TSTP Solution File: RNG003-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : RNG003-1 : 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 : n020.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 20:33:54 EDT 2022

% Result   : Unsatisfiable 0.55s 0.72s
% Output   : CNFRefutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  227 ( 122 unt;  10 typ;   0 def)
%            Number of atoms       : 1511 ( 400 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives : 3191 ( 415   ~; 552   |;   0   &;2224   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 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   : 1072 (   0   ^1072   !;   0   ?;1072   :)

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

thf(2,axiom,
    ! [X: $i,Y: $i,U: $i,V: $i] :
      ( ~ ( sum @ X @ Y @ U )
      | ~ ( sum @ X @ Y @ V )
      | ( U = V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).

thf(3,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/sandbox/benchmark/theBenchmark.p',distributivity4) ).

thf(4,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/sandbox/benchmark/theBenchmark.p',distributivity3) ).

thf(5,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/sandbox/benchmark/theBenchmark.p',distributivity2) ).

thf(6,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/sandbox/benchmark/theBenchmark.p',distributivity1) ).

thf(7,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/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).

thf(8,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/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).

thf(9,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( sum @ X @ Y @ Z )
      | ( sum @ Y @ X @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).

thf(11,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/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).

thf(12,axiom,
    ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).

thf(13,axiom,
    ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

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

thf(15,axiom,
    ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).

thf(16,axiom,
    ! [X: $i] : ( sum @ X @ additive_identity @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).

thf(17,axiom,
    ! [X: $i] : ( sum @ additive_identity @ X @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).

thf(18,axiom,
    sum @ b @ c @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c_is_d) ).

thf(19,axiom,
    sum @ a @ c @ d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_plus_c_is_d) ).

thf(20,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(21,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[20]) ).

thf(22,negated_conjecture,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_b) ).

thf(23,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[21]) ).

thf(24,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)],[1]) ).

thf(25,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)],[2]) ).

thf(26,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)],[3]) ).

thf(27,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)],[4]) ).

thf(28,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)],[5]) ).

thf(29,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)],[6]) ).

thf(30,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)],[7]) ).

thf(31,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)],[8]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ Z )
          | ( sum @ Y @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(33,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)],[10]) ).

thf(34,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)],[11]) ).

thf(35,plain,
    ( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(36,plain,
    ( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(37,plain,
    ( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(38,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(39,plain,
    ( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(40,plain,
    ( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(41,plain,
    ( ( sum @ b @ c @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(42,plain,
    ( ( sum @ a @ c @ d )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(43,plain,
    ( ( ( a != b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(44,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[23]) ).

thf(45,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)],[24]) ).

thf(46,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)],[25]) ).

thf(47,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)],[26]) ).

thf(48,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)],[27]) ).

thf(49,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)],[28]) ).

thf(50,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)],[29]) ).

thf(51,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)],[30]) ).

thf(52,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)],[31]) ).

thf(53,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)],[33]) ).

thf(54,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)],[34]) ).

thf(55,plain,
    ( ( ( a != b ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[43]) ).

thf(56,plain,
    ( ( ( a != b ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(57,plain,
    ( ( sum @ a @ c @ d )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(58,plain,
    ( ( sum @ b @ c @ d )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(59,plain,
    ( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(60,plain,
    ( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(61,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(62,plain,
    ( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(63,plain,
    ( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(64,plain,
    ( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(65,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)],[54]) ).

thf(66,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)],[53]) ).

thf(67,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( sum @ X @ Y @ Z )
          | ( sum @ Y @ X @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(68,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)],[52]) ).

thf(69,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)],[51]) ).

thf(70,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)],[50]) ).

thf(71,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)],[49]) ).

thf(72,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)],[48]) ).

thf(73,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)],[47]) ).

