV62: $i,SV51: $i,SV34: $i,SV7: $i] :
      ( ( ( sum @ SV7 @ SV34 @ SV51 )
        = $false )
      | ( ( ! [SY222: $i] :
              ( ~ ( sum @ SV34 @ SV62 @ SY222 )
              | ! [SY223: $i] :
                  ( ~ ( sum @ SV51 @ SV62 @ SY223 )
                  | ( sum @ SV7 @ SY222 @ SY223 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[271]) ).

thf(283,plain,
    ! [SV63: $i,SV52: $i,SV35: $i,SV8: $i] :
      ( ( ( sum @ SV8 @ SV35 @ SV52 )
        = $false )
      | ( ( ! [SY224: $i] :
              ( ~ ( sum @ SV35 @ SV63 @ SY224 )
              | ! [SY225: $i] :
                  ( ~ ( sum @ SV8 @ SY224 @ SY225 )
                  | ( sum @ SV52 @ SV63 @ SY225 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[272]) ).

thf(284,plain,
    ! [SV64: $i,SV54: $i,SV37: $i,SV10: $i] :
      ( ( ( product @ SV10 @ SV37 @ SV54 )
        = $false )
      | ( ( ! [SY226: $i] :
              ( ~ ( product @ SV37 @ SV64 @ SY226 )
              | ! [SY227: $i] :
                  ( ~ ( product @ SV54 @ SV64 @ SY227 )
                  | ( product @ SV10 @ SY226 @ SY227 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[274]) ).

thf(285,plain,
    ! [SV65: $i,SV55: $i,SV38: $i,SV11: $i] :
      ( ( ( product @ SV11 @ SV38 @ SV55 )
        = $false )
      | ( ( ! [SY228: $i] :
              ( ~ ( product @ SV38 @ SV65 @ SY228 )
              | ! [SY229: $i] :
                  ( ~ ( product @ SV11 @ SY228 @ SY229 )
                  | ( product @ SV55 @ SV65 @ SY229 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[275]) ).

thf(286,plain,
    ! [SV70: $i,SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV39 @ SV56 ) )
        = $true )
      | ( ( ~ ( product @ SV12 @ SV66 @ SV70 )
          | ! [SY242: $i] :
              ( ~ ( sum @ SV39 @ SV66 @ SY242 )
              | ! [SY243: $i] :
                  ( ~ ( product @ SV12 @ SY242 @ SY243 )
                  | ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[276]) ).

thf(287,plain,
    ! [SV71: $i,SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
      ( ( ( ~ ( product @ SV13 @ SV40 @ SV57 ) )
        = $true )
      | ( ( ~ ( product @ SV13 @ SV67 @ SV71 )
          | ! [SY244: $i] :
              ( ~ ( sum @ SV40 @ SV67 @ SY244 )
              | ! [SY245: $i] :
                  ( ~ ( sum @ SV57 @ SV71 @ SY245 )
                  | ( product @ SV13 @ SY244 @ SY245 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[277]) ).

thf(288,plain,
    ! [SV72: $i,SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
      ( ( ( ~ ( product @ SV14 @ SV41 @ SV58 ) )
        = $true )
      | ( ( ~ ( product @ SV68 @ SV41 @ SV72 )
          | ! [SY246: $i] :
              ( ~ ( sum @ SV14 @ SV68 @ SY246 )
              | ! [SY247: $i] :
                  ( ~ ( product @ SY246 @ SV41 @ SY247 )
                  | ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[278]) ).

thf(289,plain,
    ! [SV73: $i,SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
      ( ( ( ~ ( product @ SV15 @ SV42 @ SV59 ) )
        = $true )
      | ( ( ~ ( product @ SV69 @ SV42 @ SV73 )
          | ! [SY248: $i] :
              ( ~ ( sum @ SV15 @ SV69 @ SY248 )
              | ! [SY249: $i] :
                  ( ~ ( sum @ SV59 @ SV73 @ SY249 )
                  | ( product @ SY248 @ SV42 @ SY249 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[279]) ).

thf(290,plain,
    ! [SV60: $i,SV74: $i,SV43: $i,SV16: $i] :
      ( ( ( ~ ( sum @ SV16 @ SV43 @ SV74 )
          | ( SV60 = SV74 ) )
        = $true )
      | ( ( sum @ SV16 @ SV43 @ SV60 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[280]) ).

thf(291,plain,
    ! [SV61: $i,SV75: $i,SV44: $i,SV17: $i] :
      ( ( ( ~ ( product @ SV17 @ SV44 @ SV75 )
          | ( SV61 = SV75 ) )
        = $true )
      | ( ( product @ SV17 @ SV44 @ SV61 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[281]) ).

