TSTP Solution File: COM003+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : COM003+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n007.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 : Fri Jul 15 01:28:31 EDT 2022

% Result   : Theorem 0.47s 0.64s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  416 (  46 unt;  21 typ;   0 def)
%            Number of atoms       : 5365 (1228 equ;   0 cnn)
%            Maximal formula atoms :   18 (  13 avg)
%            Number of connectives : 10908 (2428   ~;2338   |; 132   &;5966   @)
%                                         (   0 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  21 usr;  11 con; 0-3 aty)
%            Number of variables   :  825 (   0   ^ 809   !;  16   ?; 825   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_algorithm,type,
    algorithm: $i > $o ).

thf(tp_bad,type,
    bad: $i ).

thf(tp_decides,type,
    decides: $i > $i > $i > $o ).

thf(tp_good,type,
    good: $i ).

thf(tp_halts2,type,
    halts2: $i > $i > $o ).

thf(tp_halts3,type,
    halts3: $i > $i > $i > $o ).

thf(tp_outputs,type,
    outputs: $i > $i > $o ).

thf(tp_program,type,
    program: $i > $o ).

thf(tp_sK10_W,type,
    sK10_W: $i ).

thf(tp_sK11_Y,type,
    sK11_Y: $i > $i ).

thf(tp_sK12_SY34,type,
    sK12_SY34: $i > $i ).

thf(tp_sK13_REN,type,
    sK13_REN: $o ).

thf(tp_sK1_X1,type,
    sK1_X1: $i ).

thf(tp_sK2_U,type,
    sK2_U: $i ).

thf(tp_sK3_Y,type,
    sK3_Y: $i > $i ).

thf(tp_sK4_REN,type,
    sK4_REN: $o ).

thf(tp_sK5_V,type,
    sK5_V: $i ).

thf(tp_sK6_Y,type,
    sK6_Y: $i > $i ).

thf(tp_sK7_REN,type,
    sK7_REN: $o ).

thf(tp_sK8_Y,type,
    sK8_Y: $i > $i ).

thf(tp_sK9_SY31,type,
    sK9_SY31: $i > $i ).

thf(1,axiom,
    ( ? [V: $i] :
        ( ( program @ V )
        & ! [Y: $i] :
            ( ( ( ( program @ Y )
                & ( halts2 @ Y @ Y ) )
             => ( ( halts2 @ V @ Y )
                & ( outputs @ V @ good ) ) )
            & ( ( ( program @ Y )
                & ~ ( halts2 @ Y @ Y ) )
             => ( ( halts2 @ V @ Y )
                & ( outputs @ V @ bad ) ) ) ) )
   => ? [U: $i] :
        ( ( program @ U )
        & ! [Y: $i] :
            ( ( ( ( program @ Y )
                & ( halts2 @ Y @ Y ) )
             => ~ ( halts2 @ U @ Y ) )
            & ( ( ( program @ Y )
                & ~ ( halts2 @ Y @ Y ) )
             => ( ( halts2 @ U @ Y )
                & ( outputs @ U @ bad ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).

thf(2,axiom,
    ( ? [W: $i] :
        ( ( program @ W )
        & ! [Y: $i] :
            ( ( ( ( program @ Y )
                & ( halts2 @ Y @ Y ) )
             => ( ( halts3 @ W @ Y @ Y )
                & ( outputs @ W @ good ) ) )
            & ( ( ( program @ Y )
                & ~ ( halts2 @ Y @ Y ) )
             => ( ( halts3 @ W @ Y @ Y )
                & ( outputs @ W @ bad ) ) ) ) )
   => ? [V: $i] :
        ( ( program @ V )
        & ! [Y: $i] :
            ( ( ( ( program @ Y )
                & ( halts2 @ Y @ Y ) )
             => ( ( halts2 @ V @ Y )
                & ( outputs @ V @ good ) ) )
            & ( ( ( program @ Y )
                & ~ ( halts2 @ Y @ Y ) )
             => ( ( halts2 @ V @ Y )
                & ( outputs @ V @ bad ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

thf(3,axiom,
    ! [W: $i] :
      ( ( ( program @ W )
        & ! [Y: $i] :
            ( ( program @ Y )
           => ! [Z: $i] : ( decides @ W @ Y @ Z ) ) )
     => ! [Y: $i,Z: $i] :
          ( ( ( ( program @ Y )
              & ( halts2 @ Y @ Z ) )
           => ( ( halts3 @ W @ Y @ Z )
              & ( outputs @ W @ good ) ) )
          & ( ( ( program @ Y )
              & ~ ( halts2 @ Y @ Z ) )
           => ( ( halts3 @ W @ Y @ Z )
              & ( outputs @ W @ bad ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

thf(4,axiom,
    ( ? [X: $i] :
        ( ( algorithm @ X )
        & ! [Y: $i] :
            ( ( program @ Y )
           => ! [Z: $i] : ( decides @ X @ Y @ Z ) ) )
   => ? [W: $i] :
        ( ( program @ W )
        & ! [Y: $i] :
            ( ( program @ Y )
           => ! [Z: $i] : ( decides @ W @ Y @ Z ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

thf(5,conjecture,
    ~ ? [X1: $i] :
        ( ( algorithm @ X1 )
        & ! [Y1: $i] :
            ( ( program @ Y1 )
           => ! [Z1: $i] : ( decides @ X1 @ Y1 @ Z1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(6,negated_conjecture,
    ( ( ~ ? [X1: $i] :
            ( ( algorithm @ X1 )
            & ! [Y1: $i] :
                ( ( program @ Y1 )
               => ! [Z1: $i] : ( decides @ X1 @ Y1 @ Z1 ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[5]) ).

