TSTP Solution File: SEV232^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV232^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n032.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 : Tue Jul 19 17:35:48 EDT 2022

% Result   : Theorem 0.14s 0.35s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  119 (  19 unt;  10 typ;   0 def)
%            Number of atoms       : 1314 ( 335 equ;   0 cnn)
%            Maximal formula atoms :    6 (  12 avg)
%            Number of connectives : 1879 ( 490   ~; 478   |;  12   &; 875   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  747 ( 747   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   2 con; 0-3 aty)
%            Number of variables   :  284 (  18   ^ 266   !;   0   ?; 284   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c0,type,
    c0: ( $i > $o ) > $o ).

thf(tp_cS,type,
    cS: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).

thf(tp_sK1_SV1,type,
    sK1_SV1: ( $i > $o ) > $o ).

thf(tp_sK2_SY10,type,
    sK2_SY10: ( ( $i > $o ) > $o ) > $o ).

thf(tp_sK3_SY12,type,
    sK3_SY12: ( ( $i > $o ) > $o ) > $o ).

thf(tp_sK4_SY14,type,
    sK4_SY14: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).

thf(tp_sK5_SY12,type,
    sK5_SY12: ( ( $i > $o ) > $o ) > $o ).

thf(tp_sK6_SY12,type,
    sK6_SY12: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(tp_sK7_SY18,type,
    sK7_SY18: ( ( ( $i > $o ) > $o ) > $o ) > ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).

thf(tp_sK8_SY19,type,
    sK8_SY19: ( ( ( $i > $o ) > $o ) > $o ) > ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).

thf(1,conjecture,
    ( ( ^ [N: ( $i > $o ) > $o] :
        ! [P: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( P @ c0 )
            & ! [X: ( $i > $o ) > $o] :
                ( ( P @ X )
               => ( P @ ( cS @ X ) ) ) )
         => ( P @ N ) ) )
    = ( ^ [Xx: ( $i > $o ) > $o] :
        ! [S0: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( S0 @ c0 )
            & ! [X: ( $i > $o ) > $o] :
                ( ( S0 @ X )
               => ( S0 @ ( cS @ X ) ) ) )
         => ( S0 @ Xx ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6007_pme) ).