thf(74,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( sum @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( sum @ X @ Y @ V )
              | ( U = V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(75,plain,
    ( ( ! [X: $i,Y: $i,U: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ! [V: $i] :
              ( ~ ( product @ X @ Y @ V )
              | ( U = V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(76,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(77,plain,
    ( ( a = b )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(78,plain,
    ! [SV1: $i] :
      ( ( sum @ additive_identity @ SV1 @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(79,plain,
    ! [SV2: $i] :
      ( ( sum @ SV2 @ additive_identity @ SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(80,plain,
    ! [SV3: $i] :
      ( ( ! [SY71: $i] : ( product @ SV3 @ SY71 @ ( multiply @ SV3 @ SY71 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(81,plain,
    ! [SV4: $i] :
      ( ( ! [SY72: $i] : ( sum @ SV4 @ SY72 @ ( add @ SV4 @ SY72 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(82,plain,
    ! [SV5: $i] :
      ( ( sum @ ( additive_inverse @ SV5 ) @ SV5 @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(83,plain,
    ! [SV6: $i] :
      ( ( sum @ SV6 @ ( additive_inverse @ SV6 ) @ additive_identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(84,plain,
    ! [SV7: $i] :
      ( ( ! [SY73: $i,SY74: $i,SY75: $i] :
            ( ~ ( sum @ SV7 @ SY73 @ SY74 )
            | ! [SY76: $i] :
                ( ~ ( sum @ SY73 @ SY75 @ SY76 )
                | ! [SY77: $i] :
                    ( ~ ( sum @ SY74 @ SY75 @ SY77 )
                    | ( sum @ SV7 @ SY76 @ SY77 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(85,plain,
    ! [SV8: $i] :
      ( ( ! [SY78: $i,SY79: $i,SY80: $i] :
            ( ~ ( sum @ SV8 @ SY78 @ SY79 )
            | ! [SY81: $i] :
                ( ~ ( sum @ SY78 @ SY80 @ SY81 )
                | ! [SY82: $i] :
                    ( ~ ( sum @ SV8 @ SY81 @ SY82 )
                    | ( sum @ SY79 @ SY80 @ SY82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(86,plain,
    ! [SV9: $i] :
      ( ( ! [SY83: $i,SY84: $i] :
            ( ~ ( sum @ SV9 @ SY83 @ SY84 )
            | ( sum @ SY83 @ SV9 @ SY84 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(87,plain,
    ! [SV10: $i] :
      ( ( ! [SY85: $i,SY86: $i,SY87: $i] :
            ( ~ ( product @ SV10 @ SY85 @ SY86 )
            | ! [SY88: $i] :
                ( ~ ( product @ SY85 @ SY87 @ SY88 )
                | ! [SY89: $i] :
                    ( ~ ( product @ SY86 @ SY87 @ SY89 )
                    | ( product @ SV10 @ SY88 @ SY89 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(88,plain,
    ! [SV11: $i] :
      ( ( ! [SY90: $i,SY91: $i,SY92: $i] :
            ( ~ ( product @ SV11 @ SY90 @ SY91 )
            | ! [SY93: $i] :
                ( ~ ( product @ SY90 @ SY92 @ SY93 )
                | ! [SY94: $i] :
                    ( ~ ( product @ SV11 @ SY93 @ SY94 )
                    | ( product @ SY91 @ SY92 @ SY94 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(89,plain,
    ! [SV12: $i] :
      ( ( ! [SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
            ( ~ ( product @ SV12 @ SY95 @ SY96 )
            | ~ ( product @ SV12 @ SY97 @ SY98 )
            | ! [SY99: $i] :
                ( ~ ( sum @ SY95 @ SY97 @ SY99 )
                | ! [SY100: $i] :
                    ( ~ ( product @ SV12 @ SY99 @ SY100 )
                    | ( sum @ SY96 @ SY98 @ SY100 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(90,plain,
    ! [SV13: $i] :
      ( ( ! [SY101: $i,SY102: $i,SY103: $i,SY104: $i] :
            ( ~ ( product @ SV13 @ SY101 @ SY102 )
            | ~ ( product @ SV13 @ SY103 @ SY104 )
            | ! [SY105: $i] :
                ( ~ ( sum @ SY101 @ SY103 @ SY105 )
                | ! [SY106: $i] :
                    ( ~ ( sum @ SY102 @ SY104 @ SY106 )
                    | ( product @ SV13 @ SY105 @ SY106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(91,plain,
    ! [SV14: $i] :
      ( ( ! [SY107: $i,SY108: $i,SY109: $i,SY110: $i] :
            ( ~ ( product @ SV14 @ SY107 @ SY108 )
            | ~ ( product @ SY109 @ SY107 @ SY110 )
            | ! [SY111: $i] :
                ( ~ ( sum @ SV14 @ SY109 @ SY111 )
                | ! [V4: $i] :
                    ( ~ ( product @ SY111 @ SY107 @ V4 )
                    | ( sum @ SY108 @ SY110 @ V4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(92,plain,
    ! [SV15: $i] :
      ( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i] :
            ( ~ ( product @ SV15 @ SY113 @ SY114 )
            | ~ ( product @ SY115 @ SY113 @ SY116 )
            | ! [SY117: $i] :
                ( ~ ( sum @ SV15 @ SY115 @ SY117 )
                | ! [V4: $i] :
                    ( ~ ( sum @ SY114 @ SY116 @ V4 )
                    | ( product @ SY117 @ SY113 @ V4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(93,plain,
    ! [SV16: $i] :
      ( ( ! [SY119: $i,SY120: $i] :
            ( ~ ( sum @ SV16 @ SY119 @ SY120 )
            | ! [SY121: $i] :
                ( ~ ( sum @ SV16 @ SY119 @ SY121 )
                | ( SY120 = SY121 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(94,plain,
    ! [SV17: $i] :
      ( ( ! [SY122: $i,SY123: $i] :
            ( ~ ( product @ SV17 @ SY122 @ SY123 )
            | ! [SY124: $i] :
                ( ~ ( product @ SV17 @ SY122 @ SY124 )
                | ( SY123 = SY124 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(95,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(96,plain,
    ! [SV18: $i,SV3: $i] :
      ( ( product @ SV3 @ SV18 @ ( multiply @ SV3 @ SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(97,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( sum @ SV4 @ SV19 @ ( add @ SV4 @ SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(98,plain,
    ! [SV20: $i,SV7: $i] :
      ( ( ! [SY125: $i,SY126: $i] :
            ( ~ ( sum @ SV7 @ SV20 @ SY125 )
            | ! [SY127: $i] :
                ( ~ ( sum @ SV20 @ SY126 @ SY127 )
                | ! [SY77: $i] :
                    ( ~ ( sum @ SY125 @ SY126 @ SY77 )
                    | ( sum @ SV7 @ SY127 @ SY77 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(99,plain,
    ! [SV21: $i,SV8: $i] :
      ( ( ! [SY129: $i,SY130: $i] :
            ( ~ ( sum @ SV8 @ SV21 @ SY129 )
            | ! [SY131: $i] :
                ( ~ ( sum @ SV21 @ SY130 @ SY131 )
                | ! [SY82: $i] :
                    ( ~ ( sum @ SV8 @ SY131 @ SY82 )
                    | ( sum @ SY129 @ SY130 @ SY82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(100,plain,
    ! [SV22: $i,SV9: $i] :
      ( ( ! [SY133: $i] :
            ( ~ ( sum @ SV9 @ SV22 @ SY133 )
            | ( sum @ SV22 @ SV9 @ SY133 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(101,plain,
    ! [SV23: $i,SV10: $i] :
      ( ( ! [SY134: $i,SY135: $i] :
            ( ~ ( product @ SV10 @ SV23 @ SY134 )
            | ! [SY136: $i] :
                ( ~ ( product @ SV23 @ SY135 @ SY136 )
                | ! [SY89: $i] :
                    ( ~ ( product @ SY134 @ SY135 @ SY89 )
                    | ( product @ SV10 @ SY136 @ SY89 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(102,plain,
    ! [SV24: $i,SV11: $i] :
      ( ( ! [SY138: $i,SY139: $i] :
            ( ~ ( product @ SV11 @ SV24 @ SY138 )
            | ! [SY140: $i] :
                ( ~ ( product @ SV24 @ SY139 @ SY140 )
                | ! [SY94: $i] :
                    ( ~ ( product @ SV11 @ SY140 @ SY94 )
                    | ( product @ SY138 @ SY139 @ SY94 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(103,plain,
    ! [SV25: $i,SV12: $i] :
      ( ( ! [SY142: $i,SY143: $i,SY144: $i] :
            ( ~ ( product @ SV12 @ SV25 @ SY142 )
            | ~ ( product @ SV12 @ SY143 @ SY144 )
            | ! [SY145: $i] :
                ( ~ ( sum @ SV25 @ SY143 @ SY145 )
                | ! [SY100: $i] :
                    ( ~ ( product @ SV12 @ SY145 @ SY100 )
                    | ( sum @ SY142 @ SY144 @ SY100 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(104,plain,
    ! [SV26: $i,SV13: $i] :
      ( ( ! [SY147: $i,SY148: $i,SY149: $i] :
            ( ~ ( product @ SV13 @ SV26 @ SY147 )
            | ~ ( product @ SV13 @ SY148 @ SY149 )
            | ! [SY150: $i] :
                ( ~ ( sum @ SV26 @ SY148 @ SY150 )
                | ! [SY106: $i] :
                    ( ~ ( sum @ SY147 @ SY149 @ SY106 )
                    | ( product @ SV13 @ SY150 @ SY106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(105,plain,
    ! [SV27: $i,SV14: $i] :
      ( ( ! [SY152: $i,SY153: $i,SY154: $i] :
            ( ~ ( product @ SV14 @ SV27 @ SY152 )
            | ~ ( product @ SY153 @ SV27 @ SY154 )
            | ! [SY155: $i] :
                ( ~ ( sum @ SV14 @ SY153 @ SY155 )
                | ! [SY156: $i] :
                    ( ~ ( product @ SY155 @ SV27 @ SY156 )
                    | ( sum @ SY152 @ SY154 @ SY156 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(106,plain,
    ! [SV28: $i,SV15: $i] :
      ( ( ! [SY157: $i,SY158: $i,SY159: $i] :
            ( ~ ( product @ SV15 @ SV28 @ SY157 )
            | ~ ( product @ SY158 @ SV28 @ SY159 )
            | ! [SY160: $i] :
                ( ~ ( sum @ SV15 @ SY158 @ SY160 )
                | ! [SY161: $i] :
                    ( ~ ( sum @ SY157 @ SY159 @ SY161 )
                    | ( product @ SY160 @ SV28 @ SY161 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(107,plain,
    ! [SV29: $i,SV16: $i] :
      ( ( ! [SY162: $i] :
            ( ~ ( sum @ SV16 @ SV29 @ SY162 )
            | ! [SY163: $i] :
                ( ~ ( sum @ SV16 @ SV29 @ SY163 )
                | ( SY162 = SY163 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(108,plain,
    ! [SV30: $i,SV17: $i] :
      ( ( ! [SY164: $i] :
            ( ~ ( product @ SV17 @ SV30 @ SY164 )
            | ! [SY165: $i] :
                ( ~ ( product @ SV17 @ SV30 @ SY165 )
                | ( SY164 = SY165 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(109,plain,
    ! [SV31: $i,SV20: $i,SV7: $i] :
      ( ( ! [SY166: $i] :
            ( ~ ( sum @ SV7 @ SV20 @ SV31 )
            | ! [SY167: $i] :
                ( ~ ( sum @ SV20 @ SY166 @ SY167 )
                | ! [SY168: $i] :
                    ( ~ ( sum @ SV31 @ SY166 @ SY168 )
                    | ( sum @ SV7 @ SY167 @ SY168 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(110,plain,
    ! [SV32: $i,SV21: $i,SV8: $i] :
      ( ( ! [SY169: $i] :
            ( ~ ( sum @ SV8 @ SV21 @ SV32 )
            | ! [SY170: $i] :
                ( ~ ( sum @ SV21 @ SY169 @ SY170 )
                | ! [SY171: $i] :
                    ( ~ ( sum @ SV8 @ SY170 @ SY171 )
                    | ( sum @ SV32 @ SY169 @ SY171 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(111,plain,
    ! [SV33: $i,SV22: $i,SV9: $i] :
      ( ( ~ ( sum @ SV9 @ SV22 @ SV33 )
        | ( sum @ SV22 @ SV9 @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(112,plain,
    ! [SV34: $i,SV23: $i,SV10: $i] :
      ( ( ! [SY172: $i] :
            ( ~ ( product @ SV10 @ SV23 @ SV34 )
            | ! [SY173: $i] :
                ( ~ ( product @ SV23 @ SY172 @ SY173 )
                | ! [SY174: $i] :
                    ( ~ ( product @ SV34 @ SY172 @ SY174 )
                    | ( product @ SV10 @ SY173 @ SY174 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(113,plain,
    ! [SV35: $i,SV24: $i,SV11: $i] :
      ( ( ! [SY175: $i] :
            ( ~ ( product @ SV11 @ SV24 @ SV35 )
            | ! [SY176: $i] :
                ( ~ ( product @ SV24 @ SY175 @ SY176 )
                | ! [SY177: $i] :
                    ( ~ ( product @ SV11 @ SY176 @ SY177 )
                    | ( product @ SV35 @ SY175 @ SY177 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(114,plain,
    ! [SV36: $i,SV25: $i,SV12: $i] :
      ( ( ! [SY178: $i,SY179: $i] :
            ( ~ ( product @ SV12 @ SV25 @ SV36 )
            | ~ ( product @ SV12 @ SY178 @ SY179 )
            | ! [SY180: $i] :
                ( ~ ( sum @ SV25 @ SY178 @ SY180 )
                | ! [SY181: $i] :
                    ( ~ ( product @ SV12 @ SY180 @ SY181 )
                    | ( sum @ SV36 @ SY179 @ SY181 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(115,plain,
    ! [SV37: $i,SV26: $i,SV13: $i] :
      ( ( ! [SY182: $i,SY183: $i] :
            ( ~ ( product @ SV13 @ SV26 @ SV37 )
            | ~ ( product @ SV13 @ SY182 @ SY183 )
            | ! [SY184: $i] :
                ( ~ ( sum @ SV26 @ SY182 @ SY184 )
                | ! [SY185: $i] :
                    ( ~ ( sum @ SV37 @ SY183 @ SY185 )
                    | ( product @ SV13 @ SY184 @ SY185 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[104]) ).