thf(292,plain,
    ! [SV7: $i,SV51: $i,SV76: $i,SV62: $i,SV34: $i] :
      ( ( ( ~ ( sum @ SV34 @ SV62 @ SV76 )
          | ! [SY250: $i] :
              ( ~ ( sum @ SV51 @ SV62 @ SY250 )
              | ( sum @ SV7 @ SV76 @ SY250 ) ) )
        = $true )
      | ( ( sum @ SV7 @ SV34 @ SV51 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[282]) ).

thf(293,plain,
    ! [SV52: $i,SV8: $i,SV77: $i,SV63: $i,SV35: $i] :
      ( ( ( ~ ( sum @ SV35 @ SV63 @ SV77 )
          | ! [SY251: $i] :
              ( ~ ( sum @ SV8 @ SV77 @ SY251 )
              | ( sum @ SV52 @ SV63 @ SY251 ) ) )
        = $true )
      | ( ( sum @ SV8 @ SV35 @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[283]) ).

thf(294,plain,
    ! [SV10: $i,SV54: $i,SV78: $i,SV64: $i,SV37: $i] :
      ( ( ( ~ ( product @ SV37 @ SV64 @ SV78 )
          | ! [SY252: $i] :
              ( ~ ( product @ SV54 @ SV64 @ SY252 )
              | ( product @ SV10 @ SV78 @ SY252 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV37 @ SV54 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[284]) ).

thf(295,plain,
    ! [SV55: $i,SV11: $i,SV79: $i,SV65: $i,SV38: $i] :
      ( ( ( ~ ( product @ SV38 @ SV65 @ SV79 )
          | ! [SY253: $i] :
              ( ~ ( product @ SV11 @ SV79 @ SY253 )
              | ( product @ SV55 @ SV65 @ SY253 ) ) )
        = $true )
      | ( ( product @ SV11 @ SV38 @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[285]) ).

thf(296,plain,
    ! [SV70: $i,SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
      ( ( ( product @ SV12 @ SV39 @ SV56 )
        = $false )
      | ( ( ~ ( product @ SV12 @ SV66 @ SV70 )
          | ! [SY242: $i] :
              ( ~ ( sum @ SV39 @ SV66 @ SY242 )
              | ! [SY243: $i] :
                  ( ~ ( product @ SV12 @ SY242 @ SY243 )
                  | ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[286]) ).

thf(297,plain,
    ! [SV71: $i,SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
      ( ( ( product @ SV13 @ SV40 @ SV57 )
        = $false )
      | ( ( ~ ( product @ SV13 @ SV67 @ SV71 )
          | ! [SY244: $i] :
              ( ~ ( sum @ SV40 @ SV67 @ SY244 )
              | ! [SY245: $i] :
                  ( ~ ( sum @ SV57 @ SV71 @ SY245 )
                  | ( product @ SV13 @ SY244 @ SY245 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[287]) ).

thf(298,plain,
    ! [SV72: $i,SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
      ( ( ( product @ SV14 @ SV41 @ SV58 )
        = $false )
      | ( ( ~ ( product @ SV68 @ SV41 @ SV72 )
          | ! [SY246: $i] :
              ( ~ ( sum @ SV14 @ SV68 @ SY246 )
              | ! [SY247: $i] :
                  ( ~ ( product @ SY246 @ SV41 @ SY247 )
                  | ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[288]) ).

thf(299,plain,
    ! [SV73: $i,SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
      ( ( ( product @ SV15 @ SV42 @ SV59 )
        = $false )
      | ( ( ~ ( product @ SV69 @ SV42 @ SV73 )
          | ! [SY248: $i] :
              ( ~ ( sum @ SV15 @ SV69 @ SY248 )
              | ! [SY249: $i] :
                  ( ~ ( sum @ SV59 @ SV73 @ SY249 )
                  | ( product @ SY248 @ SV42 @ SY249 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[289]) ).

thf(300,plain,
    ! [SV60: $i,SV74: $i,SV43: $i,SV16: $i] :
      ( ( ( ~ ( sum @ SV16 @ SV43 @ SV74 ) )
        = $true )
      | ( ( SV60 = SV74 )
        = $true )
      | ( ( sum @ SV16 @ SV43 @ SV60 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[290]) ).

thf(301,plain,
    ! [SV61: $i,SV75: $i,SV44: $i,SV17: $i] :
      ( ( ( ~ ( product @ SV17 @ SV44 @ SV75 ) )
        = $true )
      | ( ( SV61 = SV75 )
        = $true )
      | ( ( product @ SV17 @ SV44 @ SV61 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[291]) ).