thf(7,plain,
    ( ( ~ ? [X1: $i] :
            ( ( algorithm @ X1 )
            & ! [Y1: $i] :
                ( ( program @ Y1 )
               => ! [Z1: $i] : ( decides @ X1 @ Y1 @ Z1 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ? [V: $i] :
          ( ( program @ V )
          & ! [Y: $i] :
              ( ( ( ( program @ Y )
                  & ( halts2 @ Y @ Y ) )
               => ( ( halts2 @ V @ Y )
                  & ( outputs @ V @ good ) ) )
              & ( ( ( program @ Y )
                  & ~ ( halts2 @ Y @ Y ) )
               => ( ( halts2 @ V @ Y )
                  & ( outputs @ V @ bad ) ) ) ) )
     => ? [U: $i] :
          ( ( program @ U )
          & ! [Y: $i] :
              ( ( ( ( program @ Y )
                  & ( halts2 @ Y @ Y ) )
               => ~ ( halts2 @ U @ Y ) )
              & ( ( ( program @ Y )
                  & ~ ( halts2 @ Y @ Y ) )
               => ( ( halts2 @ U @ Y )
                  & ( outputs @ U @ bad ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(9,plain,
    ( ( ? [W: $i] :
          ( ( program @ W )
          & ! [Y: $i] :
              ( ( ( ( program @ Y )
                  & ( halts2 @ Y @ Y ) )
               => ( ( halts3 @ W @ Y @ Y )
                  & ( outputs @ W @ good ) ) )
              & ( ( ( program @ Y )
                  & ~ ( halts2 @ Y @ Y ) )
               => ( ( halts3 @ W @ Y @ Y )
                  & ( outputs @ W @ bad ) ) ) ) )
     => ? [V: $i] :
          ( ( program @ V )
          & ! [Y: $i] :
              ( ( ( ( program @ Y )
                  & ( halts2 @ Y @ Y ) )
               => ( ( halts2 @ V @ Y )
                  & ( outputs @ V @ good ) ) )
              & ( ( ( program @ Y )
                  & ~ ( halts2 @ Y @ Y ) )
               => ( ( halts2 @ V @ Y )
                  & ( outputs @ V @ bad ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(10,plain,
    ( ( ! [W: $i] :
          ( ( ( program @ W )
            & ! [Y: $i] :
                ( ( program @ Y )
               => ! [Z: $i] : ( decides @ W @ Y @ Z ) ) )
         => ! [Y: $i,Z: $i] :
              ( ( ( ( program @ Y )
                  & ( halts2 @ Y @ Z ) )
               => ( ( halts3 @ W @ Y @ Z )
                  & ( outputs @ W @ good ) ) )
              & ( ( ( program @ Y )
                  & ~ ( halts2 @ Y @ Z ) )
               => ( ( halts3 @ W @ Y @ Z )
                  & ( outputs @ W @ bad ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(11,plain,
    ( ( ? [X: $i] :
          ( ( algorithm @ X )
          & ! [Y: $i] :
              ( ( program @ Y )
             => ! [Z: $i] : ( decides @ X @ Y @ Z ) ) )
     => ? [W: $i] :
          ( ( program @ W )
          & ! [Y: $i] :
              ( ( program @ Y )
             => ! [Z: $i] : ( decides @ W @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(12,plain,
    ( ( ? [X1: $i] :
          ( ( algorithm @ X1 )
          & ! [Y1: $i] :
              ( ( program @ Y1 )
             => ! [Z1: $i] : ( decides @ X1 @ Y1 @ Z1 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(13,plain,
    ( ( ! [SY22: $i] :
          ( ~ ( program @ SY22 )
          | ! [SY23: $i] : ( decides @ sK1_X1 @ SY22 @ SY23 ) )
      & ( algorithm @ sK1_X1 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(14,plain,
    ( ( ( ! [V: $i] :
            ( ( ( ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) )
                | ( program @ ( sK3_Y @ V ) ) )
              & ( ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) ) )
              & ( ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ bad ) )
              & ( ( program @ ( sK3_Y @ V ) )
                | ( program @ ( sK3_Y @ V ) ) )
              & ( ( program @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) ) )
              & ( ( program @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ bad ) )
              & ( ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ good )
                | ( program @ ( sK3_Y @ V ) ) )
              & ( ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ good )
                | ~ ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) ) )
              & ( ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ good )
                | ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ bad ) ) )
            | ~ ( program @ V ) )
        | sK4_REN )
      & ( sK4_REN
       => ( ! [SY24: $i] :
              ( ~ ( halts2 @ SY24 @ SY24 )
              | ~ ( program @ SY24 )
              | ~ ( halts2 @ sK2_U @ SY24 ) )
          & ! [SY25: $i] :
              ( ~ ( program @ SY25 )
              | ( halts2 @ SY25 @ SY25 )
              | ( halts2 @ sK2_U @ SY25 ) )
          & ( ! [Y: $i] :
                ( ~ ( program @ Y )
                | ( halts2 @ Y @ Y ) )
            | ( outputs @ sK2_U @ bad ) )
          & ( program @ sK2_U ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ( ! [W: $i] :
            ( ( ( ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ( program @ ( sK6_Y @ W ) ) )
              & ( ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) ) )
              & ( ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ bad ) )
              & ( ( program @ ( sK6_Y @ W ) )
                | ( program @ ( sK6_Y @ W ) ) )
              & ( ( program @ ( sK6_Y @ W ) )
                | ~ ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) ) )
              & ( ( program @ ( sK6_Y @ W ) )
                | ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ bad ) )
              & ( ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ good )
                | ( program @ ( sK6_Y @ W ) ) )
              & ( ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ good )
                | ~ ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) ) )
              & ( ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ good )
                | ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ bad ) ) )
            | ~ ( program @ W ) )
        | sK7_REN )
      & ( sK7_REN
       => ( ! [SY27: $i] :
              ( ~ ( halts2 @ SY27 @ SY27 )
              | ~ ( program @ SY27 )
              | ( halts2 @ sK5_V @ SY27 ) )
          & ( ! [Y: $i] :
                ( ~ ( halts2 @ Y @ Y )
                | ~ ( program @ Y ) )
            | ( outputs @ sK5_V @ good ) )
          & ! [SY29: $i] :
              ( ~ ( program @ SY29 )
              | ( halts2 @ SY29 @ SY29 )
              | ( halts2 @ sK5_V @ SY29 ) )
          & ( ! [Y: $i] :
                ( ~ ( program @ Y )
                | ( halts2 @ Y @ Y ) )
            | ( outputs @ sK5_V @ bad ) )
          & ( program @ sK5_V ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(16,plain,
    ( ( ! [W: $i] :
          ( ( ( program @ ( sK8_Y @ W ) )
            & ~ ( decides @ W @ ( sK8_Y @ W ) @ ( sK9_SY31 @ W ) ) )
          | ~ ( program @ W )
          | ( ! [Y: $i,Z: $i] :
                ( ~ ( halts2 @ Y @ Z )
                | ~ ( program @ Y )
                | ( halts3 @ W @ Y @ Z ) )
            & ( ! [Y: $i] :
                  ( ! [Z: $i] :
                      ~ ( halts2 @ Y @ Z )
                  | ~ ( program @ Y ) )
              | ( outputs @ W @ good ) )
            & ! [Y: $i,Z: $i] :
                ( ~ ( program @ Y )
                | ( halts2 @ Y @ Z )
                | ( halts3 @ W @ Y @ Z ) )
            & ( ! [Y: $i] :
                  ( ~ ( program @ Y )
                  | ! [Z: $i] : ( halts2 @ Y @ Z ) )
              | ( outputs @ W @ bad ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(17,plain,
    ( ( ( ! [X: $i] :
            ( ( ( program @ ( sK11_Y @ X ) )
              & ~ ( decides @ X @ ( sK11_Y @ X ) @ ( sK12_SY34 @ X ) ) )
            | ~ ( algorithm @ X ) )
        | sK13_REN )
      & ( sK13_REN
       => ( ! [SY32: $i] :
              ( ~ ( program @ SY32 )
              | ! [SY33: $i] : ( decides @ sK10_W @ SY32 @ SY33 ) )
          & ( program @ sK10_W ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(18,plain,
    ( ( ( ! [X: $i] :
            ( ( ( program @ ( sK11_Y @ X ) )
              & ~ ( decides @ X @ ( sK11_Y @ X ) @ ( sK12_SY34 @ X ) ) )
            | ~ ( algorithm @ X ) )
        | sK13_REN )
      & ( sK13_REN
       => ( ! [SY32: $i] :
              ( ~ ( program @ SY32 )
              | ! [SY33: $i] : ( decides @ sK10_W @ SY32 @ SY33 ) )
          & ( program @ sK10_W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(19,plain,
    ( ( ! [W: $i] :
          ( ( ( program @ ( sK8_Y @ W ) )
            & ~ ( decides @ W @ ( sK8_Y @ W ) @ ( sK9_SY31 @ W ) ) )
          | ~ ( program @ W )
          | ( ! [Y: $i,Z: $i] :
                ( ~ ( halts2 @ Y @ Z )
                | ~ ( program @ Y )
                | ( halts3 @ W @ Y @ Z ) )
            & ( ! [Y: $i] :
                  ( ! [Z: $i] :
                      ~ ( halts2 @ Y @ Z )
                  | ~ ( program @ Y ) )
              | ( outputs @ W @ good ) )
            & ! [Y: $i,Z: $i] :
                ( ~ ( program @ Y )
                | ( halts2 @ Y @ Z )
                | ( halts3 @ W @ Y @ Z ) )
            & ( ! [Y: $i] :
                  ( ~ ( program @ Y )
                  | ! [Z: $i] : ( halts2 @ Y @ Z ) )
              | ( outputs @ W @ bad ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ( ! [W: $i] :
            ( ( ( ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ( program @ ( sK6_Y @ W ) ) )
              & ( ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) ) )
              & ( ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ bad ) )
              & ( ( program @ ( sK6_Y @ W ) )
                | ( program @ ( sK6_Y @ W ) ) )
              & ( ( program @ ( sK6_Y @ W ) )
                | ~ ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) ) )
              & ( ( program @ ( sK6_Y @ W ) )
                | ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ bad ) )
              & ( ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ good )
                | ( program @ ( sK6_Y @ W ) ) )
              & ( ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ good )
                | ~ ( halts2 @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) ) )
              & ( ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ good )
                | ~ ( halts3 @ W @ ( sK6_Y @ W ) @ ( sK6_Y @ W ) )
                | ~ ( outputs @ W @ bad ) ) )
            | ~ ( program @ W ) )
        | sK7_REN )
      & ( sK7_REN
       => ( ! [SY27: $i] :
              ( ~ ( halts2 @ SY27 @ SY27 )
              | ~ ( program @ SY27 )
              | ( halts2 @ sK5_V @ SY27 ) )
          & ( ! [Y: $i] :
                ( ~ ( halts2 @ Y @ Y )
                | ~ ( program @ Y ) )
            | ( outputs @ sK5_V @ good ) )
          & ! [SY29: $i] :
              ( ~ ( program @ SY29 )
              | ( halts2 @ SY29 @ SY29 )
              | ( halts2 @ sK5_V @ SY29 ) )
          & ( ! [Y: $i] :
                ( ~ ( program @ Y )
                | ( halts2 @ Y @ Y ) )
            | ( outputs @ sK5_V @ bad ) )
          & ( program @ sK5_V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(21,plain,
    ( ( ( ! [V: $i] :
            ( ( ( ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) )
                | ( program @ ( sK3_Y @ V ) ) )
              & ( ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) ) )
              & ( ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ bad ) )
              & ( ( program @ ( sK3_Y @ V ) )
                | ( program @ ( sK3_Y @ V ) ) )
              & ( ( program @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) ) )
              & ( ( program @ ( sK3_Y @ V ) )
                | ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ bad ) )
              & ( ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ good )
                | ( program @ ( sK3_Y @ V ) ) )
              & ( ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ good )
                | ~ ( halts2 @ ( sK3_Y @ V ) @ ( sK3_Y @ V ) ) )
              & ( ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ good )
                | ~ ( halts2 @ V @ ( sK3_Y @ V ) )
                | ~ ( outputs @ V @ bad ) ) )
            | ~ ( program @ V ) )
        | sK4_REN )
      & ( sK4_REN
       => ( ! [SY24: $i] :
              ( ~ ( halts2 @ SY24 @ SY24 )
              | ~ ( program @ SY24 )
              | ~ ( halts2 @ sK2_U @ SY24 ) )
          & ! [SY25: $i] :
              ( ~ ( program @ SY25 )
              | ( halts2 @ SY25 @ SY25 )
              | ( halts2 @ sK2_U @ SY25 ) )
          & ( ! [Y: $i] :
                ( ~ ( program @ Y )
                | ( halts2 @ Y @ Y ) )
            | ( outputs @ sK2_U @ bad ) )
          & ( program @ sK2_U ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(22,plain,
    ( ( ! [SY22: $i] :
          ( ~ ( program @ SY22 )
          | ! [SY23: $i] : ( decides @ sK1_X1 @ SY22 @ SY23 ) )
      & ( algorithm @ sK1_X1 ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(23,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                            | ( program @ ( sK6_Y @ SX0 ) ) )
                                        | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                            | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                                  | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                      | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ bad ) ) )
                            | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                            | ( program @ ( sK6_Y @ SX0 ) ) )
                                        | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                            | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                                  | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                      | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ bad ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ good )
                                      | ( program @ ( sK6_Y @ SX0 ) ) )
                                  | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ good )
                                      | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                            | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ good )
                                | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ bad ) ) ) )
                  | ~ ( program @ SX0 ) )
              | sK7_REN )
          | ~ ( ~ sK7_REN
              | ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( halts2 @ SX0 @ SX0 )
                                    | ~ ( program @ SX0 )
                                    | ( halts2 @ sK5_V @ SX0 ) )
                              | ~ ( ! [SX0: $i] :
                                      ( ~ ( halts2 @ SX0 @ SX0 )
                                      | ~ ( program @ SX0 ) )
                                  | ( outputs @ sK5_V @ good ) ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( program @ SX0 )
                                    | ( halts2 @ SX0 @ SX0 )
                                    | ( halts2 @ sK5_V @ SX0 ) )
                              | ~ ( ! [SX0: $i] :
                                      ( ~ ( program @ SX0 )
                                      | ( halts2 @ SX0 @ SX0 ) )
                                  | ( outputs @ sK5_V @ bad ) ) ) )
                  | ~ ( program @ sK5_V ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                            | ( program @ ( sK3_Y @ SX0 ) ) )
                                        | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                            | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                                  | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                      | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ bad ) ) )
                            | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                            | ( program @ ( sK3_Y @ SX0 ) ) )
                                        | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                            | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                                  | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                      | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ bad ) ) ) )
                      | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ good )
                                      | ( program @ ( sK3_Y @ SX0 ) ) )
                                  | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                      | ~ ( outputs @ SX0 @ good )
                                      | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                            | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ good )
                                | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ bad ) ) ) )
                  | ~ ( program @ SX0 ) )
              | sK4_REN )
          | ~ ( ~ sK4_REN
              | ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( halts2 @ SX0 @ SX0 )
                              | ~ ( program @ SX0 )
                              | ~ ( halts2 @ sK2_U @ SX0 ) )
                        | ~ ~ ( ~ ! [SX0: $i] :
                                    ( ~ ( program @ SX0 )
                                    | ( halts2 @ SX0 @ SX0 )
                                    | ( halts2 @ sK2_U @ SX0 ) )
                              | ~ ( ! [SX0: $i] :
                                      ( ~ ( program @ SX0 )
                                      | ( halts2 @ SX0 @ SX0 ) )
                                  | ( outputs @ sK2_U @ bad ) ) ) )
                  | ~ ( program @ sK2_U ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( program @ ( sK8_Y @ SX0 ) )
              | ~ ~ ( decides @ SX0 @ ( sK8_Y @ SX0 ) @ ( sK9_SY31 @ SX0 ) ) )
          | ~ ( program @ SX0 )
          | ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
                          ( ~ ( halts2 @ SX1 @ SX2 )
                          | ~ ( program @ SX1 )
                          | ( halts3 @ SX0 @ SX1 @ SX2 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SX0 @ good ) ) )
              | ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
                          ( ~ ( program @ SX1 )
                          | ( halts2 @ SX1 @ SX2 )
                          | ( halts3 @ SX0 @ SX1 @ SX2 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SX0 @ bad ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(26,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
                      | ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY34 @ SX0 ) ) )
                  | ~ ( algorithm @ SX0 ) )
              | sK13_REN )
          | ~ ( ~ sK13_REN
              | ~ ( ~ ! [SX0: $i] :
                        ( ~ ( program @ SX0 )
                        | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) )
                  | ~ ( program @ sK10_W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(27,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( program @ SX0 )
                | ! [SX1: $i] : ( decides @ sK1_X1 @ SX0 @ SX1 ) )
          | ~ ( algorithm @ sK1_X1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(28,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                        | ( program @ ( sK6_Y @ SX0 ) ) )
                                    | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                              | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) )
                        | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                        | ( program @ ( sK6_Y @ SX0 ) ) )
                                    | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                              | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                  | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ( program @ ( sK6_Y @ SX0 ) ) )
                              | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                        | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ good )
                            | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ bad ) ) ) )
              | ~ ( program @ SX0 ) )
          | sK7_REN )
      | ~ ( ~ sK7_REN
          | ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                ( ~ ( halts2 @ SX0 @ SX0 )
                                | ~ ( program @ SX0 )
                                | ( halts2 @ sK5_V @ SX0 ) )
                          | ~ ( ! [SX0: $i] :
                                  ( ~ ( halts2 @ SX0 @ SX0 )
                                  | ~ ( program @ SX0 ) )
                              | ( outputs @ sK5_V @ good ) ) )
                    | ~ ~ ( ~ ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 )
                                | ( halts2 @ sK5_V @ SX0 ) )
                          | ~ ( ! [SX0: $i] :
                                  ( ~ ( program @ SX0 )
                                  | ( halts2 @ SX0 @ SX0 ) )
                              | ( outputs @ sK5_V @ bad ) ) ) )
              | ~ ( program @ sK5_V ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(29,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                        | ( program @ ( sK3_Y @ SX0 ) ) )
                                    | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                              | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                  | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) )
                        | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                        | ( program @ ( sK3_Y @ SX0 ) ) )
                                    | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                              | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                  | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ( program @ ( sK3_Y @ SX0 ) ) )
                              | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                        | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ good )
                            | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ bad ) ) ) )
              | ~ ( program @ SX0 ) )
          | sK4_REN )
      | ~ ( ~ sK4_REN
          | ~ ( ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( halts2 @ SX0 @ SX0 )
                          | ~ ( program @ SX0 )
                          | ~ ( halts2 @ sK2_U @ SX0 ) )
                    | ~ ~ ( ~ ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 )
                                | ( halts2 @ sK2_U @ SX0 ) )
                          | ~ ( ! [SX0: $i] :
                                  ( ~ ( program @ SX0 )
                                  | ( halts2 @ SX0 @ SX0 ) )
                              | ( outputs @ sK2_U @ bad ) ) ) )
              | ~ ( program @ sK2_U ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(30,plain,
    ! [SV1: $i] :
      ( ( ~ ( ~ ( program @ ( sK8_Y @ SV1 ) )
            | ~ ~ ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) ) )
        | ~ ( program @ SV1 )
        | ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                        ( ~ ( halts2 @ SY35 @ SY36 )
                        | ~ ( program @ SY35 )
                        | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                  | ~ ( ! [SX1: $i] :
                          ( ! [SX2: $i] :
                              ~ ( halts2 @ SX1 @ SX2 )
                          | ~ ( program @ SX1 ) )
                      | ( outputs @ SV1 @ good ) ) )
            | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                        ( ~ ( program @ SY39 )
                        | ( halts2 @ SY39 @ SY40 )
                        | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                  | ~ ( ! [SX1: $i] :
                          ( ~ ( program @ SX1 )
                          | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                      | ( outputs @ SV1 @ bad ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(31,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
                  | ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY34 @ SX0 ) ) )
              | ~ ( algorithm @ SX0 ) )
          | sK13_REN )
      | ~ ( ~ sK13_REN
          | ~ ( ~ ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) )
              | ~ ( program @ sK10_W ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(32,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ! [SX1: $i] : ( decides @ sK1_X1 @ SX0 @ SX1 ) )
      | ~ ( algorithm @ sK1_X1 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(33,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                        | ( program @ ( sK6_Y @ SX0 ) ) )
                                    | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                              | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) )
                        | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                        | ( program @ ( sK6_Y @ SX0 ) ) )
                                    | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                              | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                  | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ( program @ ( sK6_Y @ SX0 ) ) )
                              | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                        | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ good )
                            | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ bad ) ) ) )
              | ~ ( program @ SX0 ) )
          | sK7_REN ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(34,plain,
    ( ( ~ ( ~ sK7_REN
          | ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                                ( ~ ( halts2 @ SX0 @ SX0 )
                                | ~ ( program @ SX0 )
                                | ( halts2 @ sK5_V @ SX0 ) )
                          | ~ ( ! [SX0: $i] :
                                  ( ~ ( halts2 @ SX0 @ SX0 )
                                  | ~ ( program @ SX0 ) )
                              | ( outputs @ sK5_V @ good ) ) )
                    | ~ ~ ( ~ ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 )
                                | ( halts2 @ sK5_V @ SX0 ) )
                          | ~ ( ! [SX0: $i] :
                                  ( ~ ( program @ SX0 )
                                  | ( halts2 @ SX0 @ SX0 ) )
                              | ( outputs @ sK5_V @ bad ) ) ) )
              | ~ ( program @ sK5_V ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(35,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                        | ( program @ ( sK3_Y @ SX0 ) ) )
                                    | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                              | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                  | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) )
                        | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                        | ( program @ ( sK3_Y @ SX0 ) ) )
                                    | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                        | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                              | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                  | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ bad ) ) ) )
                  | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ( program @ ( sK3_Y @ SX0 ) ) )
                              | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                  | ~ ( outputs @ SX0 @ good )
                                  | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                        | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ good )
                            | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                            | ~ ( outputs @ SX0 @ bad ) ) ) )
              | ~ ( program @ SX0 ) )
          | sK4_REN ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[29]) ).