thf(116,plain,
    ! [SV38: $i,SV27: $i,SV14: $i] :
      ( ( ! [SY186: $i,SY187: $i] :
            ( ~ ( product @ SV14 @ SV27 @ SV38 )
            | ~ ( product @ SY186 @ SV27 @ SY187 )
            | ! [SY188: $i] :
                ( ~ ( sum @ SV14 @ SY186 @ SY188 )
                | ! [SY189: $i] :
                    ( ~ ( product @ SY188 @ SV27 @ SY189 )
                    | ( sum @ SV38 @ SY187 @ SY189 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(117,plain,
    ! [SV39: $i,SV28: $i,SV15: $i] :
      ( ( ! [SY190: $i,SY191: $i] :
            ( ~ ( product @ SV15 @ SV28 @ SV39 )
            | ~ ( product @ SY190 @ SV28 @ SY191 )
            | ! [SY192: $i] :
                ( ~ ( sum @ SV15 @ SY190 @ SY192 )
                | ! [SY193: $i] :
                    ( ~ ( sum @ SV39 @ SY191 @ SY193 )
                    | ( product @ SY192 @ SV28 @ SY193 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(118,plain,
    ! [SV40: $i,SV29: $i,SV16: $i] :
      ( ( ~ ( sum @ SV16 @ SV29 @ SV40 )
        | ! [SY194: $i] :
            ( ~ ( sum @ SV16 @ SV29 @ SY194 )
            | ( SV40 = SY194 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(119,plain,
    ! [SV41: $i,SV30: $i,SV17: $i] :
      ( ( ~ ( product @ SV17 @ SV30 @ SV41 )
        | ! [SY195: $i] :
            ( ~ ( product @ SV17 @ SV30 @ SY195 )
            | ( SV41 = SY195 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(120,plain,
    ! [SV42: $i,SV31: $i,SV20: $i,SV7: $i] :
      ( ( ~ ( sum @ SV7 @ SV20 @ SV31 )
        | ! [SY196: $i] :
            ( ~ ( sum @ SV20 @ SV42 @ SY196 )
            | ! [SY197: $i] :
                ( ~ ( sum @ SV31 @ SV42 @ SY197 )
                | ( sum @ SV7 @ SY196 @ SY197 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(121,plain,
    ! [SV43: $i,SV32: $i,SV21: $i,SV8: $i] :
      ( ( ~ ( sum @ SV8 @ SV21 @ SV32 )
        | ! [SY198: $i] :
            ( ~ ( sum @ SV21 @ SV43 @ SY198 )
            | ! [SY199: $i] :
                ( ~ ( sum @ SV8 @ SY198 @ SY199 )
                | ( sum @ SV32 @ SV43 @ SY199 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(122,plain,
    ! [SV33: $i,SV22: $i,SV9: $i] :
      ( ( ( ~ ( sum @ SV9 @ SV22 @ SV33 ) )
        = $true )
      | ( ( sum @ SV22 @ SV9 @ SV33 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[111]) ).

thf(123,plain,
    ! [SV44: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ~ ( product @ SV10 @ SV23 @ SV34 )
        | ! [SY200: $i] :
            ( ~ ( product @ SV23 @ SV44 @ SY200 )
            | ! [SY201: $i] :
                ( ~ ( product @ SV34 @ SV44 @ SY201 )
                | ( product @ SV10 @ SY200 @ SY201 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(124,plain,
    ! [SV45: $i,SV35: $i,SV24: $i,SV11: $i] :
      ( ( ~ ( product @ SV11 @ SV24 @ SV35 )
        | ! [SY202: $i] :
            ( ~ ( product @ SV24 @ SV45 @ SY202 )
            | ! [SY203: $i] :
                ( ~ ( product @ SV11 @ SY202 @ SY203 )
                | ( product @ SV35 @ SV45 @ SY203 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(125,plain,
    ! [SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
      ( ( ! [SY204: $i] :
            ( ~ ( product @ SV12 @ SV25 @ SV36 )
            | ~ ( product @ SV12 @ SV46 @ SY204 )
            | ! [SY205: $i] :
                ( ~ ( sum @ SV25 @ SV46 @ SY205 )
                | ! [SY181: $i] :
                    ( ~ ( product @ SV12 @ SY205 @ SY181 )
                    | ( sum @ SV36 @ SY204 @ SY181 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(126,plain,
    ! [SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
      ( ( ! [SY207: $i] :
            ( ~ ( product @ SV13 @ SV26 @ SV37 )
            | ~ ( product @ SV13 @ SV47 @ SY207 )
            | ! [SY208: $i] :
                ( ~ ( sum @ SV26 @ SV47 @ SY208 )
                | ! [SY185: $i] :
                    ( ~ ( sum @ SV37 @ SY207 @ SY185 )
                    | ( product @ SV13 @ SY208 @ SY185 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(127,plain,
    ! [SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
      ( ( ! [SY210: $i] :
            ( ~ ( product @ SV14 @ SV27 @ SV38 )
            | ~ ( product @ SV48 @ SV27 @ SY210 )
            | ! [SY211: $i] :
                ( ~ ( sum @ SV14 @ SV48 @ SY211 )
                | ! [SY189: $i] :
                    ( ~ ( product @ SY211 @ SV27 @ SY189 )
                    | ( sum @ SV38 @ SY210 @ SY189 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(128,plain,
    ! [SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
      ( ( ! [SY213: $i] :
            ( ~ ( product @ SV15 @ SV28 @ SV39 )
            | ~ ( product @ SV49 @ SV28 @ SY213 )
            | ! [SY214: $i] :
                ( ~ ( sum @ SV15 @ SV49 @ SY214 )
                | ! [SY193: $i] :
                    ( ~ ( sum @ SV39 @ SY213 @ SY193 )
                    | ( product @ SY214 @ SV28 @ SY193 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(129,plain,
    ! [SV40: $i,SV29: $i,SV16: $i] :
      ( ( ( ~ ( sum @ SV16 @ SV29 @ SV40 ) )
        = $true )
      | ( ( ! [SY194: $i] :
              ( ~ ( sum @ SV16 @ SV29 @ SY194 )
              | ( SV40 = SY194 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[118]) ).

thf(130,plain,
    ! [SV41: $i,SV30: $i,SV17: $i] :
      ( ( ( ~ ( product @ SV17 @ SV30 @ SV41 ) )
        = $true )
      | ( ( ! [SY195: $i] :
              ( ~ ( product @ SV17 @ SV30 @ SY195 )
              | ( SV41 = SY195 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[119]) ).