thf(2,negated_conjecture,
    ( ( ( ^ [N: ( $i > $o ) > $o] :
          ! [P: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( P @ c0 )
              & ! [X: ( $i > $o ) > $o] :
                  ( ( P @ X )
                 => ( P @ ( cS @ X ) ) ) )
           => ( P @ N ) ) )
      = ( ^ [Xx: ( $i > $o ) > $o] :
          ! [S0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( S0 @ c0 )
              & ! [X: ( $i > $o ) > $o] :
                  ( ( S0 @ X )
                 => ( S0 @ ( cS @ X ) ) ) )
           => ( S0 @ Xx ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ^ [N: ( $i > $o ) > $o] :
          ! [P: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( P @ c0 )
              & ! [X: ( $i > $o ) > $o] :
                  ( ( P @ X )
                 => ( P @ ( cS @ X ) ) ) )
           => ( P @ N ) ) )
      = ( ^ [Xx: ( $i > $o ) > $o] :
          ! [S0: ( ( $i > $o ) > $o ) > $o] :
            ( ( ( S0 @ c0 )
              & ! [X: ( $i > $o ) > $o] :
                  ( ( S0 @ X )
                 => ( S0 @ ( cS @ X ) ) ) )
           => ( S0 @ Xx ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ( ^ [N: ( $i > $o ) > $o] :
            ! [P: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( P @ c0 )
                & ! [X: ( $i > $o ) > $o] :
                    ( ( P @ X )
                   => ( P @ ( cS @ X ) ) ) )
             => ( P @ N ) ) )
       != ( ^ [Xx: ( $i > $o ) > $o] :
            ! [S0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( S0 @ c0 )
                & ! [X: ( $i > $o ) > $o] :
                    ( ( S0 @ X )
                   => ( S0 @ ( cS @ X ) ) ) )
             => ( S0 @ Xx ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ( ( ^ [N: ( $i > $o ) > $o] :
            ! [P: ( ( $i > $o ) > $o ) > $o] :
              ( ( ! [X: ( $i > $o ) > $o] :
                    ( ( P @ X )
                   => ( P @ ( cS @ X ) ) )
                & ( P @ c0 ) )
             => ( P @ N ) ) )
       != ( ^ [Xx: ( $i > $o ) > $o] :
            ! [S0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ! [X: ( $i > $o ) > $o] :
                    ( ( S0 @ X )
                   => ( S0 @ ( cS @ X ) ) )
                & ( S0 @ c0 ) )
             => ( S0 @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ( ( ^ [N: ( $i > $o ) > $o] :
            ! [P: ( ( $i > $o ) > $o ) > $o] :
              ( ( ! [X: ( $i > $o ) > $o] :
                    ( ( P @ X )
                   => ( P @ ( cS @ X ) ) )
                & ( P @ c0 ) )
             => ( P @ N ) ) )
       != ( ^ [Xx: ( $i > $o ) > $o] :
            ! [S0: ( ( $i > $o ) > $o ) > $o] :
              ( ( ! [X: ( $i > $o ) > $o] :
                    ( ( S0 @ X )
                   => ( S0 @ ( cS @ X ) ) )
                & ( S0 @ c0 ) )
             => ( S0 @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ( ( ^ [SX0: ( $i > $o ) > $o] :
            ! [SX1: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SX1 @ SX2 )
                          | ( SX1 @ ( cS @ SX2 ) ) )
                    | ~ ( SX1 @ c0 ) )
              | ( SX1 @ SX0 ) ) )
       != ( ^ [SX0: ( $i > $o ) > $o] :
            ! [SX1: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SX1 @ SX2 )
                          | ( SX1 @ ( cS @ SX2 ) ) )
                    | ~ ( SX1 @ c0 ) )
              | ( SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( ^ [SX0: ( $i > $o ) > $o] :
          ! [SX1: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SX1 @ SX2 )
                        | ( SX1 @ ( cS @ SX2 ) ) )
                  | ~ ( SX1 @ c0 ) )
            | ( SX1 @ SX0 ) ) )
      = ( ^ [SX0: ( $i > $o ) > $o] :
          ! [SX1: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SX1 @ SX2 )
                        | ( SX1 @ ( cS @ SX2 ) ) )
                  | ~ ( SX1 @ c0 ) )
            | ( SX1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SV1: ( $i > $o ) > $o] :
          ( ( ! [SY6: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY6 @ SX2 )
                            | ( SY6 @ ( cS @ SX2 ) ) )
                      | ~ ( SY6 @ c0 ) )
                | ( SY6 @ SV1 ) ) )
          = ( ! [SY8: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY8 @ SX2 )
                            | ( SY8 @ ( cS @ SX2 ) ) )
                      | ~ ( SY8 @ c0 ) )
                | ( SY8 @ SV1 ) ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( ^ [SX0: ( $i > $o ) > $o] :
          ! [SX1: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SX1 @ SX2 )
                        | ( SX1 @ ( cS @ SX2 ) ) )
                  | ~ ( SX1 @ c0 ) )
            | ( SX1 @ SX0 ) ) )
      = ( ^ [SX0: ( $i > $o ) > $o] :
          ! [SX1: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SX1 @ SX2 )
                        | ( SX1 @ ( cS @ SX2 ) ) )
                  | ~ ( SX1 @ c0 ) )
            | ( SX1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ( ! [SY10: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY10 @ SX2 )
                        | ( SY10 @ ( cS @ SX2 ) ) )
                  | ~ ( SY10 @ c0 ) )
            | ( SY10 @ sK1_SV1 ) ) )
      = ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY12 @ SX2 )
                        | ( SY12 @ ( cS @ SX2 ) ) )
                  | ~ ( SY12 @ c0 ) )
            | ( SY12 @ sK1_SV1 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[9]) ).