thf(36,plain,
    ( ( ~ ( ~ sK4_REN
          | ~ ( ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( halts2 @ SX0 @ SX0 )
                          | ~ ( program @ SX0 )
                          | ~ ( halts2 @ sK2_U @ SX0 ) )
                    | ~ ~ ( ~ ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 )
                                | ( halts2 @ sK2_U @ SX0 ) )
                          | ~ ( ! [SX0: $i] :
                                  ( ~ ( program @ SX0 )
                                  | ( halts2 @ SX0 @ SX0 ) )
                              | ( outputs @ sK2_U @ bad ) ) ) )
              | ~ ( program @ sK2_U ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[29]) ).

thf(37,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ~ ( program @ ( sK8_Y @ SV1 ) )
              | ~ ~ ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) ) )
          | ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(38,plain,
    ( ( ~ ( ! [SX0: $i] :
              ( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
                  | ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY34 @ SX0 ) ) )
              | ~ ( algorithm @ SX0 ) )
          | sK13_REN ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(39,plain,
    ( ( ~ ( ~ sK13_REN
          | ~ ( ~ ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) )
              | ~ ( program @ sK10_W ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(40,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ! [SX1: $i] : ( decides @ sK1_X1 @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(41,plain,
    ( ( ~ ( algorithm @ sK1_X1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(42,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                    | ( program @ ( sK6_Y @ SX0 ) ) )
                                | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                    | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                          | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                              | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ bad ) ) )
                    | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                    | ( program @ ( sK6_Y @ SX0 ) ) )
                                | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                    | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                          | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                              | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ bad ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ good )
                              | ( program @ ( sK6_Y @ SX0 ) ) )
                          | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ good )
                              | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                    | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                        | ~ ( outputs @ SX0 @ good )
                        | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                        | ~ ( outputs @ SX0 @ bad ) ) ) )
          | ~ ( program @ SX0 ) )
      | sK7_REN )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(43,plain,
    ( ( ~ sK7_REN
      | ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( halts2 @ SX0 @ SX0 )
                            | ~ ( program @ SX0 )
                            | ( halts2 @ sK5_V @ SX0 ) )
                      | ~ ( ! [SX0: $i] :
                              ( ~ ( halts2 @ SX0 @ SX0 )
                              | ~ ( program @ SX0 ) )
                          | ( outputs @ sK5_V @ good ) ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( program @ SX0 )
                            | ( halts2 @ SX0 @ SX0 )
                            | ( halts2 @ sK5_V @ SX0 ) )
                      | ~ ( ! [SX0: $i] :
                              ( ~ ( program @ SX0 )
                              | ( halts2 @ SX0 @ SX0 ) )
                          | ( outputs @ sK5_V @ bad ) ) ) )
          | ~ ( program @ sK5_V ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(44,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                    | ( program @ ( sK3_Y @ SX0 ) ) )
                                | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                    | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                          | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                              | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ bad ) ) )
                    | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                    | ( program @ ( sK3_Y @ SX0 ) ) )
                                | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                    | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                          | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                              | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ bad ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ good )
                              | ( program @ ( sK3_Y @ SX0 ) ) )
                          | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                              | ~ ( outputs @ SX0 @ good )
                              | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                    | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                        | ~ ( outputs @ SX0 @ good )
                        | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                        | ~ ( outputs @ SX0 @ bad ) ) ) )
          | ~ ( program @ SX0 ) )
      | sK4_REN )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(45,plain,
    ( ( ~ sK4_REN
      | ~ ( ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( halts2 @ SX0 @ SX0 )
                      | ~ ( program @ SX0 )
                      | ~ ( halts2 @ sK2_U @ SX0 ) )
                | ~ ~ ( ~ ! [SX0: $i] :
                            ( ~ ( program @ SX0 )
                            | ( halts2 @ SX0 @ SX0 )
                            | ( halts2 @ sK2_U @ SX0 ) )
                      | ~ ( ! [SX0: $i] :
                              ( ~ ( program @ SX0 )
                              | ( halts2 @ SX0 @ SX0 ) )
                          | ( outputs @ sK2_U @ bad ) ) ) )
          | ~ ( program @ sK2_U ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(46,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ~ ( program @ ( sK8_Y @ SV1 ) )
              | ~ ~ ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(47,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
              | ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY34 @ SX0 ) ) )
          | ~ ( algorithm @ SX0 ) )
      | sK13_REN )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(48,plain,
    ( ( ~ sK13_REN
      | ~ ( ~ ! [SX0: $i] :
                ( ~ ( program @ SX0 )
                | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) )
          | ~ ( program @ sK10_W ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(49,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( program @ SX0 )
          | ! [SX1: $i] : ( decides @ sK1_X1 @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(50,plain,
    ( ( algorithm @ sK1_X1 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(51,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                      | ( program @ ( sK6_Y @ SX0 ) ) )
                                  | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                      | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                            | ~ ( ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ bad ) ) )
                      | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                      | ( program @ ( sK6_Y @ SX0 ) ) )
                                  | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                      | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                            | ~ ( ( program @ ( sK6_Y @ SX0 ) )
                                | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ bad ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ good )
                                | ( program @ ( sK6_Y @ SX0 ) ) )
                            | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ good )
                                | ~ ( halts2 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) ) ) )
                      | ~ ( ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                          | ~ ( outputs @ SX0 @ good )
                          | ~ ( halts3 @ SX0 @ ( sK6_Y @ SX0 ) @ ( sK6_Y @ SX0 ) )
                          | ~ ( outputs @ SX0 @ bad ) ) ) )
            | ~ ( program @ SX0 ) ) )
      = $true )
    | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(52,plain,
    ( ( ( ~ sK7_REN )
      = $true )
    | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( halts2 @ SX0 @ SX0 )
                              | ~ ( program @ SX0 )
                              | ( halts2 @ sK5_V @ SX0 ) )
                        | ~ ( ! [SX0: $i] :
                                ( ~ ( halts2 @ SX0 @ SX0 )
                                | ~ ( program @ SX0 ) )
                            | ( outputs @ sK5_V @ good ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( program @ SX0 )
                              | ( halts2 @ SX0 @ SX0 )
                              | ( halts2 @ sK5_V @ SX0 ) )
                        | ~ ( ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 ) )
                            | ( outputs @ sK5_V @ bad ) ) ) )
            | ~ ( program @ sK5_V ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(53,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                      | ( program @ ( sK3_Y @ SX0 ) ) )
                                  | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                      | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                            | ~ ( ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) )
                                | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ bad ) ) )
                      | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                      | ( program @ ( sK3_Y @ SX0 ) ) )
                                  | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                      | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                            | ~ ( ( program @ ( sK3_Y @ SX0 ) )
                                | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ bad ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ good )
                                | ( program @ ( sK3_Y @ SX0 ) ) )
                            | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                                | ~ ( outputs @ SX0 @ good )
                                | ~ ( halts2 @ ( sK3_Y @ SX0 ) @ ( sK3_Y @ SX0 ) ) ) )
                      | ~ ( ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                          | ~ ( outputs @ SX0 @ good )
                          | ~ ( halts2 @ SX0 @ ( sK3_Y @ SX0 ) )
                          | ~ ( outputs @ SX0 @ bad ) ) ) )
            | ~ ( program @ SX0 ) ) )
      = $true )
    | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(54,plain,
    ( ( ( ~ sK4_REN )
      = $true )
    | ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( halts2 @ SX0 @ SX0 )
                        | ~ ( program @ SX0 )
                        | ~ ( halts2 @ sK2_U @ SX0 ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( program @ SX0 )
                              | ( halts2 @ SX0 @ SX0 )
                              | ( halts2 @ sK2_U @ SX0 ) )
                        | ~ ( ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 ) )
                            | ( outputs @ sK2_U @ bad ) ) ) )
            | ~ ( program @ sK2_U ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(55,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( program @ ( sK8_Y @ SV1 ) )
          | ~ ~ ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) ) )
        = $false )
      | ( ( ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(56,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
                | ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY34 @ SX0 ) ) )
            | ~ ( algorithm @ SX0 ) ) )
      = $true )
    | ( sK13_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(57,plain,
    ( ( ( ~ sK13_REN )
      = $true )
    | ( ( ~ ( ~ ! [SX0: $i] :
                  ( ~ ( program @ SX0 )
                  | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) )
            | ~ ( program @ sK10_W ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(58,plain,
    ! [SV2: $i] :
      ( ( ~ ( program @ SV2 )
        | ! [SY43: $i] : ( decides @ sK1_X1 @ SV2 @ SY43 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(59,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                    | ( program @ ( sK6_Y @ SV3 ) ) )
                                | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                          | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ bad ) ) )
                    | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                    | ( program @ ( sK6_Y @ SV3 ) ) )
                                | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                          | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ bad ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ good )
                              | ( program @ ( sK6_Y @ SV3 ) ) )
                          | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ good )
                              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                    | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ good )
                        | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ bad ) ) ) )
          | ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(60,plain,
    ( ( sK7_REN = $false )
    | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( halts2 @ SX0 @ SX0 )
                              | ~ ( program @ SX0 )
                              | ( halts2 @ sK5_V @ SX0 ) )
                        | ~ ( ! [SX0: $i] :
                                ( ~ ( halts2 @ SX0 @ SX0 )
                                | ~ ( program @ SX0 ) )
                            | ( outputs @ sK5_V @ good ) ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( program @ SX0 )
                              | ( halts2 @ SX0 @ SX0 )
                              | ( halts2 @ sK5_V @ SX0 ) )
                        | ~ ( ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 ) )
                            | ( outputs @ sK5_V @ bad ) ) ) )
            | ~ ( program @ sK5_V ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(61,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                    | ( program @ ( sK3_Y @ SV4 ) ) )
                                | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                          | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ bad ) ) )
                    | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                    | ( program @ ( sK3_Y @ SV4 ) ) )
                                | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                          | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ bad ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ good )
                              | ( program @ ( sK3_Y @ SV4 ) ) )
                          | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ good )
                              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                    | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ good )
                        | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ bad ) ) ) )
          | ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(62,plain,
    ( ( sK4_REN = $false )
    | ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( halts2 @ SX0 @ SX0 )
                        | ~ ( program @ SX0 )
                        | ~ ( halts2 @ sK2_U @ SX0 ) )
                  | ~ ~ ( ~ ! [SX0: $i] :
                              ( ~ ( program @ SX0 )
                              | ( halts2 @ SX0 @ SX0 )
                              | ( halts2 @ sK2_U @ SX0 ) )
                        | ~ ( ! [SX0: $i] :
                                ( ~ ( program @ SX0 )
                                | ( halts2 @ SX0 @ SX0 ) )
                            | ( outputs @ sK2_U @ bad ) ) ) )
            | ~ ( program @ sK2_U ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(63,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( program @ ( sK8_Y @ SV1 ) ) )
        = $false )
      | ( ( ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(64,plain,
    ! [SV1: $i] :
      ( ( ( ~ ~ ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) ) )
        = $false )
      | ( ( ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(65,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ~ ( program @ ( sK11_Y @ SV5 ) )
              | ~ ~ ( decides @ SV5 @ ( sK11_Y @ SV5 ) @ ( sK12_SY34 @ SV5 ) ) )
          | ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(66,plain,
    ( ( sK13_REN = $false )
    | ( ( ~ ( ~ ! [SX0: $i] :
                  ( ~ ( program @ SX0 )
                  | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) )
            | ~ ( program @ sK10_W ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(67,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( program @ SV2 ) )
        = $true )
      | ( ( ! [SY43: $i] : ( decides @ sK1_X1 @ SV2 @ SY43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(68,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                    | ( program @ ( sK6_Y @ SV3 ) ) )
                                | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                          | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ bad ) ) )
                    | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                    | ( program @ ( sK6_Y @ SV3 ) ) )
                                | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                          | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ bad ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ good )
                              | ( program @ ( sK6_Y @ SV3 ) ) )
                          | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( outputs @ SV3 @ good )
                              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                    | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ good )
                        | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ bad ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(69,plain,
    ( ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( halts2 @ SX0 @ SX0 )
                          | ~ ( program @ SX0 )
                          | ( halts2 @ sK5_V @ SX0 ) )
                    | ~ ( ! [SX0: $i] :
                            ( ~ ( halts2 @ SX0 @ SX0 )
                            | ~ ( program @ SX0 ) )
                        | ( outputs @ sK5_V @ good ) ) )
              | ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( program @ SX0 )
                          | ( halts2 @ SX0 @ SX0 )
                          | ( halts2 @ sK5_V @ SX0 ) )
                    | ~ ( ! [SX0: $i] :
                            ( ~ ( program @ SX0 )
                            | ( halts2 @ SX0 @ SX0 ) )
                        | ( outputs @ sK5_V @ bad ) ) ) )
        | ~ ( program @ sK5_V ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(70,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                    | ( program @ ( sK3_Y @ SV4 ) ) )
                                | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                          | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ bad ) ) )
                    | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                    | ( program @ ( sK3_Y @ SV4 ) ) )
                                | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                          | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ bad ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ good )
                              | ( program @ ( sK3_Y @ SV4 ) ) )
                          | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                              | ~ ( outputs @ SV4 @ good )
                              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                    | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ good )
                        | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ bad ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[61]) ).