thf(131,plain,
    ! [SV42: $i,SV31: $i,SV20: $i,SV7: $i] :
      ( ( ( ~ ( sum @ SV7 @ SV20 @ SV31 ) )
        = $true )
      | ( ( ! [SY196: $i] :
              ( ~ ( sum @ SV20 @ SV42 @ SY196 )
              | ! [SY197: $i] :
                  ( ~ ( sum @ SV31 @ SV42 @ SY197 )
                  | ( sum @ SV7 @ SY196 @ SY197 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[120]) ).

thf(132,plain,
    ! [SV43: $i,SV32: $i,SV21: $i,SV8: $i] :
      ( ( ( ~ ( sum @ SV8 @ SV21 @ SV32 ) )
        = $true )
      | ( ( ! [SY198: $i] :
              ( ~ ( sum @ SV21 @ SV43 @ SY198 )
              | ! [SY199: $i] :
                  ( ~ ( sum @ SV8 @ SY198 @ SY199 )
                  | ( sum @ SV32 @ SV43 @ SY199 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[121]) ).

thf(133,plain,
    ! [SV33: $i,SV22: $i,SV9: $i] :
      ( ( ( sum @ SV9 @ SV22 @ SV33 )
        = $false )
      | ( ( sum @ SV22 @ SV9 @ SV33 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[122]) ).

thf(134,plain,
    ! [SV44: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ( ~ ( product @ SV10 @ SV23 @ SV34 ) )
        = $true )
      | ( ( ! [SY200: $i] :
              ( ~ ( product @ SV23 @ SV44 @ SY200 )
              | ! [SY201: $i] :
                  ( ~ ( product @ SV34 @ SV44 @ SY201 )
                  | ( product @ SV10 @ SY200 @ SY201 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[123]) ).

thf(135,plain,
    ! [SV45: $i,SV35: $i,SV24: $i,SV11: $i] :
      ( ( ( ~ ( product @ SV11 @ SV24 @ SV35 ) )
        = $true )
      | ( ( ! [SY202: $i] :
              ( ~ ( product @ SV24 @ SV45 @ SY202 )
              | ! [SY203: $i] :
                  ( ~ ( product @ SV11 @ SY202 @ SY203 )
                  | ( product @ SV35 @ SV45 @ SY203 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[124]) ).

thf(136,plain,
    ! [SV50: $i,SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
      ( ( ~ ( product @ SV12 @ SV25 @ SV36 )
        | ~ ( product @ SV12 @ SV46 @ SV50 )
        | ! [SY216: $i] :
            ( ~ ( sum @ SV25 @ SV46 @ SY216 )
            | ! [SY217: $i] :
                ( ~ ( product @ SV12 @ SY216 @ SY217 )
                | ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(137,plain,
    ! [SV51: $i,SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
      ( ( ~ ( product @ SV13 @ SV26 @ SV37 )
        | ~ ( product @ SV13 @ SV47 @ SV51 )
        | ! [SY218: $i] :
            ( ~ ( sum @ SV26 @ SV47 @ SY218 )
            | ! [SY219: $i] :
                ( ~ ( sum @ SV37 @ SV51 @ SY219 )
                | ( product @ SV13 @ SY218 @ SY219 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(138,plain,
    ! [SV52: $i,SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
      ( ( ~ ( product @ SV14 @ SV27 @ SV38 )
        | ~ ( product @ SV48 @ SV27 @ SV52 )
        | ! [SY220: $i] :
            ( ~ ( sum @ SV14 @ SV48 @ SY220 )
            | ! [SY221: $i] :
                ( ~ ( product @ SY220 @ SV27 @ SY221 )
                | ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(139,plain,
    ! [SV53: $i,SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
      ( ( ~ ( product @ SV15 @ SV28 @ SV39 )
        | ~ ( product @ SV49 @ SV28 @ SV53 )
        | ! [SY222: $i] :
            ( ~ ( sum @ SV15 @ SV49 @ SY222 )
            | ! [SY223: $i] :
                ( ~ ( sum @ SV39 @ SV53 @ SY223 )
                | ( product @ SY222 @ SV28 @ SY223 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(140,plain,
    ! [SV40: $i,SV29: $i,SV16: $i] :
      ( ( ( sum @ SV16 @ SV29 @ SV40 )
        = $false )
      | ( ( ! [SY194: $i] :
              ( ~ ( sum @ SV16 @ SV29 @ SY194 )
              | ( SV40 = SY194 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[129]) ).

thf(141,plain,
    ! [SV41: $i,SV30: $i,SV17: $i] :
      ( ( ( product @ SV17 @ SV30 @ SV41 )
        = $false )
      | ( ( ! [SY195: $i] :
              ( ~ ( product @ SV17 @ SV30 @ SY195 )
              | ( SV41 = SY195 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[130]) ).

thf(142,plain,
    ! [SV42: $i,SV31: $i,SV20: $i,SV7: $i] :
      ( ( ( sum @ SV7 @ SV20 @ SV31 )
        = $false )
      | ( ( ! [SY196: $i] :
              ( ~ ( sum @ SV20 @ SV42 @ SY196 )
              | ! [SY197: $i] :
                  ( ~ ( sum @ SV31 @ SV42 @ SY197 )
                  | ( sum @ SV7 @ SY196 @ SY197 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[131]) ).

thf(143,plain,
    ! [SV43: $i,SV32: $i,SV21: $i,SV8: $i] :
      ( ( ( sum @ SV8 @ SV21 @ SV32 )
        = $false )
      | ( ( ! [SY198: $i] :
              ( ~ ( sum @ SV21 @ SV43 @ SY198 )
              | ! [SY199: $i] :
                  ( ~ ( sum @ SV8 @ SY198 @ SY199 )
                  | ( sum @ SV32 @ SV43 @ SY199 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[132]) ).

thf(144,plain,
    ! [SV44: $i,SV34: $i,SV23: $i,SV10: $i] :
      ( ( ( product @ SV10 @ SV23 @ SV34 )
        = $false )
      | ( ( ! [SY200: $i] :
              ( ~ ( product @ SV23 @ SV44 @ SY200 )
              | ! [SY201: $i] :
                  ( ~ ( product @ SV34 @ SV44 @ SY201 )
                  | ( product @ SV10 @ SY200 @ SY201 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[134]) ).

thf(145,plain,
    ! [SV45: $i,SV35: $i,SV24: $i,SV11: $i] :
      ( ( ( product @ SV11 @ SV24 @ SV35 )
        = $false )
      | ( ( ! [SY202: $i] :
              ( ~ ( product @ SV24 @ SV45 @ SY202 )
              | ! [SY203: $i] :
                  ( ~ ( product @ SV11 @ SY202 @ SY203 )
                  | ( product @ SV35 @ SV45 @ SY203 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[135]) ).

thf(146,plain,
    ! [SV50: $i,SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV25 @ SV36 ) )
        = $true )
      | ( ( ~ ( product @ SV12 @ SV46 @ SV50 )
          | ! [SY216: $i] :
              ( ~ ( sum @ SV25 @ SV46 @ SY216 )
              | ! [SY217: $i] :
                  ( ~ ( product @ SV12 @ SY216 @ SY217 )
                  | ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[136]) ).

thf(147,plain,
    ! [SV51: $i,SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
      ( ( ( ~ ( product @ SV13 @ SV26 @ SV37 ) )
        = $true )
      | ( ( ~ ( product @ SV13 @ SV47 @ SV51 )
          | ! [SY218: $i] :
              ( ~ ( sum @ SV26 @ SV47 @ SY218 )
              | ! [SY219: $i] :
                  ( ~ ( sum @ SV37 @ SV51 @ SY219 )
                  | ( product @ SV13 @ SY218 @ SY219 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[137]) ).

thf(148,plain,
    ! [SV52: $i,SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
      ( ( ( ~ ( product @ SV14 @ SV27 @ SV38 ) )
        = $true )
      | ( ( ~ ( product @ SV48 @ SV27 @ SV52 )
          | ! [SY220: $i] :
              ( ~ ( sum @ SV14 @ SV48 @ SY220 )
              | ! [SY221: $i] :
                  ( ~ ( product @ SY220 @ SV27 @ SY221 )
                  | ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[138]) ).