thf(302,plain,
    ! [SV7: $i,SV51: $i,SV76: $i,SV62: $i,SV34: $i] :
      ( ( ( ~ ( sum @ SV34 @ SV62 @ SV76 ) )
        = $true )
      | ( ( ! [SY250: $i] :
              ( ~ ( sum @ SV51 @ SV62 @ SY250 )
              | ( sum @ SV7 @ SV76 @ SY250 ) ) )
        = $true )
      | ( ( sum @ SV7 @ SV34 @ SV51 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[292]) ).

thf(303,plain,
    ! [SV52: $i,SV8: $i,SV77: $i,SV63: $i,SV35: $i] :
      ( ( ( ~ ( sum @ SV35 @ SV63 @ SV77 ) )
        = $true )
      | ( ( ! [SY251: $i] :
              ( ~ ( sum @ SV8 @ SV77 @ SY251 )
              | ( sum @ SV52 @ SV63 @ SY251 ) ) )
        = $true )
      | ( ( sum @ SV8 @ SV35 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[293]) ).

thf(304,plain,
    ! [SV10: $i,SV54: $i,SV78: $i,SV64: $i,SV37: $i] :
      ( ( ( ~ ( product @ SV37 @ SV64 @ SV78 ) )
        = $true )
      | ( ( ! [SY252: $i] :
              ( ~ ( product @ SV54 @ SV64 @ SY252 )
              | ( product @ SV10 @ SV78 @ SY252 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV37 @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[294]) ).

thf(305,plain,
    ! [SV55: $i,SV11: $i,SV79: $i,SV65: $i,SV38: $i] :
      ( ( ( ~ ( product @ SV38 @ SV65 @ SV79 ) )
        = $true )
      | ( ( ! [SY253: $i] :
              ( ~ ( product @ SV11 @ SV79 @ SY253 )
              | ( product @ SV55 @ SV65 @ SY253 ) ) )
        = $true )
      | ( ( product @ SV11 @ SV38 @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[295]) ).

thf(306,plain,
    ! [SV56: $i,SV39: $i,SV70: $i,SV66: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV66 @ SV70 ) )
        = $true )
      | ( ( ! [SY242: $i] :
              ( ~ ( sum @ SV39 @ SV66 @ SY242 )
              | ! [SY243: $i] :
                  ( ~ ( product @ SV12 @ SY242 @ SY243 )
                  | ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
        = $true )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[296]) ).

thf(307,plain,
    ! [SV57: $i,SV40: $i,SV71: $i,SV67: $i,SV13: $i] :
      ( ( ( ~ ( product @ SV13 @ SV67 @ SV71 ) )
        = $true )
      | ( ( ! [SY244: $i] :
              ( ~ ( sum @ SV40 @ SV67 @ SY244 )
              | ! [SY245: $i] :
                  ( ~ ( sum @ SV57 @ SV71 @ SY245 )
                  | ( product @ SV13 @ SY244 @ SY245 ) ) ) )
        = $true )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[297]) ).

thf(308,plain,
    ! [SV58: $i,SV14: $i,SV72: $i,SV41: $i,SV68: $i] :
      ( ( ( ~ ( product @ SV68 @ SV41 @ SV72 ) )
        = $true )
      | ( ( ! [SY246: $i] :
              ( ~ ( sum @ SV14 @ SV68 @ SY246 )
              | ! [SY247: $i] :
                  ( ~ ( product @ SY246 @ SV41 @ SY247 )
                  | ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
        = $true )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[298]) ).

thf(309,plain,
    ! [SV59: $i,SV15: $i,SV73: $i,SV42: $i,SV69: $i] :
      ( ( ( ~ ( product @ SV69 @ SV42 @ SV73 ) )
        = $true )
      | ( ( ! [SY248: $i] :
              ( ~ ( sum @ SV15 @ SV69 @ SY248 )
              | ! [SY249: $i] :
                  ( ~ ( sum @ SV59 @ SV73 @ SY249 )
                  | ( product @ SY248 @ SV42 @ SY249 ) ) ) )
        = $true )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[299]) ).

thf(310,plain,
    ! [SV60: $i,SV74: $i,SV43: $i,SV16: $i] :
      ( ( ( sum @ SV16 @ SV43 @ SV74 )
        = $false )
      | ( ( SV60 = SV74 )
        = $true )
      | ( ( sum @ SV16 @ SV43 @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[300]) ).

thf(311,plain,
    ! [SV61: $i,SV75: $i,SV44: $i,SV17: $i] :
      ( ( ( product @ SV17 @ SV44 @ SV75 )
        = $false )
      | ( ( SV61 = SV75 )
        = $true )
      | ( ( product @ SV17 @ SV44 @ SV61 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[301]) ).

thf(312,plain,
    ! [SV7: $i,SV51: $i,SV76: $i,SV62: $i,SV34: $i] :
      ( ( ( sum @ SV34 @ SV62 @ SV76 )
        = $false )
      | ( ( ! [SY250: $i] :
              ( ~ ( sum @ SV51 @ SV62 @ SY250 )
              | ( sum @ SV7 @ SV76 @ SY250 ) ) )
        = $true )
      | ( ( sum @ SV7 @ SV34 @ SV51 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[302]) ).