thf(71,plain,
    ( ( ( ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( halts2 @ SX0 @ SX0 )
                    | ~ ( program @ SX0 )
                    | ~ ( halts2 @ sK2_U @ SX0 ) )
              | ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( program @ SX0 )
                          | ( halts2 @ SX0 @ SX0 )
                          | ( halts2 @ sK2_U @ SX0 ) )
                    | ~ ( ! [SX0: $i] :
                            ( ~ ( program @ SX0 )
                            | ( halts2 @ SX0 @ SX0 ) )
                        | ( outputs @ sK2_U @ bad ) ) ) )
        | ~ ( program @ sK2_U ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(72,plain,
    ! [SV1: $i] :
      ( ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[63]) ).

thf(73,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) ) )
        = $true )
      | ( ( ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[64]) ).

thf(74,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ~ ( program @ ( sK11_Y @ SV5 ) )
              | ~ ~ ( decides @ SV5 @ ( sK11_Y @ SV5 ) @ ( sK12_SY34 @ SV5 ) ) ) )
        = $true )
      | ( ( ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(75,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( program @ SX0 )
              | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) )
        | ~ ( program @ sK10_W ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[66]) ).

thf(76,plain,
    ! [SV2: $i] :
      ( ( ( program @ SV2 )
        = $false )
      | ( ( ! [SY43: $i] : ( decides @ sK1_X1 @ SV2 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(77,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                | ( program @ ( sK6_Y @ SV3 ) ) )
                            | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                      | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ bad ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                | ( program @ ( sK6_Y @ SV3 ) ) )
                            | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                      | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ bad ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ good )
                          | ( program @ ( sK6_Y @ SV3 ) ) )
                      | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ good )
                          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ good )
                    | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(78,plain,
    ( ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( halts2 @ SX0 @ SX0 )
                          | ~ ( program @ SX0 )
                          | ( halts2 @ sK5_V @ SX0 ) )
                    | ~ ( ! [SX0: $i] :
                            ( ~ ( halts2 @ SX0 @ SX0 )
                            | ~ ( program @ SX0 ) )
                        | ( outputs @ sK5_V @ good ) ) )
              | ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( program @ SX0 )
                          | ( halts2 @ SX0 @ SX0 )
                          | ( halts2 @ sK5_V @ SX0 ) )
                    | ~ ( ! [SX0: $i] :
                            ( ~ ( program @ SX0 )
                            | ( halts2 @ SX0 @ SX0 ) )
                        | ( outputs @ sK5_V @ bad ) ) ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(79,plain,
    ( ( ( ~ ( program @ sK5_V ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(80,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                | ( program @ ( sK3_Y @ SV4 ) ) )
                            | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                      | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ bad ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                | ( program @ ( sK3_Y @ SV4 ) ) )
                            | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                      | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ bad ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ good )
                          | ( program @ ( sK3_Y @ SV4 ) ) )
                      | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ good )
                          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ good )
                    | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(81,plain,
    ( ( ( ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( halts2 @ SX0 @ SX0 )
                    | ~ ( program @ SX0 )
                    | ~ ( halts2 @ sK2_U @ SX0 ) )
              | ~ ~ ( ~ ! [SX0: $i] :
                          ( ~ ( program @ SX0 )
                          | ( halts2 @ SX0 @ SX0 )
                          | ( halts2 @ sK2_U @ SX0 ) )
                    | ~ ( ! [SX0: $i] :
                            ( ~ ( program @ SX0 )
                            | ( halts2 @ SX0 @ SX0 ) )
                        | ( outputs @ sK2_U @ bad ) ) ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(82,plain,
    ( ( ( ~ ( program @ sK2_U ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(83,plain,
    ! [SV1: $i] :
      ( ( ( program @ SV1 )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(84,plain,
    ! [SV1: $i] :
      ( ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( ~ ( program @ SV1 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(85,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( program @ ( sK11_Y @ SV5 ) )
          | ~ ~ ( decides @ SV5 @ ( sK11_Y @ SV5 ) @ ( sK12_SY34 @ SV5 ) ) )
        = $false )
      | ( ( ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(86,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( program @ SX0 )
              | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(87,plain,
    ( ( ( ~ ( program @ sK10_W ) )
      = $false )
    | ( sK13_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(88,plain,
    ! [SV6: $i,SV2: $i] :
      ( ( ( decides @ sK1_X1 @ SV2 @ SV6 )
        = $true )
      | ( ( program @ SV2 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(89,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                | ( program @ ( sK6_Y @ SV3 ) ) )
                            | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                                | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                      | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ bad ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                | ( program @ ( sK6_Y @ SV3 ) ) )
                            | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                                | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                      | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ bad ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[77]) ).

thf(90,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ good )
                          | ( program @ ( sK6_Y @ SV3 ) ) )
                      | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( outputs @ SV3 @ good )
                          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ good )
                    | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[77]) ).

thf(91,plain,
    ( ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( halts2 @ SX0 @ SX0 )
                        | ~ ( program @ SX0 )
                        | ( halts2 @ sK5_V @ SX0 ) )
                  | ~ ( ! [SX0: $i] :
                          ( ~ ( halts2 @ SX0 @ SX0 )
                          | ~ ( program @ SX0 ) )
                      | ( outputs @ sK5_V @ good ) ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( program @ SX0 )
                        | ( halts2 @ SX0 @ SX0 )
                        | ( halts2 @ sK5_V @ SX0 ) )
                  | ~ ( ! [SX0: $i] :
                          ( ~ ( program @ SX0 )
                          | ( halts2 @ SX0 @ SX0 ) )
                      | ( outputs @ sK5_V @ bad ) ) ) ) )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(92,plain,
    ( ( ( program @ sK5_V )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(93,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                | ( program @ ( sK3_Y @ SV4 ) ) )
                            | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                                | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                      | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ bad ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                | ( program @ ( sK3_Y @ SV4 ) ) )
                            | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                                | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                      | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ bad ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(94,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ good )
                          | ( program @ ( sK3_Y @ SV4 ) ) )
                      | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                          | ~ ( outputs @ SV4 @ good )
                          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ good )
                    | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(95,plain,
    ( ( ( ~ ( ~ ! [SX0: $i] :
                  ( ~ ( halts2 @ SX0 @ SX0 )
                  | ~ ( program @ SX0 )
                  | ~ ( halts2 @ sK2_U @ SX0 ) )
            | ~ ~ ( ~ ! [SX0: $i] :
                        ( ~ ( program @ SX0 )
                        | ( halts2 @ SX0 @ SX0 )
                        | ( halts2 @ sK2_U @ SX0 ) )
                  | ~ ( ! [SX0: $i] :
                          ( ~ ( program @ SX0 )
                          | ( halts2 @ SX0 @ SX0 ) )
                      | ( outputs @ sK2_U @ bad ) ) ) ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[81]) ).

thf(96,plain,
    ( ( ( program @ sK2_U )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[82]) ).

thf(97,plain,
    ! [SV1: $i] :
      ( ( ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                      ( ~ ( halts2 @ SY35 @ SY36 )
                      | ~ ( program @ SY35 )
                      | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                | ~ ( ! [SX1: $i] :
                        ( ! [SX2: $i] :
                            ~ ( halts2 @ SX1 @ SX2 )
                        | ~ ( program @ SX1 ) )
                    | ( outputs @ SV1 @ good ) ) )
          | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                      ( ~ ( program @ SY39 )
                      | ( halts2 @ SY39 @ SY40 )
                      | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                | ~ ( ! [SX1: $i] :
                        ( ~ ( program @ SX1 )
                        | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                    | ( outputs @ SV1 @ bad ) ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(98,plain,
    ! [SV1: $i] :
      ( ( ( program @ SV1 )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                          ( ~ ( halts2 @ SY35 @ SY36 )
                          | ~ ( program @ SY35 )
                          | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ! [SX2: $i] :
                                ~ ( halts2 @ SX1 @ SX2 )
                            | ~ ( program @ SX1 ) )
                        | ( outputs @ SV1 @ good ) ) )
              | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                          ( ~ ( program @ SY39 )
                          | ( halts2 @ SY39 @ SY40 )
                          | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                    | ~ ( ! [SX1: $i] :
                            ( ~ ( program @ SX1 )
                            | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                        | ( outputs @ SV1 @ bad ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(99,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( program @ ( sK11_Y @ SV5 ) ) )
        = $false )
      | ( ( ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[85]) ).

thf(100,plain,
    ! [SV5: $i] :
      ( ( ( ~ ~ ( decides @ SV5 @ ( sK11_Y @ SV5 ) @ ( sK12_SY34 @ SV5 ) ) )
        = $false )
      | ( ( ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[85]) ).

thf(101,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ! [SX1: $i] : ( decides @ sK10_W @ SX0 @ SX1 ) ) )
      = $true )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[86]) ).

thf(102,plain,
    ( ( ( program @ sK10_W )
      = $true )
    | ( sK13_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(103,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ( program @ ( sK6_Y @ SV3 ) ) )
                          | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                    | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ bad ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                              | ( program @ ( sK6_Y @ SV3 ) ) )
                          | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                    | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                        | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ bad ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(104,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ good )
                        | ( program @ ( sK6_Y @ SV3 ) ) )
                    | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( outputs @ SV3 @ good )
                        | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
              | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( outputs @ SV3 @ good )
                  | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[90]) ).

thf(105,plain,
    ( ( ( ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( halts2 @ SX0 @ SX0 )
                    | ~ ( program @ SX0 )
                    | ( halts2 @ sK5_V @ SX0 ) )
              | ~ ( ! [SX0: $i] :
                      ( ~ ( halts2 @ SX0 @ SX0 )
                      | ~ ( program @ SX0 ) )
                  | ( outputs @ sK5_V @ good ) ) )
        | ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ( halts2 @ SX0 @ SX0 )
                    | ( halts2 @ sK5_V @ SX0 ) )
              | ~ ( ! [SX0: $i] :
                      ( ~ ( program @ SX0 )
                      | ( halts2 @ SX0 @ SX0 ) )
                  | ( outputs @ sK5_V @ bad ) ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[91]) ).

thf(106,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                              | ( program @ ( sK3_Y @ SV4 ) ) )
                          | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                    | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                        | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ bad ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                              | ( program @ ( sK3_Y @ SV4 ) ) )
                          | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                    | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                        | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ bad ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[93]) ).

thf(107,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ good )
                        | ( program @ ( sK3_Y @ SV4 ) ) )
                    | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                        | ~ ( outputs @ SV4 @ good )
                        | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
              | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                  | ~ ( outputs @ SV4 @ good )
                  | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                  | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[94]) ).

thf(108,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( halts2 @ SX0 @ SX0 )
              | ~ ( program @ SX0 )
              | ~ ( halts2 @ sK2_U @ SX0 ) )
        | ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ( halts2 @ SX0 @ SX0 )
                    | ( halts2 @ sK2_U @ SX0 ) )
              | ~ ( ! [SX0: $i] :
                      ( ~ ( program @ SX0 )
                      | ( halts2 @ SX0 @ SX0 ) )
                  | ( outputs @ sK2_U @ bad ) ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(109,plain,
    ! [SV1: $i] :
      ( ( ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                      ( ~ ( halts2 @ SY35 @ SY36 )
                      | ~ ( program @ SY35 )
                      | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                | ~ ( ! [SX1: $i] :
                        ( ! [SX2: $i] :
                            ~ ( halts2 @ SX1 @ SX2 )
                        | ~ ( program @ SX1 ) )
                    | ( outputs @ SV1 @ good ) ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[97]) ).