thf(149,plain,
    ! [SV53: $i,SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
      ( ( ( ~ ( product @ SV15 @ SV28 @ SV39 ) )
        = $true )
      | ( ( ~ ( product @ SV49 @ SV28 @ SV53 )
          | ! [SY222: $i] :
              ( ~ ( sum @ SV15 @ SV49 @ SY222 )
              | ! [SY223: $i] :
                  ( ~ ( sum @ SV39 @ SV53 @ SY223 )
                  | ( product @ SY222 @ SV28 @ SY223 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[139]) ).

thf(150,plain,
    ! [SV40: $i,SV54: $i,SV29: $i,SV16: $i] :
      ( ( ( ~ ( sum @ SV16 @ SV29 @ SV54 )
          | ( SV40 = SV54 ) )
        = $true )
      | ( ( sum @ SV16 @ SV29 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(151,plain,
    ! [SV41: $i,SV55: $i,SV30: $i,SV17: $i] :
      ( ( ( ~ ( product @ SV17 @ SV30 @ SV55 )
          | ( SV41 = SV55 ) )
        = $true )
      | ( ( product @ SV17 @ SV30 @ SV41 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(152,plain,
    ! [SV7: $i,SV31: $i,SV56: $i,SV42: $i,SV20: $i] :
      ( ( ( ~ ( sum @ SV20 @ SV42 @ SV56 )
          | ! [SY224: $i] :
              ( ~ ( sum @ SV31 @ SV42 @ SY224 )
              | ( sum @ SV7 @ SV56 @ SY224 ) ) )
        = $true )
      | ( ( sum @ SV7 @ SV20 @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(153,plain,
    ! [SV32: $i,SV8: $i,SV57: $i,SV43: $i,SV21: $i] :
      ( ( ( ~ ( sum @ SV21 @ SV43 @ SV57 )
          | ! [SY225: $i] :
              ( ~ ( sum @ SV8 @ SV57 @ SY225 )
              | ( sum @ SV32 @ SV43 @ SY225 ) ) )
        = $true )
      | ( ( sum @ SV8 @ SV21 @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(154,plain,
    ! [SV10: $i,SV34: $i,SV58: $i,SV44: $i,SV23: $i] :
      ( ( ( ~ ( product @ SV23 @ SV44 @ SV58 )
          | ! [SY226: $i] :
              ( ~ ( product @ SV34 @ SV44 @ SY226 )
              | ( product @ SV10 @ SV58 @ SY226 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV23 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(155,plain,
    ! [SV35: $i,SV11: $i,SV59: $i,SV45: $i,SV24: $i] :
      ( ( ( ~ ( product @ SV24 @ SV45 @ SV59 )
          | ! [SY227: $i] :
              ( ~ ( product @ SV11 @ SV59 @ SY227 )
              | ( product @ SV35 @ SV45 @ SY227 ) ) )
        = $true )
      | ( ( product @ SV11 @ SV24 @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(156,plain,
    ! [SV50: $i,SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
      ( ( ( product @ SV12 @ SV25 @ SV36 )
        = $false )
      | ( ( ~ ( product @ SV12 @ SV46 @ SV50 )
          | ! [SY216: $i] :
              ( ~ ( sum @ SV25 @ SV46 @ SY216 )
              | ! [SY217: $i] :
                  ( ~ ( product @ SV12 @ SY216 @ SY217 )
                  | ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[146]) ).

thf(157,plain,
    ! [SV51: $i,SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
      ( ( ( product @ SV13 @ SV26 @ SV37 )
        = $false )
      | ( ( ~ ( product @ SV13 @ SV47 @ SV51 )
          | ! [SY218: $i] :
              ( ~ ( sum @ SV26 @ SV47 @ SY218 )
              | ! [SY219: $i] :
                  ( ~ ( sum @ SV37 @ SV51 @ SY219 )
                  | ( product @ SV13 @ SY218 @ SY219 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[147]) ).

thf(158,plain,
    ! [SV52: $i,SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
      ( ( ( product @ SV14 @ SV27 @ SV38 )
        = $false )
      | ( ( ~ ( product @ SV48 @ SV27 @ SV52 )
          | ! [SY220: $i] :
              ( ~ ( sum @ SV14 @ SV48 @ SY220 )
              | ! [SY221: $i] :
                  ( ~ ( product @ SY220 @ SV27 @ SY221 )
                  | ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(159,plain,
    ! [SV53: $i,SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
      ( ( ( product @ SV15 @ SV28 @ SV39 )
        = $false )
      | ( ( ~ ( product @ SV49 @ SV28 @ SV53 )
          | ! [SY222: $i] :
              ( ~ ( sum @ SV15 @ SV49 @ SY222 )
              | ! [SY223: $i] :
                  ( ~ ( sum @ SV39 @ SV53 @ SY223 )
                  | ( product @ SY222 @ SV28 @ SY223 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(160,plain,
    ! [SV40: $i,SV54: $i,SV29: $i,SV16: $i] :
      ( ( ( ~ ( sum @ SV16 @ SV29 @ SV54 ) )
        = $true )
      | ( ( SV40 = SV54 )
        = $true )
      | ( ( sum @ SV16 @ SV29 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[150]) ).

thf(161,plain,
    ! [SV41: $i,SV55: $i,SV30: $i,SV17: $i] :
      ( ( ( ~ ( product @ SV17 @ SV30 @ SV55 ) )
        = $true )
      | ( ( SV41 = SV55 )
        = $true )
      | ( ( product @ SV17 @ SV30 @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[151]) ).

thf(162,plain,
    ! [SV7: $i,SV31: $i,SV56: $i,SV42: $i,SV20: $i] :
      ( ( ( ~ ( sum @ SV20 @ SV42 @ SV56 ) )
        = $true )
      | ( ( ! [SY224: $i] :
              ( ~ ( sum @ SV31 @ SV42 @ SY224 )
              | ( sum @ SV7 @ SV56 @ SY224 ) ) )
        = $true )
      | ( ( sum @ SV7 @ SV20 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[152]) ).

thf(163,plain,
    ! [SV32: $i,SV8: $i,SV57: $i,SV43: $i,SV21: $i] :
      ( ( ( ~ ( sum @ SV21 @ SV43 @ SV57 ) )
        = $true )
      | ( ( ! [SY225: $i] :
              ( ~ ( sum @ SV8 @ SV57 @ SY225 )
              | ( sum @ SV32 @ SV43 @ SY225 ) ) )
        = $true )
      | ( ( sum @ SV8 @ SV21 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[153]) ).

thf(164,plain,
    ! [SV10: $i,SV34: $i,SV58: $i,SV44: $i,SV23: $i] :
      ( ( ( ~ ( product @ SV23 @ SV44 @ SV58 ) )
        = $true )
      | ( ( ! [SY226: $i] :
              ( ~ ( product @ SV34 @ SV44 @ SY226 )
              | ( product @ SV10 @ SV58 @ SY226 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV23 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[154]) ).

thf(165,plain,
    ! [SV35: $i,SV11: $i,SV59: $i,SV45: $i,SV24: $i] :
      ( ( ( ~ ( product @ SV24 @ SV45 @ SV59 ) )
        = $true )
      | ( ( ! [SY227: $i] :
              ( ~ ( product @ SV11 @ SV59 @ SY227 )
              | ( product @ SV35 @ SV45 @ SY227 ) ) )
        = $true )
      | ( ( product @ SV11 @ SV24 @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[155]) ).

thf(166,plain,
    ! [SV36: $i,SV25: $i,SV50: $i,SV46: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV46 @ SV50 ) )
        = $true )
      | ( ( ! [SY216: $i] :
              ( ~ ( sum @ SV25 @ SV46 @ SY216 )
              | ! [SY217: $i] :
                  ( ~ ( product @ SV12 @ SY216 @ SY217 )
                  | ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
        = $true )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[156]) ).

thf(167,plain,
    ! [SV37: $i,SV26: $i,SV51: $i,SV47: $i,SV13: $i] :
      ( ( ( ~ ( product @ SV13 @ SV47 @ SV51 ) )
        = $true )
      | ( ( ! [SY218: $i] :
              ( ~ ( sum @ SV26 @ SV47 @ SY218 )
              | ! [SY219: $i] :
                  ( ~ ( sum @ SV37 @ SV51 @ SY219 )
                  | ( product @ SV13 @ SY218 @ SY219 ) ) ) )
        = $true )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[157]) ).