thf(313,plain,
    ! [SV52: $i,SV8: $i,SV77: $i,SV63: $i,SV35: $i] :
      ( ( ( sum @ SV35 @ SV63 @ SV77 )
        = $false )
      | ( ( ! [SY251: $i] :
              ( ~ ( sum @ SV8 @ SV77 @ SY251 )
              | ( sum @ SV52 @ SV63 @ SY251 ) ) )
        = $true )
      | ( ( sum @ SV8 @ SV35 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[303]) ).

thf(314,plain,
    ! [SV10: $i,SV54: $i,SV78: $i,SV64: $i,SV37: $i] :
      ( ( ( product @ SV37 @ SV64 @ SV78 )
        = $false )
      | ( ( ! [SY252: $i] :
              ( ~ ( product @ SV54 @ SV64 @ SY252 )
              | ( product @ SV10 @ SV78 @ SY252 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV37 @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[304]) ).

thf(315,plain,
    ! [SV55: $i,SV11: $i,SV79: $i,SV65: $i,SV38: $i] :
      ( ( ( product @ SV38 @ SV65 @ SV79 )
        = $false )
      | ( ( ! [SY253: $i] :
              ( ~ ( product @ SV11 @ SV79 @ SY253 )
              | ( product @ SV55 @ SV65 @ SY253 ) ) )
        = $true )
      | ( ( product @ SV11 @ SV38 @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[305]) ).

thf(316,plain,
    ! [SV56: $i,SV39: $i,SV70: $i,SV66: $i,SV12: $i] :
      ( ( ( product @ SV12 @ SV66 @ SV70 )
        = $false )
      | ( ( ! [SY242: $i] :
              ( ~ ( sum @ SV39 @ SV66 @ SY242 )
              | ! [SY243: $i] :
                  ( ~ ( product @ SV12 @ SY242 @ SY243 )
                  | ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
        = $true )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[306]) ).

thf(317,plain,
    ! [SV57: $i,SV40: $i,SV71: $i,SV67: $i,SV13: $i] :
      ( ( ( product @ SV13 @ SV67 @ SV71 )
        = $false )
      | ( ( ! [SY244: $i] :
              ( ~ ( sum @ SV40 @ SV67 @ SY244 )
              | ! [SY245: $i] :
                  ( ~ ( sum @ SV57 @ SV71 @ SY245 )
                  | ( product @ SV13 @ SY244 @ SY245 ) ) ) )
        = $true )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[307]) ).

thf(318,plain,
    ! [SV58: $i,SV14: $i,SV72: $i,SV41: $i,SV68: $i] :
      ( ( ( product @ SV68 @ SV41 @ SV72 )
        = $false )
      | ( ( ! [SY246: $i] :
              ( ~ ( sum @ SV14 @ SV68 @ SY246 )
              | ! [SY247: $i] :
                  ( ~ ( product @ SY246 @ SV41 @ SY247 )
                  | ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
        = $true )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[308]) ).

thf(319,plain,
    ! [SV59: $i,SV15: $i,SV73: $i,SV42: $i,SV69: $i] :
      ( ( ( product @ SV69 @ SV42 @ SV73 )
        = $false )
      | ( ( ! [SY248: $i] :
              ( ~ ( sum @ SV15 @ SV69 @ SY248 )
              | ! [SY249: $i] :
                  ( ~ ( sum @ SV59 @ SV73 @ SY249 )
                  | ( product @ SY248 @ SV42 @ SY249 ) ) ) )
        = $true )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[309]) ).

thf(320,plain,
    ! [SV34: $i,SV76: $i,SV7: $i,SV80: $i,SV62: $i,SV51: $i] :
      ( ( ( ~ ( sum @ SV51 @ SV62 @ SV80 )
          | ( sum @ SV7 @ SV76 @ SV80 ) )
        = $true )
      | ( ( sum @ SV34 @ SV62 @ SV76 )
        = $false )
      | ( ( sum @ SV7 @ SV34 @ SV51 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[312]) ).

thf(321,plain,
    ! [SV35: $i,SV63: $i,SV52: $i,SV81: $i,SV77: $i,SV8: $i] :
      ( ( ( ~ ( sum @ SV8 @ SV77 @ SV81 )
          | ( sum @ SV52 @ SV63 @ SV81 ) )
        = $true )
      | ( ( sum @ SV35 @ SV63 @ SV77 )
        = $false )
      | ( ( sum @ SV8 @ SV35 @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[313]) ).