thf(110,plain,
    ! [SV1: $i] :
      ( ( ( ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                      ( ~ ( program @ SY39 )
                      | ( halts2 @ SY39 @ SY40 )
                      | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                | ~ ( ! [SX1: $i] :
                        ( ~ ( program @ SX1 )
                        | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                    | ( outputs @ SV1 @ bad ) ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[97]) ).

thf(111,plain,
    ! [SV1: $i] :
      ( ( ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                      ( ~ ( halts2 @ SY35 @ SY36 )
                      | ~ ( program @ SY35 )
                      | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                | ~ ( ! [SX1: $i] :
                        ( ! [SX2: $i] :
                            ~ ( halts2 @ SX1 @ SX2 )
                        | ~ ( program @ SX1 ) )
                    | ( outputs @ SV1 @ good ) ) )
          | ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                      ( ~ ( program @ SY39 )
                      | ( halts2 @ SY39 @ SY40 )
                      | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                | ~ ( ! [SX1: $i] :
                        ( ~ ( program @ SX1 )
                        | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                    | ( outputs @ SV1 @ bad ) ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(112,plain,
    ! [SV5: $i] :
      ( ( ( program @ ( sK11_Y @ SV5 ) )
        = $true )
      | ( ( ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[99]) ).

thf(113,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( decides @ SV5 @ ( sK11_Y @ SV5 ) @ ( sK12_SY34 @ SV5 ) ) )
        = $true )
      | ( ( ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[100]) ).

thf(114,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( program @ SV7 )
          | ! [SY44: $i] : ( decides @ sK10_W @ SV7 @ SY44 ) )
        = $true )
      | ( sK13_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(115,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ( program @ ( sK6_Y @ SV3 ) ) )
                      | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ bad ) ) )
          | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                          | ( program @ ( sK6_Y @ SV3 ) ) )
                      | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[103]) ).

thf(116,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ good )
                    | ( program @ ( sK6_Y @ SV3 ) ) )
                | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ good )
                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
          | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ good )
              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(117,plain,
    ( ( ( ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( halts2 @ SX0 @ SX0 )
                    | ~ ( program @ SX0 )
                    | ( halts2 @ sK5_V @ SX0 ) )
              | ~ ( ! [SX0: $i] :
                      ( ~ ( halts2 @ SX0 @ SX0 )
                      | ~ ( program @ SX0 ) )
                  | ( outputs @ sK5_V @ good ) ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[105]) ).

thf(118,plain,
    ( ( ( ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ( halts2 @ SX0 @ SX0 )
                    | ( halts2 @ sK5_V @ SX0 ) )
              | ~ ( ! [SX0: $i] :
                      ( ~ ( program @ SX0 )
                      | ( halts2 @ SX0 @ SX0 ) )
                  | ( outputs @ sK5_V @ bad ) ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[105]) ).

thf(119,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                          | ( program @ ( sK3_Y @ SV4 ) ) )
                      | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ bad ) ) )
          | ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                          | ( program @ ( sK3_Y @ SV4 ) ) )
                      | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[106]) ).

thf(120,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ good )
                    | ( program @ ( sK3_Y @ SV4 ) ) )
                | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ good )
                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
          | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ good )
              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[107]) ).

thf(121,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( halts2 @ SX0 @ SX0 )
              | ~ ( program @ SX0 )
              | ~ ( halts2 @ sK2_U @ SX0 ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[108]) ).

thf(122,plain,
    ( ( ( ~ ~ ( ~ ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ( halts2 @ SX0 @ SX0 )
                    | ( halts2 @ sK2_U @ SX0 ) )
              | ~ ( ! [SX0: $i] :
                      ( ~ ( program @ SX0 )
                      | ( halts2 @ SX0 @ SX0 ) )
                  | ( outputs @ sK2_U @ bad ) ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[108]) ).

thf(123,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ~ ! [SY35: $i,SY36: $i] :
                    ( ~ ( halts2 @ SY35 @ SY36 )
                    | ~ ( program @ SY35 )
                    | ( halts3 @ SV1 @ SY35 @ SY36 ) )
              | ~ ( ! [SX1: $i] :
                      ( ! [SX2: $i] :
                          ~ ( halts2 @ SX1 @ SX2 )
                      | ~ ( program @ SX1 ) )
                  | ( outputs @ SV1 @ good ) ) ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[109]) ).

thf(124,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ~ ! [SY39: $i,SY40: $i] :
                    ( ~ ( program @ SY39 )
                    | ( halts2 @ SY39 @ SY40 )
                    | ( halts3 @ SV1 @ SY39 @ SY40 ) )
              | ~ ( ! [SX1: $i] :
                      ( ~ ( program @ SX1 )
                      | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                  | ( outputs @ SV1 @ bad ) ) ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[110]) ).

thf(125,plain,
    ! [SV1: $i] :
      ( ( ( ~ ~ ( ~ ! [SY35: $i,SY36: $i] :
                      ( ~ ( halts2 @ SY35 @ SY36 )
                      | ~ ( program @ SY35 )
                      | ( halts3 @ SV1 @ SY35 @ SY36 ) )
                | ~ ( ! [SX1: $i] :
                        ( ! [SX2: $i] :
                            ~ ( halts2 @ SX1 @ SX2 )
                        | ~ ( program @ SX1 ) )
                    | ( outputs @ SV1 @ good ) ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[111]) ).

thf(126,plain,
    ! [SV1: $i] :
      ( ( ( ~ ~ ( ~ ! [SY39: $i,SY40: $i] :
                      ( ~ ( program @ SY39 )
                      | ( halts2 @ SY39 @ SY40 )
                      | ( halts3 @ SV1 @ SY39 @ SY40 ) )
                | ~ ( ! [SX1: $i] :
                        ( ~ ( program @ SX1 )
                        | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                    | ( outputs @ SV1 @ bad ) ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[111]) ).

thf(127,plain,
    ! [SV5: $i] :
      ( ( ( algorithm @ SV5 )
        = $false )
      | ( ( program @ ( sK11_Y @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(128,plain,
    ! [SV5: $i] :
      ( ( ( decides @ SV5 @ ( sK11_Y @ SV5 ) @ ( sK12_SY34 @ SV5 ) )
        = $false )
      | ( ( ~ ( algorithm @ SV5 ) )
        = $true )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(129,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( program @ SV7 ) )
        = $true )
      | ( ( ! [SY44: $i] : ( decides @ sK10_W @ SV7 @ SY44 ) )
        = $true )
      | ( sK13_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[114]) ).

thf(130,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ( program @ ( sK6_Y @ SV3 ) ) )
                      | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[115]) ).

thf(131,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                          | ( program @ ( sK6_Y @ SV3 ) ) )
                      | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
                | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[115]) ).

thf(132,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ good )
                    | ( program @ ( sK6_Y @ SV3 ) ) )
                | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( outputs @ SV3 @ good )
                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[116]) ).

thf(133,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ good )
              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[116]) ).

thf(134,plain,
    ( ( ( ~ ( ~ ! [SX0: $i] :
                  ( ~ ( halts2 @ SX0 @ SX0 )
                  | ~ ( program @ SX0 )
                  | ( halts2 @ sK5_V @ SX0 ) )
            | ~ ( ! [SX0: $i] :
                    ( ~ ( halts2 @ SX0 @ SX0 )
                    | ~ ( program @ SX0 ) )
                | ( outputs @ sK5_V @ good ) ) ) )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[117]) ).

thf(135,plain,
    ( ( ( ~ ( ~ ! [SX0: $i] :
                  ( ~ ( program @ SX0 )
                  | ( halts2 @ SX0 @ SX0 )
                  | ( halts2 @ sK5_V @ SX0 ) )
            | ~ ( ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ( halts2 @ SX0 @ SX0 ) )
                | ( outputs @ sK5_V @ bad ) ) ) )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[118]) ).

thf(136,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                          | ( program @ ( sK3_Y @ SV4 ) ) )
                      | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[119]) ).

thf(137,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                          | ( program @ ( sK3_Y @ SV4 ) ) )
                      | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
                | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[119]) ).

thf(138,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ good )
                    | ( program @ ( sK3_Y @ SV4 ) ) )
                | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                    | ~ ( outputs @ SV4 @ good )
                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[120]) ).

thf(139,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ good )
              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[120]) ).

thf(140,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( halts2 @ SX0 @ SX0 )
            | ~ ( program @ SX0 )
            | ~ ( halts2 @ sK2_U @ SX0 ) ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[121]) ).

thf(141,plain,
    ( ( ( ~ ( ~ ! [SX0: $i] :
                  ( ~ ( program @ SX0 )
                  | ( halts2 @ SX0 @ SX0 )
                  | ( halts2 @ sK2_U @ SX0 ) )
            | ~ ( ! [SX0: $i] :
                    ( ~ ( program @ SX0 )
                    | ( halts2 @ SX0 @ SX0 ) )
                | ( outputs @ sK2_U @ bad ) ) ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[122]) ).

thf(142,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY35: $i,SY36: $i] :
                ( ~ ( halts2 @ SY35 @ SY36 )
                | ~ ( program @ SY35 )
                | ( halts3 @ SV1 @ SY35 @ SY36 ) )
          | ~ ( ! [SX1: $i] :
                  ( ! [SX2: $i] :
                      ~ ( halts2 @ SX1 @ SX2 )
                  | ~ ( program @ SX1 ) )
              | ( outputs @ SV1 @ good ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[123]) ).

thf(143,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY39: $i,SY40: $i] :
                ( ~ ( program @ SY39 )
                | ( halts2 @ SY39 @ SY40 )
                | ( halts3 @ SV1 @ SY39 @ SY40 ) )
          | ~ ( ! [SX1: $i] :
                  ( ~ ( program @ SX1 )
                  | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
              | ( outputs @ SV1 @ bad ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[124]) ).

thf(144,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ~ ! [SY35: $i,SY36: $i] :
                    ( ~ ( halts2 @ SY35 @ SY36 )
                    | ~ ( program @ SY35 )
                    | ( halts3 @ SV1 @ SY35 @ SY36 ) )
              | ~ ( ! [SX1: $i] :
                      ( ! [SX2: $i] :
                          ~ ( halts2 @ SX1 @ SX2 )
                      | ~ ( program @ SX1 ) )
                  | ( outputs @ SV1 @ good ) ) ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[125]) ).

thf(145,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ~ ! [SY39: $i,SY40: $i] :
                    ( ~ ( program @ SY39 )
                    | ( halts2 @ SY39 @ SY40 )
                    | ( halts3 @ SV1 @ SY39 @ SY40 ) )
              | ~ ( ! [SX1: $i] :
                      ( ~ ( program @ SX1 )
                      | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
                  | ( outputs @ SV1 @ bad ) ) ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[126]) ).

thf(146,plain,
    ! [SV5: $i] :
      ( ( ( algorithm @ SV5 )
        = $false )
      | ( ( decides @ SV5 @ ( sK11_Y @ SV5 ) @ ( sK12_SY34 @ SV5 ) )
        = $false )
      | ( sK13_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[128]) ).

thf(147,plain,
    ! [SV7: $i] :
      ( ( ( program @ SV7 )
        = $false )
      | ( ( ! [SY44: $i] : ( decides @ sK10_W @ SV7 @ SY44 ) )
        = $true )
      | ( sK13_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[129]) ).

thf(148,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ( program @ ( sK6_Y @ SV3 ) ) )
                    | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                        | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
              | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[130]) ).

thf(149,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                        | ( program @ ( sK6_Y @ SV3 ) ) )
                    | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                        | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
              | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                  | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( outputs @ SV3 @ bad ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[131]) ).

thf(150,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( outputs @ SV3 @ good )
                  | ( program @ ( sK6_Y @ SV3 ) ) )
              | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( outputs @ SV3 @ good )
                  | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[132]) ).

thf(151,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ good )
          | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[133]) ).

thf(152,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( halts2 @ SX0 @ SX0 )
              | ~ ( program @ SX0 )
              | ( halts2 @ sK5_V @ SX0 ) )
        | ~ ( ! [SX0: $i] :
                ( ~ ( halts2 @ SX0 @ SX0 )
                | ~ ( program @ SX0 ) )
            | ( outputs @ sK5_V @ good ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[134]) ).

thf(153,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( program @ SX0 )
              | ( halts2 @ SX0 @ SX0 )
              | ( halts2 @ sK5_V @ SX0 ) )
        | ~ ( ! [SX0: $i] :
                ( ~ ( program @ SX0 )
                | ( halts2 @ SX0 @ SX0 ) )
            | ( outputs @ sK5_V @ bad ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[135]) ).

thf(154,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                        | ( program @ ( sK3_Y @ SV4 ) ) )
                    | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                        | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
              | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                  | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                  | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[136]) ).

thf(155,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                        | ( program @ ( sK3_Y @ SV4 ) ) )
                    | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                        | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
              | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                  | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                  | ~ ( outputs @ SV4 @ bad ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[137]) ).