thf(168,plain,
    ! [SV38: $i,SV14: $i,SV52: $i,SV27: $i,SV48: $i] :
      ( ( ( ~ ( product @ SV48 @ SV27 @ SV52 ) )
        = $true )
      | ( ( ! [SY220: $i] :
              ( ~ ( sum @ SV14 @ SV48 @ SY220 )
              | ! [SY221: $i] :
                  ( ~ ( product @ SY220 @ SV27 @ SY221 )
                  | ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
        = $true )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[158]) ).

thf(169,plain,
    ! [SV39: $i,SV15: $i,SV53: $i,SV28: $i,SV49: $i] :
      ( ( ( ~ ( product @ SV49 @ SV28 @ SV53 ) )
        = $true )
      | ( ( ! [SY222: $i] :
              ( ~ ( sum @ SV15 @ SV49 @ SY222 )
              | ! [SY223: $i] :
                  ( ~ ( sum @ SV39 @ SV53 @ SY223 )
                  | ( product @ SY222 @ SV28 @ SY223 ) ) ) )
        = $true )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[159]) ).

thf(170,plain,
    ! [SV40: $i,SV54: $i,SV29: $i,SV16: $i] :
      ( ( ( sum @ SV16 @ SV29 @ SV54 )
        = $false )
      | ( ( SV40 = SV54 )
        = $true )
      | ( ( sum @ SV16 @ SV29 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[160]) ).

thf(171,plain,
    ! [SV41: $i,SV55: $i,SV30: $i,SV17: $i] :
      ( ( ( product @ SV17 @ SV30 @ SV55 )
        = $false )
      | ( ( SV41 = SV55 )
        = $true )
      | ( ( product @ SV17 @ SV30 @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(172,plain,
    ! [SV7: $i,SV31: $i,SV56: $i,SV42: $i,SV20: $i] :
      ( ( ( sum @ SV20 @ SV42 @ SV56 )
        = $false )
      | ( ( ! [SY224: $i] :
              ( ~ ( sum @ SV31 @ SV42 @ SY224 )
              | ( sum @ SV7 @ SV56 @ SY224 ) ) )
        = $true )
      | ( ( sum @ SV7 @ SV20 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(173,plain,
    ! [SV32: $i,SV8: $i,SV57: $i,SV43: $i,SV21: $i] :
      ( ( ( sum @ SV21 @ SV43 @ SV57 )
        = $false )
      | ( ( ! [SY225: $i] :
              ( ~ ( sum @ SV8 @ SV57 @ SY225 )
              | ( sum @ SV32 @ SV43 @ SY225 ) ) )
        = $true )
      | ( ( sum @ SV8 @ SV21 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(174,plain,
    ! [SV10: $i,SV34: $i,SV58: $i,SV44: $i,SV23: $i] :
      ( ( ( product @ SV23 @ SV44 @ SV58 )
        = $false )
      | ( ( ! [SY226: $i] :
              ( ~ ( product @ SV34 @ SV44 @ SY226 )
              | ( product @ SV10 @ SV58 @ SY226 ) ) )
        = $true )
      | ( ( product @ SV10 @ SV23 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[164]) ).

thf(175,plain,
    ! [SV35: $i,SV11: $i,SV59: $i,SV45: $i,SV24: $i] :
      ( ( ( product @ SV24 @ SV45 @ SV59 )
        = $false )
      | ( ( ! [SY227: $i] :
              ( ~ ( product @ SV11 @ SV59 @ SY227 )
              | ( product @ SV35 @ SV45 @ SY227 ) ) )
        = $true )
      | ( ( product @ SV11 @ SV24 @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[165]) ).

thf(176,plain,
    ! [SV36: $i,SV25: $i,SV50: $i,SV46: $i,SV12: $i] :
      ( ( ( product @ SV12 @ SV46 @ SV50 )
        = $false )
      | ( ( ! [SY216: $i] :
              ( ~ ( sum @ SV25 @ SV46 @ SY216 )
              | ! [SY217: $i] :
                  ( ~ ( product @ SV12 @ SY216 @ SY217 )
                  | ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
        = $true )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[166]) ).

thf(177,plain,
    ! [SV37: $i,SV26: $i,SV51: $i,SV47: $i,SV13: $i] :
      ( ( ( product @ SV13 @ SV47 @ SV51 )
        = $false )
      | ( ( ! [SY218: $i] :
              ( ~ ( sum @ SV26 @ SV47 @ SY218 )
              | ! [SY219: $i] :
                  ( ~ ( sum @ SV37 @ SV51 @ SY219 )
                  | ( product @ SV13 @ SY218 @ SY219 ) ) ) )
        = $true )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[167]) ).

thf(178,plain,
    ! [SV38: $i,SV14: $i,SV52: $i,SV27: $i,SV48: $i] :
      ( ( ( product @ SV48 @ SV27 @ SV52 )
        = $false )
      | ( ( ! [SY220: $i] :
              ( ~ ( sum @ SV14 @ SV48 @ SY220 )
              | ! [SY221: $i] :
                  ( ~ ( product @ SY220 @ SV27 @ SY221 )
                  | ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
        = $true )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[168]) ).

thf(179,plain,
    ! [SV39: $i,SV15: $i,SV53: $i,SV28: $i,SV49: $i] :
      ( ( ( product @ SV49 @ SV28 @ SV53 )
        = $false )
      | ( ( ! [SY222: $i] :
              ( ~ ( sum @ SV15 @ SV49 @ SY222 )
              | ! [SY223: $i] :
                  ( ~ ( sum @ SV39 @ SV53 @ SY223 )
                  | ( product @ SY222 @ SV28 @ SY223 ) ) ) )
        = $true )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[169]) ).

thf(180,plain,
    ! [SV20: $i,SV56: $i,SV7: $i,SV60: $i,SV42: $i,SV31: $i] :
      ( ( ( ~ ( sum @ SV31 @ SV42 @ SV60 )
          | ( sum @ SV7 @ SV56 @ SV60 ) )
        = $true )
      | ( ( sum @ SV20 @ SV42 @ SV56 )
        = $false )
      | ( ( sum @ SV7 @ SV20 @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(181,plain,
    ! [SV21: $i,SV43: $i,SV32: $i,SV61: $i,SV57: $i,SV8: $i] :
      ( ( ( ~ ( sum @ SV8 @ SV57 @ SV61 )
          | ( sum @ SV32 @ SV43 @ SV61 ) )
        = $true )
      | ( ( sum @ SV21 @ SV43 @ SV57 )
        = $false )
      | ( ( sum @ SV8 @ SV21 @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[173]) ).

thf(182,plain,
    ! [SV23: $i,SV58: $i,SV10: $i,SV62: $i,SV44: $i,SV34: $i] :
      ( ( ( ~ ( product @ SV34 @ SV44 @ SV62 )
          | ( product @ SV10 @ SV58 @ SV62 ) )
        = $true )
      | ( ( product @ SV23 @ SV44 @ SV58 )
        = $false )
      | ( ( product @ SV10 @ SV23 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[174]) ).

thf(183,plain,
    ! [SV24: $i,SV45: $i,SV35: $i,SV63: $i,SV59: $i,SV11: $i] :
      ( ( ( ~ ( product @ SV11 @ SV59 @ SV63 )
          | ( product @ SV35 @ SV45 @ SV63 ) )
        = $true )
      | ( ( product @ SV24 @ SV45 @ SV59 )
        = $false )
      | ( ( product @ SV11 @ SV24 @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[175]) ).

thf(184,plain,
    ! [SV50: $i,SV36: $i,SV12: $i,SV64: $i,SV46: $i,SV25: $i] :
      ( ( ( ~ ( sum @ SV25 @ SV46 @ SV64 )
          | ! [SY228: $i] :
              ( ~ ( product @ SV12 @ SV64 @ SY228 )
              | ( sum @ SV36 @ SV50 @ SY228 ) ) )
        = $true )
      | ( ( product @ SV12 @ SV46 @ SV50 )
        = $false )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[176]) ).

thf(185,plain,
    ! [SV13: $i,SV51: $i,SV37: $i,SV65: $i,SV47: $i,SV26: $i] :
      ( ( ( ~ ( sum @ SV26 @ SV47 @ SV65 )
          | ! [SY229: $i] :
              ( ~ ( sum @ SV37 @ SV51 @ SY229 )
              | ( product @ SV13 @ SV65 @ SY229 ) ) )
        = $true )
      | ( ( product @ SV13 @ SV47 @ SV51 )
        = $false )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[177]) ).