thf(322,plain,
    ! [SV37: $i,SV78: $i,SV10: $i,SV82: $i,SV64: $i,SV54: $i] :
      ( ( ( ~ ( product @ SV54 @ SV64 @ SV82 )
          | ( product @ SV10 @ SV78 @ SV82 ) )
        = $true )
      | ( ( product @ SV37 @ SV64 @ SV78 )
        = $false )
      | ( ( product @ SV10 @ SV37 @ SV54 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[314]) ).

thf(323,plain,
    ! [SV38: $i,SV65: $i,SV55: $i,SV83: $i,SV79: $i,SV11: $i] :
      ( ( ( ~ ( product @ SV11 @ SV79 @ SV83 )
          | ( product @ SV55 @ SV65 @ SV83 ) )
        = $true )
      | ( ( product @ SV38 @ SV65 @ SV79 )
        = $false )
      | ( ( product @ SV11 @ SV38 @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[315]) ).

thf(324,plain,
    ! [SV70: $i,SV56: $i,SV12: $i,SV84: $i,SV66: $i,SV39: $i] :
      ( ( ( ~ ( sum @ SV39 @ SV66 @ SV84 )
          | ! [SY254: $i] :
              ( ~ ( product @ SV12 @ SV84 @ SY254 )
              | ( sum @ SV56 @ SV70 @ SY254 ) ) )
        = $true )
      | ( ( product @ SV12 @ SV66 @ SV70 )
        = $false )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[316]) ).

thf(325,plain,
    ! [SV13: $i,SV71: $i,SV57: $i,SV85: $i,SV67: $i,SV40: $i] :
      ( ( ( ~ ( sum @ SV40 @ SV67 @ SV85 )
          | ! [SY255: $i] :
              ( ~ ( sum @ SV57 @ SV71 @ SY255 )
              | ( product @ SV13 @ SV85 @ SY255 ) ) )
        = $true )
      | ( ( product @ SV13 @ SV67 @ SV71 )
        = $false )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[317]) ).

thf(326,plain,
    ! [SV72: $i,SV58: $i,SV41: $i,SV86: $i,SV68: $i,SV14: $i] :
      ( ( ( ~ ( sum @ SV14 @ SV68 @ SV86 )
          | ! [SY256: $i] :
              ( ~ ( product @ SV86 @ SV41 @ SY256 )
              | ( sum @ SV58 @ SV72 @ SY256 ) ) )
        = $true )
      | ( ( product @ SV68 @ SV41 @ SV72 )
        = $false )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[318]) ).

thf(327,plain,
    ! [SV42: $i,SV73: $i,SV59: $i,SV87: $i,SV69: $i,SV15: $i] :
      ( ( ( ~ ( sum @ SV15 @ SV69 @ SV87 )
          | ! [SY257: $i] :
              ( ~ ( sum @ SV59 @ SV73 @ SY257 )
              | ( product @ SV87 @ SV42 @ SY257 ) ) )
        = $true )
      | ( ( product @ SV69 @ SV42 @ SV73 )
        = $false )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[319]) ).

thf(328,plain,
    ! [SV34: $i,SV76: $i,SV7: $i,SV80: $i,SV62: $i,SV51: $i] :
      ( ( ( ~ ( sum @ SV51 @ SV62 @ SV80 ) )
        = $true )
      | ( ( sum @ SV7 @ SV76 @ SV80 )
        = $true )
      | ( ( sum @ SV34 @ SV62 @ SV76 )
        = $false )
      | ( ( sum @ SV7 @ SV34 @ SV51 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[320]) ).

thf(329,plain,
    ! [SV35: $i,SV63: $i,SV52: $i,SV81: $i,SV77: $i,SV8: $i] :
      ( ( ( ~ ( sum @ SV8 @ SV77 @ SV81 ) )
        = $true )
      | ( ( sum @ SV52 @ SV63 @ SV81 )
        = $true )
      | ( ( sum @ SV35 @ SV63 @ SV77 )
        = $false )
      | ( ( sum @ SV8 @ SV35 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[321]) ).

thf(330,plain,
    ! [SV37: $i,SV78: $i,SV10: $i,SV82: $i,SV64: $i,SV54: $i] :
      ( ( ( ~ ( product @ SV54 @ SV64 @ SV82 ) )
        = $true )
      | ( ( product @ SV10 @ SV78 @ SV82 )
        = $true )
      | ( ( product @ SV37 @ SV64 @ SV78 )
        = $false )
      | ( ( product @ SV10 @ SV37 @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[322]) ).

thf(331,plain,
    ! [SV38: $i,SV65: $i,SV55: $i,SV83: $i,SV79: $i,SV11: $i] :
      ( ( ( ~ ( product @ SV11 @ SV79 @ SV83 ) )
        = $true )
      | ( ( product @ SV55 @ SV65 @ SV83 )
        = $true )
      | ( ( product @ SV38 @ SV65 @ SV79 )
        = $false )
      | ( ( product @ SV11 @ SV38 @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[323]) ).