thf(156,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                  | ~ ( outputs @ SV4 @ good )
                  | ( program @ ( sK3_Y @ SV4 ) ) )
              | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
                  | ~ ( outputs @ SV4 @ good )
                  | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[138]) ).

thf(157,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ good )
          | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[139]) ).

thf(158,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( halts2 @ SV8 @ SV8 )
          | ~ ( program @ SV8 )
          | ~ ( halts2 @ sK2_U @ SV8 ) )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(159,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( program @ SX0 )
              | ( halts2 @ SX0 @ SX0 )
              | ( halts2 @ sK2_U @ SX0 ) )
        | ~ ( ! [SX0: $i] :
                ( ~ ( program @ SX0 )
                | ( halts2 @ SX0 @ SX0 ) )
            | ( outputs @ sK2_U @ bad ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[141]) ).

thf(160,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY35: $i,SY36: $i] :
                ( ~ ( halts2 @ SY35 @ SY36 )
                | ~ ( program @ SY35 )
                | ( halts3 @ SV1 @ SY35 @ SY36 ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[142]) ).

thf(161,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ! [SX1: $i] :
                  ( ! [SX2: $i] :
                      ~ ( halts2 @ SX1 @ SX2 )
                  | ~ ( program @ SX1 ) )
              | ( outputs @ SV1 @ good ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[142]) ).

thf(162,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY39: $i,SY40: $i] :
                ( ~ ( program @ SY39 )
                | ( halts2 @ SY39 @ SY40 )
                | ( halts3 @ SV1 @ SY39 @ SY40 ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[143]) ).

thf(163,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ! [SX1: $i] :
                  ( ~ ( program @ SX1 )
                  | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
              | ( outputs @ SV1 @ bad ) ) )
        = $false )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[143]) ).

thf(164,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY35: $i,SY36: $i] :
                ( ~ ( halts2 @ SY35 @ SY36 )
                | ~ ( program @ SY35 )
                | ( halts3 @ SV1 @ SY35 @ SY36 ) )
          | ~ ( ! [SX1: $i] :
                  ( ! [SX2: $i] :
                      ~ ( halts2 @ SX1 @ SX2 )
                  | ~ ( program @ SX1 ) )
              | ( outputs @ SV1 @ good ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[144]) ).

thf(165,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY39: $i,SY40: $i] :
                ( ~ ( program @ SY39 )
                | ( halts2 @ SY39 @ SY40 )
                | ( halts3 @ SV1 @ SY39 @ SY40 ) )
          | ~ ( ! [SX1: $i] :
                  ( ~ ( program @ SX1 )
                  | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
              | ( outputs @ SV1 @ bad ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[145]) ).

thf(166,plain,
    ! [SV9: $i,SV7: $i] :
      ( ( ( decides @ sK10_W @ SV7 @ SV9 )
        = $true )
      | ( ( program @ SV7 )
        = $false )
      | ( sK13_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[147]) ).

thf(167,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ( program @ ( sK6_Y @ SV3 ) ) )
                | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
          | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[148]) ).

thf(168,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                    | ( program @ ( sK6_Y @ SV3 ) ) )
                | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
          | ~ ( ( program @ ( sK6_Y @ SV3 ) )
              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[149]) ).

thf(169,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ good )
              | ( program @ ( sK6_Y @ SV3 ) ) )
          | ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ good )
              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(170,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[151]) ).

thf(171,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( halts2 @ SX0 @ SX0 )
              | ~ ( program @ SX0 )
              | ( halts2 @ sK5_V @ SX0 ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[152]) ).

thf(172,plain,
    ( ( ( ~ ( ! [SX0: $i] :
                ( ~ ( halts2 @ SX0 @ SX0 )
                | ~ ( program @ SX0 ) )
            | ( outputs @ sK5_V @ good ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[152]) ).

thf(173,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( program @ SX0 )
              | ( halts2 @ SX0 @ SX0 )
              | ( halts2 @ sK5_V @ SX0 ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[153]) ).

thf(174,plain,
    ( ( ( ~ ( ! [SX0: $i] :
                ( ~ ( program @ SX0 )
                | ( halts2 @ SX0 @ SX0 ) )
            | ( outputs @ sK5_V @ bad ) ) )
      = $false )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[153]) ).

thf(175,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                    | ( program @ ( sK3_Y @ SV4 ) ) )
                | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
          | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[154]) ).

thf(176,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                    | ( program @ ( sK3_Y @ SV4 ) ) )
                | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
          | ~ ( ( program @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(177,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ good )
              | ( program @ ( sK3_Y @ SV4 ) ) )
          | ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ good )
              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(178,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[157]) ).

thf(179,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( halts2 @ SV8 @ SV8 )
          | ~ ( program @ SV8 ) )
        = $true )
      | ( ( ~ ( halts2 @ sK2_U @ SV8 ) )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[158]) ).

thf(180,plain,
    ( ( ( ~ ! [SX0: $i] :
              ( ~ ( program @ SX0 )
              | ( halts2 @ SX0 @ SX0 )
              | ( halts2 @ sK2_U @ SX0 ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[159]) ).

thf(181,plain,
    ( ( ( ~ ( ! [SX0: $i] :
                ( ~ ( program @ SX0 )
                | ( halts2 @ SX0 @ SX0 ) )
            | ( outputs @ sK2_U @ bad ) ) )
      = $false )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[159]) ).

thf(182,plain,
    ! [SV1: $i] :
      ( ( ( ! [SY35: $i,SY36: $i] :
              ( ~ ( halts2 @ SY35 @ SY36 )
              | ~ ( program @ SY35 )
              | ( halts3 @ SV1 @ SY35 @ SY36 ) ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[160]) ).

thf(183,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ! [SX2: $i] :
                  ~ ( halts2 @ SX1 @ SX2 )
              | ~ ( program @ SX1 ) )
          | ( outputs @ SV1 @ good ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[161]) ).

thf(184,plain,
    ! [SV1: $i] :
      ( ( ( ! [SY39: $i,SY40: $i] :
              ( ~ ( program @ SY39 )
              | ( halts2 @ SY39 @ SY40 )
              | ( halts3 @ SV1 @ SY39 @ SY40 ) ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[162]) ).

thf(185,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ~ ( program @ SX1 )
              | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
          | ( outputs @ SV1 @ bad ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[163]) ).

thf(186,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY35: $i,SY36: $i] :
                ( ~ ( halts2 @ SY35 @ SY36 )
                | ~ ( program @ SY35 )
                | ( halts3 @ SV1 @ SY35 @ SY36 ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[164]) ).

thf(187,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ! [SX1: $i] :
                  ( ! [SX2: $i] :
                      ~ ( halts2 @ SX1 @ SX2 )
                  | ~ ( program @ SX1 ) )
              | ( outputs @ SV1 @ good ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[164]) ).

thf(188,plain,
    ! [SV1: $i] :
      ( ( ( ~ ! [SY39: $i,SY40: $i] :
                ( ~ ( program @ SY39 )
                | ( halts2 @ SY39 @ SY40 )
                | ( halts3 @ SV1 @ SY39 @ SY40 ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[165]) ).

thf(189,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( ! [SX1: $i] :
                  ( ~ ( program @ SX1 )
                  | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
              | ( outputs @ SV1 @ bad ) ) )
        = $false )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[165]) ).

thf(190,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ( program @ ( sK6_Y @ SV3 ) ) )
                | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[167]) ).

thf(191,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[167]) ).

thf(192,plain,
    ! [SV3: $i] :
      ( ( ( ~ ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                    | ( program @ ( sK6_Y @ SV3 ) ) )
                | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                    | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[168]) ).

thf(193,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
              | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[168]) ).

thf(194,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ good )
              | ( program @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[169]) ).

thf(195,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( outputs @ SV3 @ good )
              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[169]) ).

thf(196,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[170]) ).

thf(197,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( halts2 @ SX0 @ SX0 )
            | ~ ( program @ SX0 )
            | ( halts2 @ sK5_V @ SX0 ) ) )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[171]) ).

thf(198,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( halts2 @ SX0 @ SX0 )
            | ~ ( program @ SX0 ) )
        | ( outputs @ sK5_V @ good ) )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[172]) ).

thf(199,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ( halts2 @ SX0 @ SX0 )
            | ( halts2 @ sK5_V @ SX0 ) ) )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[173]) ).

thf(200,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ( halts2 @ SX0 @ SX0 ) )
        | ( outputs @ sK5_V @ bad ) )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[174]) ).

thf(201,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                    | ( program @ ( sK3_Y @ SV4 ) ) )
                | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[175]) ).

thf(202,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[175]) ).

thf(203,plain,
    ! [SV4: $i] :
      ( ( ( ~ ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                    | ( program @ ( sK3_Y @ SV4 ) ) )
                | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                    | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[176]) ).

thf(204,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ bad ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[176]) ).

thf(205,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ good )
              | ( program @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[177]) ).

thf(206,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
              | ~ ( outputs @ SV4 @ good )
              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[177]) ).

thf(207,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[178]) ).

thf(208,plain,
    ! [SV8: $i] :
      ( ( ( ~ ( halts2 @ SV8 @ SV8 ) )
        = $true )
      | ( ( ~ ( program @ SV8 ) )
        = $true )
      | ( ( ~ ( halts2 @ sK2_U @ SV8 ) )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[179]) ).

thf(209,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ( halts2 @ SX0 @ SX0 )
            | ( halts2 @ sK2_U @ SX0 ) ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[180]) ).

thf(210,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ( halts2 @ SX0 @ SX0 ) )
        | ( outputs @ sK2_U @ bad ) )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[181]) ).

thf(211,plain,
    ! [SV1: $i,SV10: $i] :
      ( ( ( ! [SY45: $i] :
              ( ~ ( halts2 @ SV10 @ SY45 )
              | ~ ( program @ SV10 )
              | ( halts3 @ SV1 @ SV10 @ SY45 ) ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[182]) ).

thf(212,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ! [SX2: $i] :
                  ~ ( halts2 @ SX1 @ SX2 )
              | ~ ( program @ SX1 ) ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[183]) ).

thf(213,plain,
    ! [SV1: $i,SV11: $i] :
      ( ( ( ! [SY46: $i] :
              ( ~ ( program @ SV11 )
              | ( halts2 @ SV11 @ SY46 )
              | ( halts3 @ SV1 @ SV11 @ SY46 ) ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[184]) ).

thf(214,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ~ ( program @ SX1 )
              | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[185]) ).

thf(215,plain,
    ! [SV1: $i] :
      ( ( ( ! [SY35: $i,SY36: $i] :
              ( ~ ( halts2 @ SY35 @ SY36 )
              | ~ ( program @ SY35 )
              | ( halts3 @ SV1 @ SY35 @ SY36 ) ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[186]) ).

thf(216,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ! [SX2: $i] :
                  ~ ( halts2 @ SX1 @ SX2 )
              | ~ ( program @ SX1 ) )
          | ( outputs @ SV1 @ good ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[187]) ).

thf(217,plain,
    ! [SV1: $i] :
      ( ( ( ! [SY39: $i,SY40: $i] :
              ( ~ ( program @ SY39 )
              | ( halts2 @ SY39 @ SY40 )
              | ( halts3 @ SV1 @ SY39 @ SY40 ) ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[188]) ).

thf(218,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ~ ( program @ SX1 )
              | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) )
          | ( outputs @ SV1 @ bad ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[189]) ).

thf(219,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ( program @ ( sK6_Y @ SV3 ) ) )
              | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
                  | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[190]) ).

thf(220,plain,
    ! [SV3: $i] :
      ( ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[191]) ).

thf(221,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
                  | ( program @ ( sK6_Y @ SV3 ) ) )
              | ~ ( ( program @ ( sK6_Y @ SV3 ) )
                  | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[192]) ).

thf(222,plain,
    ! [SV3: $i] :
      ( ( ( ( program @ ( sK6_Y @ SV3 ) )
          | ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[193]) ).

thf(223,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ good )
          | ( program @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[194]) ).

thf(224,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ good )
          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[195]) ).

thf(225,plain,
    ! [SV3: $i] :
      ( ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[196]) ).

thf(226,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( halts2 @ SV12 @ SV12 )
          | ~ ( program @ SV12 )
          | ( halts2 @ sK5_V @ SV12 ) )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[197]) ).

thf(227,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( halts2 @ SX0 @ SX0 )
            | ~ ( program @ SX0 ) ) )
      = $true )
    | ( ( outputs @ sK5_V @ good )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[198]) ).

thf(228,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( program @ SV13 )
          | ( halts2 @ SV13 @ SV13 )
          | ( halts2 @ sK5_V @ SV13 ) )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[199]) ).

thf(229,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ( halts2 @ SX0 @ SX0 ) ) )
      = $true )
    | ( ( outputs @ sK5_V @ bad )
      = $true )
    | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[200]) ).

thf(230,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                  | ( program @ ( sK3_Y @ SV4 ) ) )
              | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
                  | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[201]) ).

thf(231,plain,
    ! [SV4: $i] :
      ( ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
          | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[202]) ).