thf(186,plain,
    ! [SV52: $i,SV38: $i,SV27: $i,SV66: $i,SV48: $i,SV14: $i] :
      ( ( ( ~ ( sum @ SV14 @ SV48 @ SV66 )
          | ! [SY230: $i] :
              ( ~ ( product @ SV66 @ SV27 @ SY230 )
              | ( sum @ SV38 @ SV52 @ SY230 ) ) )
        = $true )
      | ( ( product @ SV48 @ SV27 @ SV52 )
        = $false )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[178]) ).

thf(187,plain,
    ! [SV28: $i,SV53: $i,SV39: $i,SV67: $i,SV49: $i,SV15: $i] :
      ( ( ( ~ ( sum @ SV15 @ SV49 @ SV67 )
          | ! [SY231: $i] :
              ( ~ ( sum @ SV39 @ SV53 @ SY231 )
              | ( product @ SV67 @ SV28 @ SY231 ) ) )
        = $true )
      | ( ( product @ SV49 @ SV28 @ SV53 )
        = $false )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[179]) ).

thf(188,plain,
    ! [SV20: $i,SV56: $i,SV7: $i,SV60: $i,SV42: $i,SV31: $i] :
      ( ( ( ~ ( sum @ SV31 @ SV42 @ SV60 ) )
        = $true )
      | ( ( sum @ SV7 @ SV56 @ SV60 )
        = $true )
      | ( ( sum @ SV20 @ SV42 @ SV56 )
        = $false )
      | ( ( sum @ SV7 @ SV20 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[180]) ).

thf(189,plain,
    ! [SV21: $i,SV43: $i,SV32: $i,SV61: $i,SV57: $i,SV8: $i] :
      ( ( ( ~ ( sum @ SV8 @ SV57 @ SV61 ) )
        = $true )
      | ( ( sum @ SV32 @ SV43 @ SV61 )
        = $true )
      | ( ( sum @ SV21 @ SV43 @ SV57 )
        = $false )
      | ( ( sum @ SV8 @ SV21 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[181]) ).

thf(190,plain,
    ! [SV23: $i,SV58: $i,SV10: $i,SV62: $i,SV44: $i,SV34: $i] :
      ( ( ( ~ ( product @ SV34 @ SV44 @ SV62 ) )
        = $true )
      | ( ( product @ SV10 @ SV58 @ SV62 )
        = $true )
      | ( ( product @ SV23 @ SV44 @ SV58 )
        = $false )
      | ( ( product @ SV10 @ SV23 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[182]) ).

thf(191,plain,
    ! [SV24: $i,SV45: $i,SV35: $i,SV63: $i,SV59: $i,SV11: $i] :
      ( ( ( ~ ( product @ SV11 @ SV59 @ SV63 ) )
        = $true )
      | ( ( product @ SV35 @ SV45 @ SV63 )
        = $true )
      | ( ( product @ SV24 @ SV45 @ SV59 )
        = $false )
      | ( ( product @ SV11 @ SV24 @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[183]) ).

thf(192,plain,
    ! [SV50: $i,SV36: $i,SV12: $i,SV64: $i,SV46: $i,SV25: $i] :
      ( ( ( ~ ( sum @ SV25 @ SV46 @ SV64 ) )
        = $true )
      | ( ( ! [SY228: $i] :
              ( ~ ( product @ SV12 @ SV64 @ SY228 )
              | ( sum @ SV36 @ SV50 @ SY228 ) ) )
        = $true )
      | ( ( product @ SV12 @ SV46 @ SV50 )
        = $false )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[184]) ).

thf(193,plain,
    ! [SV13: $i,SV51: $i,SV37: $i,SV65: $i,SV47: $i,SV26: $i] :
      ( ( ( ~ ( sum @ SV26 @ SV47 @ SV65 ) )
        = $true )
      | ( ( ! [SY229: $i] :
              ( ~ ( sum @ SV37 @ SV51 @ SY229 )
              | ( product @ SV13 @ SV65 @ SY229 ) ) )
        = $true )
      | ( ( product @ SV13 @ SV47 @ SV51 )
        = $false )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[185]) ).

thf(194,plain,
    ! [SV52: $i,SV38: $i,SV27: $i,SV66: $i,SV48: $i,SV14: $i] :
      ( ( ( ~ ( sum @ SV14 @ SV48 @ SV66 ) )
        = $true )
      | ( ( ! [SY230: $i] :
              ( ~ ( product @ SV66 @ SV27 @ SY230 )
              | ( sum @ SV38 @ SV52 @ SY230 ) ) )
        = $true )
      | ( ( product @ SV48 @ SV27 @ SV52 )
        = $false )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[186]) ).

thf(195,plain,
    ! [SV28: $i,SV53: $i,SV39: $i,SV67: $i,SV49: $i,SV15: $i] :
      ( ( ( ~ ( sum @ SV15 @ SV49 @ SV67 ) )
        = $true )
      | ( ( ! [SY231: $i] :
              ( ~ ( sum @ SV39 @ SV53 @ SY231 )
              | ( product @ SV67 @ SV28 @ SY231 ) ) )
        = $true )
      | ( ( product @ SV49 @ SV28 @ SV53 )
        = $false )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[187]) ).

thf(196,plain,
    ! [SV20: $i,SV56: $i,SV7: $i,SV60: $i,SV42: $i,SV31: $i] :
      ( ( ( sum @ SV31 @ SV42 @ SV60 )
        = $false )
      | ( ( sum @ SV7 @ SV56 @ SV60 )
        = $true )
      | ( ( sum @ SV20 @ SV42 @ SV56 )
        = $false )
      | ( ( sum @ SV7 @ SV20 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[188]) ).

thf(197,plain,
    ! [SV21: $i,SV43: $i,SV32: $i,SV61: $i,SV57: $i,SV8: $i] :
      ( ( ( sum @ SV8 @ SV57 @ SV61 )
        = $false )
      | ( ( sum @ SV32 @ SV43 @ SV61 )
        = $true )
      | ( ( sum @ SV21 @ SV43 @ SV57 )
        = $false )
      | ( ( sum @ SV8 @ SV21 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[189]) ).

thf(198,plain,
    ! [SV23: $i,SV58: $i,SV10: $i,SV62: $i,SV44: $i,SV34: $i] :
      ( ( ( product @ SV34 @ SV44 @ SV62 )
        = $false )
      | ( ( product @ SV10 @ SV58 @ SV62 )
        = $true )
      | ( ( product @ SV23 @ SV44 @ SV58 )
        = $false )
      | ( ( product @ SV10 @ SV23 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[190]) ).

thf(199,plain,
    ! [SV24: $i,SV45: $i,SV35: $i,SV63: $i,SV59: $i,SV11: $i] :
      ( ( ( product @ SV11 @ SV59 @ SV63 )
        = $false )
      | ( ( product @ SV35 @ SV45 @ SV63 )
        = $true )
      | ( ( product @ SV24 @ SV45 @ SV59 )
        = $false )
      | ( ( product @ SV11 @ SV24 @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[191]) ).

thf(200,plain,
    ! [SV50: $i,SV36: $i,SV12: $i,SV64: $i,SV46: $i,SV25: $i] :
      ( ( ( sum @ SV25 @ SV46 @ SV64 )
        = $false )
      | ( ( ! [SY228: $i] :
              ( ~ ( product @ SV12 @ SV64 @ SY228 )
              | ( sum @ SV36 @ SV50 @ SY228 ) ) )
        = $true )
      | ( ( product @ SV12 @ SV46 @ SV50 )
        = $false )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[192]) ).

thf(201,plain,
    ! [SV13: $i,SV51: $i,SV37: $i,SV65: $i,SV47: $i,SV26: $i] :
      ( ( ( sum @ SV26 @ SV47 @ SV65 )
        = $false )
      | ( ( ! [SY229: $i] :
              ( ~ ( sum @ SV37 @ SV51 @ SY229 )
              | ( product @ SV13 @ SV65 @ SY229 ) ) )
        = $true )
      | ( ( product @ SV13 @ SV47 @ SV51 )
        = $false )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[193]) ).