thf(332,plain,
    ! [SV70: $i,SV56: $i,SV12: $i,SV84: $i,SV66: $i,SV39: $i] :
      ( ( ( ~ ( sum @ SV39 @ SV66 @ SV84 ) )
        = $true )
      | ( ( ! [SY254: $i] :
              ( ~ ( product @ SV12 @ SV84 @ SY254 )
              | ( sum @ SV56 @ SV70 @ SY254 ) ) )
        = $true )
      | ( ( product @ SV12 @ SV66 @ SV70 )
        = $false )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[324]) ).

thf(333,plain,
    ! [SV13: $i,SV71: $i,SV57: $i,SV85: $i,SV67: $i,SV40: $i] :
      ( ( ( ~ ( sum @ SV40 @ SV67 @ SV85 ) )
        = $true )
      | ( ( ! [SY255: $i] :
              ( ~ ( sum @ SV57 @ SV71 @ SY255 )
              | ( product @ SV13 @ SV85 @ SY255 ) ) )
        = $true )
      | ( ( product @ SV13 @ SV67 @ SV71 )
        = $false )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[325]) ).

thf(334,plain,
    ! [SV72: $i,SV58: $i,SV41: $i,SV86: $i,SV68: $i,SV14: $i] :
      ( ( ( ~ ( sum @ SV14 @ SV68 @ SV86 ) )
        = $true )
      | ( ( ! [SY256: $i] :
              ( ~ ( product @ SV86 @ SV41 @ SY256 )
              | ( sum @ SV58 @ SV72 @ SY256 ) ) )
        = $true )
      | ( ( product @ SV68 @ SV41 @ SV72 )
        = $false )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[326]) ).

thf(335,plain,
    ! [SV42: $i,SV73: $i,SV59: $i,SV87: $i,SV69: $i,SV15: $i] :
      ( ( ( ~ ( sum @ SV15 @ SV69 @ SV87 ) )
        = $true )
      | ( ( ! [SY257: $i] :
              ( ~ ( sum @ SV59 @ SV73 @ SY257 )
              | ( product @ SV87 @ SV42 @ SY257 ) ) )
        = $true )
      | ( ( product @ SV69 @ SV42 @ SV73 )
        = $false )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[327]) ).

thf(336,plain,
    ! [SV34: $i,SV76: $i,SV7: $i,SV80: $i,SV62: $i,SV51: $i] :
      ( ( ( sum @ SV51 @ SV62 @ SV80 )
        = $false )
      | ( ( sum @ SV7 @ SV76 @ SV80 )
        = $true )
      | ( ( sum @ SV34 @ SV62 @ SV76 )
        = $false )
      | ( ( sum @ SV7 @ SV34 @ SV51 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[328]) ).

thf(337,plain,
    ! [SV35: $i,SV63: $i,SV52: $i,SV81: $i,SV77: $i,SV8: $i] :
      ( ( ( sum @ SV8 @ SV77 @ SV81 )
        = $false )
      | ( ( sum @ SV52 @ SV63 @ SV81 )
        = $true )
      | ( ( sum @ SV35 @ SV63 @ SV77 )
        = $false )
      | ( ( sum @ SV8 @ SV35 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[329]) ).

thf(338,plain,
    ! [SV37: $i,SV78: $i,SV10: $i,SV82: $i,SV64: $i,SV54: $i] :
      ( ( ( product @ SV54 @ SV64 @ SV82 )
        = $false )
      | ( ( product @ SV10 @ SV78 @ SV82 )
        = $true )
      | ( ( product @ SV37 @ SV64 @ SV78 )
        = $false )
      | ( ( product @ SV10 @ SV37 @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[330]) ).

thf(339,plain,
    ! [SV38: $i,SV65: $i,SV55: $i,SV83: $i,SV79: $i,SV11: $i] :
      ( ( ( product @ SV11 @ SV79 @ SV83 )
        = $false )
      | ( ( product @ SV55 @ SV65 @ SV83 )
        = $true )
      | ( ( product @ SV38 @ SV65 @ SV79 )
        = $false )
      | ( ( product @ SV11 @ SV38 @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[331]) ).

thf(340,plain,
    ! [SV70: $i,SV56: $i,SV12: $i,SV84: $i,SV66: $i,SV39: $i] :
      ( ( ( sum @ SV39 @ SV66 @ SV84 )
        = $false )
      | ( ( ! [SY254: $i] :
              ( ~ ( product @ SV12 @ SV84 @ SY254 )
              | ( sum @ SV56 @ SV70 @ SY254 ) ) )
        = $true )
      | ( ( product @ SV12 @ SV66 @ SV70 )
        = $false )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[332]) ).