thf(12,plain,
    ( ( ~ ( ! [SY10: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY10 @ SX2 )
                          | ( SY10 @ ( cS @ SX2 ) ) )
                    | ~ ( SY10 @ c0 ) )
              | ( SY10 @ sK1_SV1 ) )
          | ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      | ~ ( ~ ! [SY10: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY10 @ SX2 )
                            | ( SY10 @ ( cS @ SX2 ) ) )
                      | ~ ( SY10 @ c0 ) )
                | ( SY10 @ sK1_SV1 ) )
          | ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY12 @ SX2 )
                            | ( SY12 @ ( cS @ SX2 ) ) )
                      | ~ ( SY12 @ c0 ) )
                | ( SY12 @ sK1_SV1 ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ( ! [SY10: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY10 @ SX2 )
                        | ( SY10 @ ( cS @ SX2 ) ) )
                  | ~ ( SY10 @ c0 ) )
            | ( SY10 @ sK1_SV1 ) ) )
      = ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY12 @ SX2 )
                        | ( SY12 @ ( cS @ SX2 ) ) )
                  | ~ ( SY12 @ c0 ) )
            | ( SY12 @ sK1_SV1 ) ) ) )
    = $false ),
    inference(extcnf_equal_neg,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( ! [SY10: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY10 @ SX2 )
                          | ( SY10 @ ( cS @ SX2 ) ) )
                    | ~ ( SY10 @ c0 ) )
              | ( SY10 @ sK1_SV1 ) )
          | ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ~ ( ~ ! [SY10: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY10 @ SX2 )
                            | ( SY10 @ ( cS @ SX2 ) ) )
                      | ~ ( SY10 @ c0 ) )
                | ( SY10 @ sK1_SV1 ) )
          | ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY12 @ SX2 )
                            | ( SY12 @ ( cS @ SX2 ) ) )
                      | ~ ( SY12 @ c0 ) )
                | ( SY12 @ sK1_SV1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ! [SY10: ( ( $i > $o ) > $o ) > $o] :
          ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                      ( ~ ( SY10 @ SX2 )
                      | ( SY10 @ ( cS @ SX2 ) ) )
                | ~ ( SY10 @ c0 ) )
          | ( SY10 @ sK1_SV1 ) )
      | ! [SY12: ( ( $i > $o ) > $o ) > $o] :
          ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                      ( ~ ( SY12 @ SX2 )
                      | ( SY12 @ ( cS @ SX2 ) ) )
                | ~ ( SY12 @ c0 ) )
          | ( SY12 @ sK1_SV1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ! [SY10: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY10 @ SX2 )
                        | ( SY10 @ ( cS @ SX2 ) ) )
                  | ~ ( SY10 @ c0 ) )
            | ( SY10 @ sK1_SV1 ) )
      | ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY12 @ SX2 )
                        | ( SY12 @ ( cS @ SX2 ) ) )
                  | ~ ( SY12 @ c0 ) )
            | ( SY12 @ sK1_SV1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ( ! [SY10: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY10 @ SX2 )
                        | ( SY10 @ ( cS @ SX2 ) ) )
                  | ~ ( SY10 @ c0 ) )
            | ( SY10 @ sK1_SV1 ) ) )
      = $true )
    | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY12 @ SX2 )
                        | ( SY12 @ ( cS @ SX2 ) ) )
                  | ~ ( SY12 @ c0 ) )
            | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ( ~ ! [SY10: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY10 @ SX2 )
                          | ( SY10 @ ( cS @ SX2 ) ) )
                    | ~ ( SY10 @ c0 ) )
              | ( SY10 @ sK1_SV1 ) ) )
      = $true )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY14: ( $i > $o ) > $o] :
                      ( ~ ( SV2 @ SY14 )
                      | ( SV2 @ ( cS @ SY14 ) ) )
                | ~ ( SV2 @ c0 ) )
          | ( SV2 @ sK1_SV1 ) )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ( ! [SY10: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY10 @ SX2 )
                        | ( SY10 @ ( cS @ SX2 ) ) )
                  | ~ ( SY10 @ c0 ) )
            | ( SY10 @ sK1_SV1 ) ) )
      = $false )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY14: ( $i > $o ) > $o] :
                      ( ~ ( SV2 @ SY14 )
                      | ( SV2 @ ( cS @ SY14 ) ) )
                | ~ ( SV2 @ c0 ) ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(23,plain,
    ( ( ( ~ ~ ( ~ ! [SY15: ( $i > $o ) > $o] :
                    ( ~ ( sK2_SY10 @ SY15 )
                    | ( sK2_SY10 @ ( cS @ SY15 ) ) )
              | ~ ( sK2_SY10 @ c0 ) )
        | ( sK2_SY10 @ sK1_SV1 ) )
      = $false )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[21]) ).