thf(202,plain,
    ! [SV52: $i,SV38: $i,SV27: $i,SV66: $i,SV48: $i,SV14: $i] :
      ( ( ( sum @ SV14 @ SV48 @ SV66 )
        = $false )
      | ( ( ! [SY230: $i] :
              ( ~ ( product @ SV66 @ SV27 @ SY230 )
              | ( sum @ SV38 @ SV52 @ SY230 ) ) )
        = $true )
      | ( ( product @ SV48 @ SV27 @ SV52 )
        = $false )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(203,plain,
    ! [SV28: $i,SV53: $i,SV39: $i,SV67: $i,SV49: $i,SV15: $i] :
      ( ( ( sum @ SV15 @ SV49 @ SV67 )
        = $false )
      | ( ( ! [SY231: $i] :
              ( ~ ( sum @ SV39 @ SV53 @ SY231 )
              | ( product @ SV67 @ SV28 @ SY231 ) ) )
        = $true )
      | ( ( product @ SV49 @ SV28 @ SV53 )
        = $false )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[195]) ).

thf(204,plain,
    ! [SV46: $i,SV25: $i,SV50: $i,SV36: $i,SV68: $i,SV64: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV64 @ SV68 )
          | ( sum @ SV36 @ SV50 @ SV68 ) )
        = $true )
      | ( ( sum @ SV25 @ SV46 @ SV64 )
        = $false )
      | ( ( product @ SV12 @ SV46 @ SV50 )
        = $false )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[200]) ).

thf(205,plain,
    ! [SV47: $i,SV26: $i,SV65: $i,SV13: $i,SV69: $i,SV51: $i,SV37: $i] :
      ( ( ( ~ ( sum @ SV37 @ SV51 @ SV69 )
          | ( product @ SV13 @ SV65 @ SV69 ) )
        = $true )
      | ( ( sum @ SV26 @ SV47 @ SV65 )
        = $false )
      | ( ( product @ SV13 @ SV47 @ SV51 )
        = $false )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[201]) ).

thf(206,plain,
    ! [SV48: $i,SV14: $i,SV52: $i,SV38: $i,SV70: $i,SV27: $i,SV66: $i] :
      ( ( ( ~ ( product @ SV66 @ SV27 @ SV70 )
          | ( sum @ SV38 @ SV52 @ SV70 ) )
        = $true )
      | ( ( sum @ SV14 @ SV48 @ SV66 )
        = $false )
      | ( ( product @ SV48 @ SV27 @ SV52 )
        = $false )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[202]) ).

thf(207,plain,
    ! [SV49: $i,SV15: $i,SV28: $i,SV67: $i,SV71: $i,SV53: $i,SV39: $i] :
      ( ( ( ~ ( sum @ SV39 @ SV53 @ SV71 )
          | ( product @ SV67 @ SV28 @ SV71 ) )
        = $true )
      | ( ( sum @ SV15 @ SV49 @ SV67 )
        = $false )
      | ( ( product @ SV49 @ SV28 @ SV53 )
        = $false )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[203]) ).

thf(208,plain,
    ! [SV46: $i,SV25: $i,SV50: $i,SV36: $i,SV68: $i,SV64: $i,SV12: $i] :
      ( ( ( ~ ( product @ SV12 @ SV64 @ SV68 ) )
        = $true )
      | ( ( sum @ SV36 @ SV50 @ SV68 )
        = $true )
      | ( ( sum @ SV25 @ SV46 @ SV64 )
        = $false )
      | ( ( product @ SV12 @ SV46 @ SV50 )
        = $false )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[204]) ).

thf(209,plain,
    ! [SV47: $i,SV26: $i,SV65: $i,SV13: $i,SV69: $i,SV51: $i,SV37: $i] :
      ( ( ( ~ ( sum @ SV37 @ SV51 @ SV69 ) )
        = $true )
      | ( ( product @ SV13 @ SV65 @ SV69 )
        = $true )
      | ( ( sum @ SV26 @ SV47 @ SV65 )
        = $false )
      | ( ( product @ SV13 @ SV47 @ SV51 )
        = $false )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[205]) ).

thf(210,plain,
    ! [SV48: $i,SV14: $i,SV52: $i,SV38: $i,SV70: $i,SV27: $i,SV66: $i] :
      ( ( ( ~ ( product @ SV66 @ SV27 @ SV70 ) )
        = $true )
      | ( ( sum @ SV38 @ SV52 @ SV70 )
        = $true )
      | ( ( sum @ SV14 @ SV48 @ SV66 )
        = $false )
      | ( ( product @ SV48 @ SV27 @ SV52 )
        = $false )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[206]) ).

thf(211,plain,
    ! [SV49: $i,SV15: $i,SV28: $i,SV67: $i,SV71: $i,SV53: $i,SV39: $i] :
      ( ( ( ~ ( sum @ SV39 @ SV53 @ SV71 ) )
        = $true )
      | ( ( product @ SV67 @ SV28 @ SV71 )
        = $true )
      | ( ( sum @ SV15 @ SV49 @ SV67 )
        = $false )
      | ( ( product @ SV49 @ SV28 @ SV53 )
        = $false )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[207]) ).

thf(212,plain,
    ! [SV46: $i,SV25: $i,SV50: $i,SV36: $i,SV68: $i,SV64: $i,SV12: $i] :
      ( ( ( product @ SV12 @ SV64 @ SV68 )
        = $false )
      | ( ( sum @ SV36 @ SV50 @ SV68 )
        = $true )
      | ( ( sum @ SV25 @ SV46 @ SV64 )
        = $false )
      | ( ( product @ SV12 @ SV46 @ SV50 )
        = $false )
      | ( ( product @ SV12 @ SV25 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[208]) ).

thf(213,plain,
    ! [SV47: $i,SV26: $i,SV65: $i,SV13: $i,SV69: $i,SV51: $i,SV37: $i] :
      ( ( ( sum @ SV37 @ SV51 @ SV69 )
        = $false )
      | ( ( product @ SV13 @ SV65 @ SV69 )
        = $true )
      | ( ( sum @ SV26 @ SV47 @ SV65 )
        = $false )
      | ( ( product @ SV13 @ SV47 @ SV51 )
        = $false )
      | ( ( product @ SV13 @ SV26 @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[209]) ).

thf(214,plain,
    ! [SV48: $i,SV14: $i,SV52: $i,SV38: $i,SV70: $i,SV27: $i,SV66: $i] :
      ( ( ( product @ SV66 @ SV27 @ SV70 )
        = $false )
      | ( ( sum @ SV38 @ SV52 @ SV70 )
        = $true )
      | ( ( sum @ SV14 @ SV48 @ SV66 )
        = $false )
      | ( ( product @ SV48 @ SV27 @ SV52 )
        = $false )
      | ( ( product @ SV14 @ SV27 @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[210]) ).

thf(215,plain,
    ! [SV49: $i,SV15: $i,SV28: $i,SV67: $i,SV71: $i,SV53: $i,SV39: $i] :
      ( ( ( sum @ SV39 @ SV53 @ SV71 )
        = $false )
      | ( ( product @ SV67 @ SV28 @ SV71 )
        = $true )
      | ( ( sum @ SV15 @ SV49 @ SV67 )
        = $false )
      | ( ( product @ SV49 @ SV28 @ SV53 )
        = $false )
      | ( ( product @ SV15 @ SV28 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[211]) ).

thf(216,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[57,215,214,213,212,199,198,197,196,171,170,133,97,96,95,83,82,79,78,77,58]) ).

thf(217,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[216]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : RNG003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon May 30 08:03:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.37  
% 0.12/0.37   No.of.Axioms: 20
% 0.12/0.37  
% 0.12/0.37   Length.of.Defs: 0
% 0.12/0.37  
% 0.12/0.37   Contains.Choice.Funs: false
% 0.12/0.40  (rf:0,axioms:20,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:22,loop_count:0,foatp_calls:0,translation:fof_full)................
% 0.55/0.72  
% 0.55/0.72  ********************************
% 0.55/0.72  *   All subproblems solved!    *
% 0.55/0.72  ********************************
% 0.55/0.72  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:216,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.73  
% 0.55/0.73  %**** Beginning of derivation protocol ****
% 0.55/0.73  % SZS output start CNFRefutation
% See solution above
% 0.55/0.74  
% 0.55/0.74  %**** End of derivation protocol ****
% 0.55/0.74  %**** no. of clauses in derivation: 217 ****
% 0.55/0.74  %**** clause counter: 216 ****
% 0.55/0.74  
% 0.55/0.74  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:216,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------