thf(341,plain,
    ! [SV13: $i,SV71: $i,SV57: $i,SV85: $i,SV67: $i,SV40: $i] :
      ( ( ( sum @ SV40 @ SV67 @ SV85 )
        = $false )
      | ( ( ! [SY255: $i] :
              ( ~ ( sum @ SV57 @ SV71 @ SY255 )
              | ( product @ SV13 @ SV85 @ SY255 ) ) )
        = $true )
      | ( ( product @ SV13 @ SV67 @ SV71 )
        = $false )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[333]) ).

thf(342,plain,
    ! [SV72: $i,SV58: $i,SV41: $i,SV86: $i,SV68: $i,SV14: $i] :
      ( ( ( sum @ SV14 @ SV68 @ SV86 )
        = $false )
      | ( ( ! [SY256: $i] :
              ( ~ ( product @ SV86 @ SV41 @ SY256 )
              | ( sum @ SV58 @ SV72 @ SY256 ) ) )
        = $true )
      | ( ( product @ SV68 @ SV41 @ SV72 )
        = $false )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[334]) ).

thf(343,plain,
    ! [SV42: $i,SV73: $i,SV59: $i,SV87: $i,SV69: $i,SV15: $i] :
      ( ( ( sum @ SV15 @ SV69 @ SV87 )
        = $false )
      | ( ( ! [SY257: $i] :
              ( ~ ( sum @ SV59 @ SV73 @ SY257 )
              | ( product @ SV87 @ SV42 @ SY257 ) ) )
        = $true )
      | ( ( product @ SV69 @ SV42 @ SV73 )
        = $false )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[335]) ).

thf(344,plain,
    ! [SV66: $i,SV39: $i,SV70: $i,SV56: $i,SV88: $i,SV84: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV84 @ SV88 )
          | ( sum @ SV56 @ SV70 @ SV88 ) )
        = $true )
      | ( ( sum @ SV39 @ SV66 @ SV84 )
        = $false )
      | ( ( product @ SV12 @ SV66 @ SV70 )
        = $false )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[340]) ).

thf(345,plain,
    ! [SV67: $i,SV40: $i,SV85: $i,SV13: $i,SV89: $i,SV71: $i,SV57: $i] :
      ( ( ( ~ ( sum @ SV57 @ SV71 @ SV89 )
          | ( product @ SV13 @ SV85 @ SV89 ) )
        = $true )
      | ( ( sum @ SV40 @ SV67 @ SV85 )
        = $false )
      | ( ( product @ SV13 @ SV67 @ SV71 )
        = $false )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[341]) ).

thf(346,plain,
    ! [SV68: $i,SV14: $i,SV72: $i,SV58: $i,SV90: $i,SV41: $i,SV86: $i] :
      ( ( ( ~ ( product @ SV86 @ SV41 @ SV90 )
          | ( sum @ SV58 @ SV72 @ SV90 ) )
        = $true )
      | ( ( sum @ SV14 @ SV68 @ SV86 )
        = $false )
      | ( ( product @ SV68 @ SV41 @ SV72 )
        = $false )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[342]) ).

thf(347,plain,
    ! [SV69: $i,SV15: $i,SV42: $i,SV87: $i,SV91: $i,SV73: $i,SV59: $i] :
      ( ( ( ~ ( sum @ SV59 @ SV73 @ SV91 )
          | ( product @ SV87 @ SV42 @ SV91 ) )
        = $true )
      | ( ( sum @ SV15 @ SV69 @ SV87 )
        = $false )
      | ( ( product @ SV69 @ SV42 @ SV73 )
        = $false )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[343]) ).

thf(348,plain,
    ! [SV66: $i,SV39: $i,SV70: $i,SV56: $i,SV88: $i,SV84: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV84 @ SV88 ) )
        = $true )
      | ( ( sum @ SV56 @ SV70 @ SV88 )
        = $true )
      | ( ( sum @ SV39 @ SV66 @ SV84 )
        = $false )
      | ( ( product @ SV12 @ SV66 @ SV70 )
        = $false )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[344]) ).

thf(349,plain,
    ! [SV67: $i,SV40: $i,SV85: $i,SV13: $i,SV89: $i,SV71: $i,SV57: $i] :
      ( ( ( ~ ( sum @ SV57 @ SV71 @ SV89 ) )
        = $true )
      | ( ( product @ SV13 @ SV85 @ SV89 )
        = $true )
      | ( ( sum @ SV40 @ SV67 @ SV85 )
        = $false )
      | ( ( product @ SV13 @ SV67 @ SV71 )
        = $false )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[345]) ).