thf(232,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
                  | ( program @ ( sK3_Y @ SV4 ) ) )
              | ~ ( ( program @ ( sK3_Y @ SV4 ) )
                  | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[203]) ).

thf(233,plain,
    ! [SV4: $i] :
      ( ( ( ( program @ ( sK3_Y @ SV4 ) )
          | ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[204]) ).

thf(234,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ good )
          | ( program @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[205]) ).

thf(235,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ good )
          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[206]) ).

thf(236,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[207]) ).

thf(237,plain,
    ! [SV8: $i] :
      ( ( ( halts2 @ SV8 @ SV8 )
        = $false )
      | ( ( ~ ( program @ SV8 ) )
        = $true )
      | ( ( ~ ( halts2 @ sK2_U @ SV8 ) )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[208]) ).

thf(238,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( program @ SV14 )
          | ( halts2 @ SV14 @ SV14 )
          | ( halts2 @ sK2_U @ SV14 ) )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[209]) ).

thf(239,plain,
    ( ( ( ! [SX0: $i] :
            ( ~ ( program @ SX0 )
            | ( halts2 @ SX0 @ SX0 ) ) )
      = $true )
    | ( ( outputs @ sK2_U @ bad )
      = $true )
    | ( sK4_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[210]) ).

thf(240,plain,
    ! [SV1: $i,SV15: $i,SV10: $i] :
      ( ( ( ~ ( halts2 @ SV10 @ SV15 )
          | ~ ( program @ SV10 )
          | ( halts3 @ SV1 @ SV10 @ SV15 ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[211]) ).

thf(241,plain,
    ! [SV1: $i,SV16: $i] :
      ( ( ( ! [SY47: $i] :
              ~ ( halts2 @ SV16 @ SY47 )
          | ~ ( program @ SV16 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[212]) ).

thf(242,plain,
    ! [SV1: $i,SV17: $i,SV11: $i] :
      ( ( ( ~ ( program @ SV11 )
          | ( halts2 @ SV11 @ SV17 )
          | ( halts3 @ SV1 @ SV11 @ SV17 ) )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[213]) ).

thf(243,plain,
    ! [SV1: $i,SV18: $i] :
      ( ( ( ~ ( program @ SV18 )
          | ! [SY48: $i] : ( halts2 @ SV18 @ SY48 ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[214]) ).

thf(244,plain,
    ! [SV1: $i,SV19: $i] :
      ( ( ( ! [SY49: $i] :
              ( ~ ( halts2 @ SV19 @ SY49 )
              | ~ ( program @ SV19 )
              | ( halts3 @ SV1 @ SV19 @ SY49 ) ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[215]) ).

thf(245,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ! [SX2: $i] :
                  ~ ( halts2 @ SX1 @ SX2 )
              | ~ ( program @ SX1 ) ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[216]) ).

thf(246,plain,
    ! [SV1: $i,SV20: $i] :
      ( ( ( ! [SY50: $i] :
              ( ~ ( program @ SV20 )
              | ( halts2 @ SV20 @ SY50 )
              | ( halts3 @ SV1 @ SV20 @ SY50 ) ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[217]) ).

thf(247,plain,
    ! [SV1: $i] :
      ( ( ( ! [SX1: $i] :
              ( ~ ( program @ SX1 )
              | ! [SX2: $i] : ( halts2 @ SX1 @ SX2 ) ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[218]) ).

thf(248,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ( program @ ( sK6_Y @ SV3 ) ) )
          | ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[219]) ).

thf(249,plain,
    ! [SV3: $i] :
      ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[220]) ).

thf(250,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
              | ( program @ ( sK6_Y @ SV3 ) ) )
          | ~ ( ( program @ ( sK6_Y @ SV3 ) )
              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[221]) ).

thf(251,plain,
    ! [SV3: $i] :
      ( ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[222]) ).

thf(252,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[223]) ).

thf(253,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[224]) ).

thf(254,plain,
    ! [SV3: $i] :
      ( ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[225]) ).

thf(255,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( halts2 @ SV12 @ SV12 )
          | ~ ( program @ SV12 ) )
        = $true )
      | ( ( halts2 @ sK5_V @ SV12 )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[226]) ).

thf(256,plain,
    ! [SV21: $i] :
      ( ( ( ~ ( halts2 @ SV21 @ SV21 )
          | ~ ( program @ SV21 ) )
        = $true )
      | ( ( outputs @ sK5_V @ good )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[227]) ).

thf(257,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( program @ SV13 )
          | ( halts2 @ SV13 @ SV13 ) )
        = $true )
      | ( ( halts2 @ sK5_V @ SV13 )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[228]) ).

thf(258,plain,
    ! [SV22: $i] :
      ( ( ( ~ ( program @ SV22 )
          | ( halts2 @ SV22 @ SV22 ) )
        = $true )
      | ( ( outputs @ sK5_V @ bad )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[229]) ).

thf(259,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
              | ( program @ ( sK3_Y @ SV4 ) ) )
          | ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[230]) ).

thf(260,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[231]) ).

thf(261,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
              | ( program @ ( sK3_Y @ SV4 ) ) )
          | ~ ( ( program @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[232]) ).

thf(262,plain,
    ! [SV4: $i] :
      ( ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[233]) ).

thf(263,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[234]) ).

thf(264,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[235]) ).

thf(265,plain,
    ! [SV4: $i] :
      ( ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
          | ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[236]) ).

thf(266,plain,
    ! [SV8: $i] :
      ( ( ( program @ SV8 )
        = $false )
      | ( ( halts2 @ SV8 @ SV8 )
        = $false )
      | ( ( ~ ( halts2 @ sK2_U @ SV8 ) )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[237]) ).

thf(267,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( program @ SV14 )
          | ( halts2 @ SV14 @ SV14 ) )
        = $true )
      | ( ( halts2 @ sK2_U @ SV14 )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[238]) ).

thf(268,plain,
    ! [SV23: $i] :
      ( ( ( ~ ( program @ SV23 )
          | ( halts2 @ SV23 @ SV23 ) )
        = $true )
      | ( ( outputs @ sK2_U @ bad )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[239]) ).

thf(269,plain,
    ! [SV1: $i,SV15: $i,SV10: $i] :
      ( ( ( ~ ( halts2 @ SV10 @ SV15 )
          | ~ ( program @ SV10 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV10 @ SV15 )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[240]) ).

thf(270,plain,
    ! [SV1: $i,SV16: $i] :
      ( ( ( ! [SY47: $i] :
              ~ ( halts2 @ SV16 @ SY47 ) )
        = $true )
      | ( ( ~ ( program @ SV16 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[241]) ).

thf(271,plain,
    ! [SV1: $i,SV17: $i,SV11: $i] :
      ( ( ( ~ ( program @ SV11 )
          | ( halts2 @ SV11 @ SV17 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV11 @ SV17 )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[242]) ).

thf(272,plain,
    ! [SV1: $i,SV18: $i] :
      ( ( ( ~ ( program @ SV18 ) )
        = $true )
      | ( ( ! [SY48: $i] : ( halts2 @ SV18 @ SY48 ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[243]) ).

thf(273,plain,
    ! [SV1: $i,SV24: $i,SV19: $i] :
      ( ( ( ~ ( halts2 @ SV19 @ SV24 )
          | ~ ( program @ SV19 )
          | ( halts3 @ SV1 @ SV19 @ SV24 ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[244]) ).

thf(274,plain,
    ! [SV1: $i,SV25: $i] :
      ( ( ( ! [SY51: $i] :
              ~ ( halts2 @ SV25 @ SY51 )
          | ~ ( program @ SV25 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[245]) ).

thf(275,plain,
    ! [SV1: $i,SV26: $i,SV20: $i] :
      ( ( ( ~ ( program @ SV20 )
          | ( halts2 @ SV20 @ SV26 )
          | ( halts3 @ SV1 @ SV20 @ SV26 ) )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[246]) ).

thf(276,plain,
    ! [SV1: $i,SV27: $i] :
      ( ( ( ~ ( program @ SV27 )
          | ! [SY52: $i] : ( halts2 @ SV27 @ SY52 ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[247]) ).

thf(277,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ( program @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[248]) ).

thf(278,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[248]) ).

thf(279,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[249]) ).

thf(280,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
              | ( program @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[250]) ).

thf(281,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( ( program @ ( sK6_Y @ SV3 ) )
              | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[250]) ).

thf(282,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[251]) ).

thf(283,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[252]) ).

thf(284,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[253]) ).

thf(285,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[254]) ).

thf(286,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( halts2 @ SV12 @ SV12 ) )
        = $true )
      | ( ( ~ ( program @ SV12 ) )
        = $true )
      | ( ( halts2 @ sK5_V @ SV12 )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[255]) ).

thf(287,plain,
    ! [SV21: $i] :
      ( ( ( ~ ( halts2 @ SV21 @ SV21 ) )
        = $true )
      | ( ( ~ ( program @ SV21 ) )
        = $true )
      | ( ( outputs @ sK5_V @ good )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[256]) ).

thf(288,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( program @ SV13 ) )
        = $true )
      | ( ( halts2 @ SV13 @ SV13 )
        = $true )
      | ( ( halts2 @ sK5_V @ SV13 )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[257]) ).

thf(289,plain,
    ! [SV22: $i] :
      ( ( ( ~ ( program @ SV22 ) )
        = $true )
      | ( ( halts2 @ SV22 @ SV22 )
        = $true )
      | ( ( outputs @ sK5_V @ bad )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[258]) ).

thf(290,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
              | ( program @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[259]) ).

thf(291,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[259]) ).

thf(292,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[260]) ).

thf(293,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
              | ( program @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[261]) ).

thf(294,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( ( program @ ( sK3_Y @ SV4 ) )
              | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[261]) ).

thf(295,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[262]) ).

thf(296,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[263]) ).

thf(297,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[264]) ).

thf(298,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[265]) ).

thf(299,plain,
    ! [SV8: $i] :
      ( ( ( halts2 @ sK2_U @ SV8 )
        = $false )
      | ( ( halts2 @ SV8 @ SV8 )
        = $false )
      | ( ( program @ SV8 )
        = $false )
      | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[266]) ).

thf(300,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( program @ SV14 ) )
        = $true )
      | ( ( halts2 @ SV14 @ SV14 )
        = $true )
      | ( ( halts2 @ sK2_U @ SV14 )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[267]) ).

thf(301,plain,
    ! [SV23: $i] :
      ( ( ( ~ ( program @ SV23 ) )
        = $true )
      | ( ( halts2 @ SV23 @ SV23 )
        = $true )
      | ( ( outputs @ sK2_U @ bad )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[268]) ).

thf(302,plain,
    ! [SV1: $i,SV15: $i,SV10: $i] :
      ( ( ( ~ ( halts2 @ SV10 @ SV15 ) )
        = $true )
      | ( ( ~ ( program @ SV10 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV10 @ SV15 )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[269]) ).

thf(303,plain,
    ! [SV1: $i,SV28: $i,SV16: $i] :
      ( ( ( ~ ( halts2 @ SV16 @ SV28 ) )
        = $true )
      | ( ( ~ ( program @ SV16 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[270]) ).

thf(304,plain,
    ! [SV1: $i,SV17: $i,SV11: $i] :
      ( ( ( ~ ( program @ SV11 ) )
        = $true )
      | ( ( halts2 @ SV11 @ SV17 )
        = $true )
      | ( ( halts3 @ SV1 @ SV11 @ SV17 )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[271]) ).

thf(305,plain,
    ! [SV1: $i,SV18: $i] :
      ( ( ( program @ SV18 )
        = $false )
      | ( ( ! [SY48: $i] : ( halts2 @ SV18 @ SY48 ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[272]) ).

thf(306,plain,
    ! [SV1: $i,SV24: $i,SV19: $i] :
      ( ( ( ~ ( halts2 @ SV19 @ SV24 )
          | ~ ( program @ SV19 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV19 @ SV24 )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[273]) ).

thf(307,plain,
    ! [SV1: $i,SV25: $i] :
      ( ( ( ! [SY51: $i] :
              ~ ( halts2 @ SV25 @ SY51 ) )
        = $true )
      | ( ( ~ ( program @ SV25 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[274]) ).

thf(308,plain,
    ! [SV1: $i,SV26: $i,SV20: $i] :
      ( ( ( ~ ( program @ SV20 )
          | ( halts2 @ SV20 @ SV26 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV20 @ SV26 )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[275]) ).

thf(309,plain,
    ! [SV1: $i,SV27: $i] :
      ( ( ( ~ ( program @ SV27 ) )
        = $true )
      | ( ( ! [SY52: $i] : ( halts2 @ SV27 @ SY52 ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[276]) ).

thf(310,plain,
    ! [SV3: $i] :
      ( ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ( program @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[277]) ).

thf(311,plain,
    ! [SV3: $i] :
      ( ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[278]) ).

thf(312,plain,
    ! [SV3: $i] :
      ( ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[279]) ).

thf(313,plain,
    ! [SV3: $i] :
      ( ( ( ( program @ ( sK6_Y @ SV3 ) )
          | ( program @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[280]) ).

thf(314,plain,
    ! [SV3: $i] :
      ( ( ( ( program @ ( sK6_Y @ SV3 ) )
          | ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[281]) ).