thf(24,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( ~ ! [SY14: ( $i > $o ) > $o] :
                    ( ~ ( SV2 @ SY14 )
                    | ( SV2 @ ( cS @ SY14 ) ) )
              | ~ ( SV2 @ c0 ) ) )
        = $false )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(25,plain,
    ( ( ( ~ ~ ( ~ ! [SY15: ( $i > $o ) > $o] :
                    ( ~ ( sK2_SY10 @ SY15 )
                    | ( sK2_SY10 @ ( cS @ SY15 ) ) )
              | ~ ( sK2_SY10 @ c0 ) ) )
      = $false )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ( sK2_SY10 @ sK1_SV1 )
      = $false )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(27,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ! [SY14: ( $i > $o ) > $o] :
                ( ~ ( SV2 @ SY14 )
                | ( SV2 @ ( cS @ SY14 ) ) )
          | ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(28,plain,
    ( ( ( ~ ( ~ ! [SY15: ( $i > $o ) > $o] :
                  ( ~ ( sK2_SY10 @ SY15 )
                  | ( sK2_SY10 @ ( cS @ SY15 ) ) )
            | ~ ( sK2_SY10 @ c0 ) ) )
      = $true )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(29,plain,
    ( ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY12 @ SX2 )
                        | ( SY12 @ ( cS @ SX2 ) ) )
                  | ~ ( SY12 @ c0 ) )
            | ( SY12 @ sK1_SV1 ) ) )
      = $false )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ! [SY14: ( $i > $o ) > $o] :
                ( ~ ( SV2 @ SY14 )
                | ( SV2 @ ( cS @ SY14 ) ) ) )
        = $true )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(31,plain,
    ( ( ( ~ ! [SY15: ( $i > $o ) > $o] :
              ( ~ ( sK2_SY10 @ SY15 )
              | ( sK2_SY10 @ ( cS @ SY15 ) ) )
        | ~ ( sK2_SY10 @ c0 ) )
      = $false )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ( ( ( ~ ~ ( ~ ! [SY16: ( $i > $o ) > $o] :
                    ( ~ ( sK3_SY12 @ SY16 )
                    | ( sK3_SY12 @ ( cS @ SY16 ) ) )
              | ~ ( sK3_SY12 @ c0 ) )
        | ( sK3_SY12 @ sK1_SV1 ) )
      = $false )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[29]) ).

thf(33,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ! [SY14: ( $i > $o ) > $o] :
              ( ~ ( SV2 @ SY14 )
              | ( SV2 @ ( cS @ SY14 ) ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(34,plain,
    ( ( ( ~ ! [SY15: ( $i > $o ) > $o] :
              ( ~ ( sK2_SY10 @ SY15 )
              | ( sK2_SY10 @ ( cS @ SY15 ) ) ) )
      = $false )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(35,plain,
    ( ( ( ~ ( sK2_SY10 @ c0 ) )
      = $false )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(36,plain,
    ( ( ( ~ ~ ( ~ ! [SY16: ( $i > $o ) > $o] :
                    ( ~ ( sK3_SY12 @ SY16 )
                    | ( sK3_SY12 @ ( cS @ SY16 ) ) )
              | ~ ( sK3_SY12 @ c0 ) ) )
      = $false )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(37,plain,
    ( ( ( sK3_SY12 @ sK1_SV1 )
      = $false )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( SV2 @ ( sK4_SY14 @ SV2 ) )
          | ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[33]) ).