thf(350,plain,
    ! [SV68: $i,SV14: $i,SV72: $i,SV58: $i,SV90: $i,SV41: $i,SV86: $i] :
      ( ( ( ~ ( product @ SV86 @ SV41 @ SV90 ) )
        = $true )
      | ( ( sum @ SV58 @ SV72 @ SV90 )
        = $true )
      | ( ( sum @ SV14 @ SV68 @ SV86 )
        = $false )
      | ( ( product @ SV68 @ SV41 @ SV72 )
        = $false )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[346]) ).

thf(351,plain,
    ! [SV69: $i,SV15: $i,SV42: $i,SV87: $i,SV91: $i,SV73: $i,SV59: $i] :
      ( ( ( ~ ( sum @ SV59 @ SV73 @ SV91 ) )
        = $true )
      | ( ( product @ SV87 @ SV42 @ SV91 )
        = $true )
      | ( ( sum @ SV15 @ SV69 @ SV87 )
        = $false )
      | ( ( product @ SV69 @ SV42 @ SV73 )
        = $false )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[347]) ).

thf(352,plain,
    ! [SV66: $i,SV39: $i,SV70: $i,SV56: $i,SV88: $i,SV84: $i,SV12: $i] :
      ( ( ( product @ SV12 @ SV84 @ SV88 )
        = $false )
      | ( ( sum @ SV56 @ SV70 @ SV88 )
        = $true )
      | ( ( sum @ SV39 @ SV66 @ SV84 )
        = $false )
      | ( ( product @ SV12 @ SV66 @ SV70 )
        = $false )
      | ( ( product @ SV12 @ SV39 @ SV56 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[348]) ).

thf(353,plain,
    ! [SV67: $i,SV40: $i,SV85: $i,SV13: $i,SV89: $i,SV71: $i,SV57: $i] :
      ( ( ( sum @ SV57 @ SV71 @ SV89 )
        = $false )
      | ( ( product @ SV13 @ SV85 @ SV89 )
        = $true )
      | ( ( sum @ SV40 @ SV67 @ SV85 )
        = $false )
      | ( ( product @ SV13 @ SV67 @ SV71 )
        = $false )
      | ( ( product @ SV13 @ SV40 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[349]) ).

thf(354,plain,
    ! [SV68: $i,SV14: $i,SV72: $i,SV58: $i,SV90: $i,SV41: $i,SV86: $i] :
      ( ( ( product @ SV86 @ SV41 @ SV90 )
        = $false )
      | ( ( sum @ SV58 @ SV72 @ SV90 )
        = $true )
      | ( ( sum @ SV14 @ SV68 @ SV86 )
        = $false )
      | ( ( product @ SV68 @ SV41 @ SV72 )
        = $false )
      | ( ( product @ SV14 @ SV41 @ SV58 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[350]) ).

thf(355,plain,
    ! [SV69: $i,SV15: $i,SV42: $i,SV87: $i,SV91: $i,SV73: $i,SV59: $i] :
      ( ( ( sum @ SV59 @ SV73 @ SV91 )
        = $false )
      | ( ( product @ SV87 @ SV42 @ SV91 )
        = $true )
      | ( ( sum @ SV15 @ SV69 @ SV87 )
        = $false )
      | ( ( product @ SV69 @ SV42 @ SV73 )
        = $false )
      | ( ( product @ SV15 @ SV42 @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[351]) ).

thf(356,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[136,355,354,353,352,339,338,337,336,311,310,273,248,247,246,245,244,243,231,230,229,228,227,226,224,220,219,218,217,203,202,199,198,197,194,193,192,191,190,189,188,187,186,185,184,182,181,180,177,176,175,174,172,171,168,167,166,165,163,162,137]) ).

thf(357,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[356]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon May 30 11:21:49 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.38  
% 0.13/0.38   No.of.Axioms: 60
% 0.13/0.38  
% 0.13/0.38   Length.of.Defs: 0
% 0.13/0.38  
% 0.13/0.38   Contains.Choice.Funs: false
% 0.13/0.39  .
% 0.18/0.42  (rf:0,axioms:60,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:62,loop_count:0,foatp_calls:0,translation:fof_full)......................
% 0.53/0.73  
% 0.53/0.73  ********************************
% 0.53/0.73  *   All subproblems solved!    *
% 0.53/0.73  ********************************
% 0.53/0.73  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:60,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.53/0.77  
% 0.53/0.77  %**** Beginning of derivation protocol ****
% 0.53/0.77  % SZS output start CNFRefutation
% See solution above
% 0.53/0.77  
% 0.53/0.77  %**** End of derivation protocol ****
% 0.53/0.77  %**** no. of clauses in derivation: 357 ****
% 0.53/0.77  %**** clause counter: 356 ****
% 0.53/0.77  
% 0.53/0.77  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:60,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------