thf(315,plain,
    ! [SV3: $i] :
      ( ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[282]) ).

thf(316,plain,
    ! [SV3: $i] :
      ( ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[283]) ).

thf(317,plain,
    ! [SV3: $i] :
      ( ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( outputs @ SV3 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[284]) ).

thf(318,plain,
    ! [SV3: $i] :
      ( ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( outputs @ SV3 @ bad ) )
        = $true )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[285]) ).

thf(319,plain,
    ! [SV12: $i] :
      ( ( ( halts2 @ SV12 @ SV12 )
        = $false )
      | ( ( ~ ( program @ SV12 ) )
        = $true )
      | ( ( halts2 @ sK5_V @ SV12 )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[286]) ).

thf(320,plain,
    ! [SV21: $i] :
      ( ( ( halts2 @ SV21 @ SV21 )
        = $false )
      | ( ( ~ ( program @ SV21 ) )
        = $true )
      | ( ( outputs @ sK5_V @ good )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[287]) ).

thf(321,plain,
    ! [SV13: $i] :
      ( ( ( program @ SV13 )
        = $false )
      | ( ( halts2 @ SV13 @ SV13 )
        = $true )
      | ( ( halts2 @ sK5_V @ SV13 )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[288]) ).

thf(322,plain,
    ! [SV22: $i] :
      ( ( ( program @ SV22 )
        = $false )
      | ( ( halts2 @ SV22 @ SV22 )
        = $true )
      | ( ( outputs @ sK5_V @ bad )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[289]) ).

thf(323,plain,
    ! [SV4: $i] :
      ( ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
          | ( program @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[290]) ).

thf(324,plain,
    ! [SV4: $i] :
      ( ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[291]) ).

thf(325,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[292]) ).

thf(326,plain,
    ! [SV4: $i] :
      ( ( ( ( program @ ( sK3_Y @ SV4 ) )
          | ( program @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[293]) ).

thf(327,plain,
    ! [SV4: $i] :
      ( ( ( ( program @ ( sK3_Y @ SV4 ) )
          | ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[294]) ).

thf(328,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[295]) ).

thf(329,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[296]) ).

thf(330,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( outputs @ SV4 @ good ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[297]) ).

thf(331,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( outputs @ SV4 @ bad ) )
        = $true )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[298]) ).

thf(332,plain,
    ! [SV14: $i] :
      ( ( ( program @ SV14 )
        = $false )
      | ( ( halts2 @ SV14 @ SV14 )
        = $true )
      | ( ( halts2 @ sK2_U @ SV14 )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[300]) ).

thf(333,plain,
    ! [SV23: $i] :
      ( ( ( program @ SV23 )
        = $false )
      | ( ( halts2 @ SV23 @ SV23 )
        = $true )
      | ( ( outputs @ sK2_U @ bad )
        = $true )
      | ( sK4_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[301]) ).

thf(334,plain,
    ! [SV1: $i,SV15: $i,SV10: $i] :
      ( ( ( halts2 @ SV10 @ SV15 )
        = $false )
      | ( ( ~ ( program @ SV10 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV10 @ SV15 )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[302]) ).

thf(335,plain,
    ! [SV1: $i,SV28: $i,SV16: $i] :
      ( ( ( halts2 @ SV16 @ SV28 )
        = $false )
      | ( ( ~ ( program @ SV16 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[303]) ).

thf(336,plain,
    ! [SV1: $i,SV17: $i,SV11: $i] :
      ( ( ( program @ SV11 )
        = $false )
      | ( ( halts2 @ SV11 @ SV17 )
        = $true )
      | ( ( halts3 @ SV1 @ SV11 @ SV17 )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[304]) ).

thf(337,plain,
    ! [SV1: $i,SV29: $i,SV18: $i] :
      ( ( ( halts2 @ SV18 @ SV29 )
        = $true )
      | ( ( program @ SV18 )
        = $false )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[305]) ).

thf(338,plain,
    ! [SV1: $i,SV24: $i,SV19: $i] :
      ( ( ( ~ ( halts2 @ SV19 @ SV24 ) )
        = $true )
      | ( ( ~ ( program @ SV19 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV19 @ SV24 )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[306]) ).

thf(339,plain,
    ! [SV1: $i,SV30: $i,SV25: $i] :
      ( ( ( ~ ( halts2 @ SV25 @ SV30 ) )
        = $true )
      | ( ( ~ ( program @ SV25 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[307]) ).

thf(340,plain,
    ! [SV1: $i,SV26: $i,SV20: $i] :
      ( ( ( ~ ( program @ SV20 ) )
        = $true )
      | ( ( halts2 @ SV20 @ SV26 )
        = $true )
      | ( ( halts3 @ SV1 @ SV20 @ SV26 )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[308]) ).

thf(341,plain,
    ! [SV1: $i,SV27: $i] :
      ( ( ( program @ SV27 )
        = $false )
      | ( ( ! [SY52: $i] : ( halts2 @ SV27 @ SY52 ) )
        = $true )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[309]) ).

thf(342,plain,
    ! [SV3: $i] :
      ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[310]) ).

thf(343,plain,
    ! [SV3: $i] :
      ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[311]) ).

thf(344,plain,
    ! [SV3: $i] :
      ( ( ( outputs @ SV3 @ bad )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[312]) ).

thf(345,plain,
    ! [SV3: $i] :
      ( ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[313]) ).

thf(346,plain,
    ! [SV3: $i] :
      ( ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[314]) ).

thf(347,plain,
    ! [SV3: $i] :
      ( ( ( outputs @ SV3 @ bad )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[315]) ).

thf(348,plain,
    ! [SV3: $i] :
      ( ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[316]) ).

thf(349,plain,
    ! [SV3: $i] :
      ( ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( ~ ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[317]) ).

thf(350,plain,
    ! [SV3: $i] :
      ( ( ( outputs @ SV3 @ bad )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[318]) ).

thf(351,plain,
    ! [SV12: $i] :
      ( ( ( program @ SV12 )
        = $false )
      | ( ( halts2 @ SV12 @ SV12 )
        = $false )
      | ( ( halts2 @ sK5_V @ SV12 )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[319]) ).

thf(352,plain,
    ! [SV21: $i] :
      ( ( ( program @ SV21 )
        = $false )
      | ( ( halts2 @ SV21 @ SV21 )
        = $false )
      | ( ( outputs @ sK5_V @ good )
        = $true )
      | ( sK7_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[320]) ).

thf(353,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[323]) ).

thf(354,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[324]) ).

thf(355,plain,
    ! [SV4: $i] :
      ( ( ( outputs @ SV4 @ bad )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[325]) ).

thf(356,plain,
    ! [SV4: $i] :
      ( ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[326]) ).

thf(357,plain,
    ! [SV4: $i] :
      ( ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[327]) ).

thf(358,plain,
    ! [SV4: $i] :
      ( ( ( outputs @ SV4 @ bad )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[328]) ).

thf(359,plain,
    ! [SV4: $i] :
      ( ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[329]) ).

thf(360,plain,
    ! [SV4: $i] :
      ( ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( ~ ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[330]) ).

thf(361,plain,
    ! [SV4: $i] :
      ( ( ( outputs @ SV4 @ bad )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[331]) ).

thf(362,plain,
    ! [SV1: $i,SV15: $i,SV10: $i] :
      ( ( ( program @ SV10 )
        = $false )
      | ( ( halts2 @ SV10 @ SV15 )
        = $false )
      | ( ( halts3 @ SV1 @ SV10 @ SV15 )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[334]) ).

thf(363,plain,
    ! [SV1: $i,SV28: $i,SV16: $i] :
      ( ( ( program @ SV16 )
        = $false )
      | ( ( halts2 @ SV16 @ SV28 )
        = $false )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( program @ ( sK8_Y @ SV1 ) )
        = $true )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[335]) ).

thf(364,plain,
    ! [SV1: $i,SV24: $i,SV19: $i] :
      ( ( ( halts2 @ SV19 @ SV24 )
        = $false )
      | ( ( ~ ( program @ SV19 ) )
        = $true )
      | ( ( halts3 @ SV1 @ SV19 @ SV24 )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[338]) ).

thf(365,plain,
    ! [SV1: $i,SV30: $i,SV25: $i] :
      ( ( ( halts2 @ SV25 @ SV30 )
        = $false )
      | ( ( ~ ( program @ SV25 ) )
        = $true )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[339]) ).

thf(366,plain,
    ! [SV1: $i,SV26: $i,SV20: $i] :
      ( ( ( program @ SV20 )
        = $false )
      | ( ( halts2 @ SV20 @ SV26 )
        = $true )
      | ( ( halts3 @ SV1 @ SV20 @ SV26 )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[340]) ).

thf(367,plain,
    ! [SV1: $i,SV31: $i,SV27: $i] :
      ( ( ( halts2 @ SV27 @ SV31 )
        = $true )
      | ( ( program @ SV27 )
        = $false )
      | ( ( outputs @ SV1 @ bad )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[341]) ).

thf(368,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[342]) ).

thf(369,plain,
    ! [SV3: $i] :
      ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[343]) ).

thf(370,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ bad )
        = $false )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[344]) ).

thf(371,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[345]) ).

thf(372,plain,
    ! [SV3: $i] :
      ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[346]) ).

thf(373,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ bad )
        = $false )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[347]) ).

thf(374,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ good )
        = $false )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[348]) ).

thf(375,plain,
    ! [SV3: $i] :
      ( ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( ~ ( program @ SV3 ) )
        = $true )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[349]) ).

thf(376,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( outputs @ SV3 @ bad )
        = $false )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[350]) ).

thf(377,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[353]) ).

thf(378,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[354]) ).

thf(379,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ bad )
        = $false )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[355]) ).

thf(380,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[356]) ).

thf(381,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[357]) ).

thf(382,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ bad )
        = $false )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[358]) ).

thf(383,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ good )
        = $false )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[359]) ).

thf(384,plain,
    ! [SV4: $i] :
      ( ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( ~ ( program @ SV4 ) )
        = $true )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[360]) ).

thf(385,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( outputs @ SV4 @ bad )
        = $false )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[361]) ).

thf(386,plain,
    ! [SV1: $i,SV24: $i,SV19: $i] :
      ( ( ( program @ SV19 )
        = $false )
      | ( ( halts2 @ SV19 @ SV24 )
        = $false )
      | ( ( halts3 @ SV1 @ SV19 @ SV24 )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[364]) ).

thf(387,plain,
    ! [SV1: $i,SV30: $i,SV25: $i] :
      ( ( ( program @ SV25 )
        = $false )
      | ( ( halts2 @ SV25 @ SV30 )
        = $false )
      | ( ( outputs @ SV1 @ good )
        = $true )
      | ( ( decides @ SV1 @ ( sK8_Y @ SV1 ) @ ( sK9_SY31 @ SV1 ) )
        = $false )
      | ( ( program @ SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[365]) ).

thf(388,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[369]) ).

thf(389,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( program @ ( sK6_Y @ SV3 ) )
        = $true )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[372]) ).

thf(390,plain,
    ! [SV3: $i] :
      ( ( ( program @ SV3 )
        = $false )
      | ( ( outputs @ SV3 @ good )
        = $false )
      | ( ( halts3 @ SV3 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( ( halts2 @ ( sK6_Y @ SV3 ) @ ( sK6_Y @ SV3 ) )
        = $false )
      | ( sK7_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[375]) ).

thf(391,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[378]) ).

thf(392,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( program @ ( sK3_Y @ SV4 ) )
        = $true )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[381]) ).

thf(393,plain,
    ! [SV4: $i] :
      ( ( ( program @ SV4 )
        = $false )
      | ( ( outputs @ SV4 @ good )
        = $false )
      | ( ( halts2 @ SV4 @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( ( halts2 @ ( sK3_Y @ SV4 ) @ ( sK3_Y @ SV4 ) )
        = $false )
      | ( sK4_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[384]) ).

thf(394,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[50,393,392,391,390,389,388,387,386,385,383,382,380,379,377,376,374,373,371,370,368,367,366,363,362,352,351,337,336,333,332,322,321,299,166,146,127,102,96,92,88]) ).

thf(395,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[394]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COM003+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Thu Jun 16 18:36:41 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.36  
% 0.14/0.36   No.of.Axioms: 4
% 0.14/0.36  
% 0.14/0.36   Length.of.Defs: 0
% 0.14/0.36  
% 0.14/0.36   Contains.Choice.Funs: false
% 0.14/0.36  (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full)......................
% 0.47/0.64  
% 0.47/0.64  ********************************
% 0.47/0.64  *   All subproblems solved!    *
% 0.47/0.64  ********************************
% 0.47/0.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:394,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.54/0.73  
% 0.54/0.73  %**** Beginning of derivation protocol ****
% 0.54/0.73  % SZS output start CNFRefutation
% See solution above
% 0.54/0.73  
% 0.54/0.73  %**** End of derivation protocol ****
% 0.54/0.73  %**** no. of clauses in derivation: 395 ****
% 0.54/0.73  %**** clause counter: 394 ****
% 0.54/0.73  
% 0.54/0.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:394,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------