thf(39,plain,
    ( ( ( ! [SY15: ( $i > $o ) > $o] :
            ( ~ ( sK2_SY10 @ SY15 )
            | ( sK2_SY10 @ ( cS @ SY15 ) ) ) )
      = $true )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(40,plain,
    ( ( ( sK2_SY10 @ c0 )
      = $true )
    | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ( ~ ( ~ ! [SY16: ( $i > $o ) > $o] :
                  ( ~ ( sK3_SY12 @ SY16 )
                  | ( sK3_SY12 @ ( cS @ SY16 ) ) )
            | ~ ( sK3_SY12 @ c0 ) ) )
      = $true )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( SV2 @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(44,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK2_SY10 @ SV3 )
          | ( sK2_SY10 @ ( cS @ SV3 ) ) )
        = $true )
      | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY12 @ SX2 )
                            | ( SY12 @ ( cS @ SX2 ) ) )
                      | ~ ( SY12 @ c0 ) )
                | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(45,plain,
    ( ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
            ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                        ( ~ ( SY12 @ SX2 )
                        | ( SY12 @ ( cS @ SX2 ) ) )
                  | ~ ( SY12 @ c0 ) )
            | ( SY12 @ sK1_SV1 ) ) )
      = $false )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(46,plain,
    ( ( ( ~ ! [SY16: ( $i > $o ) > $o] :
              ( ~ ( sK3_SY12 @ SY16 )
              | ( sK3_SY12 @ ( cS @ SY16 ) ) )
        | ~ ( sK3_SY12 @ c0 ) )
      = $false )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(47,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV2 @ c0 )
        = $false )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(49,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK2_SY10 @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY12 @ SX2 )
                            | ( SY12 @ ( cS @ SX2 ) ) )
                      | ~ ( SY12 @ c0 ) )
                | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(50,plain,
    ( ( ( ~ ~ ( ~ ! [SY17: ( $i > $o ) > $o] :
                    ( ~ ( sK5_SY12 @ SY17 )
                    | ( sK5_SY12 @ ( cS @ SY17 ) ) )
              | ~ ( sK5_SY12 @ c0 ) )
        | ( sK5_SY12 @ sK1_SV1 ) )
      = $false )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[45]) ).

thf(51,plain,
    ( ( ( ~ ! [SY16: ( $i > $o ) > $o] :
              ( ~ ( sK3_SY12 @ SY16 )
              | ( sK3_SY12 @ ( cS @ SY16 ) ) ) )
      = $false )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(52,plain,
    ( ( ( ~ ( sK3_SY12 @ c0 ) )
      = $false )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(53,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV2 @ c0 )
        = $false )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(54,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY18: ( $i > $o ) > $o] :
                      ( ~ ( SV4 @ SY18 )
                      | ( SV4 @ ( cS @ SY18 ) ) )
                | ~ ( SV4 @ c0 ) )
          | ( SV4 @ sK1_SV1 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(55,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( sK2_SY10 @ SV3 )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( ~ ! [SY12: ( ( $i > $o ) > $o ) > $o] :
                ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                            ( ~ ( SY12 @ SX2 )
                            | ( SY12 @ ( cS @ SX2 ) ) )
                      | ~ ( SY12 @ c0 ) )
                | ( SY12 @ sK1_SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(56,plain,
    ( ( ( ~ ~ ( ~ ! [SY17: ( $i > $o ) > $o] :
                    ( ~ ( sK5_SY12 @ SY17 )
                    | ( sK5_SY12 @ ( cS @ SY17 ) ) )
              | ~ ( sK5_SY12 @ c0 ) ) )
      = $false )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(57,plain,
    ( ( ( sK5_SY12 @ sK1_SV1 )
      = $false )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(58,plain,
    ( ( ( ! [SY16: ( $i > $o ) > $o] :
            ( ~ ( sK3_SY12 @ SY16 )
            | ( sK3_SY12 @ ( cS @ SY16 ) ) ) )
      = $true )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(59,plain,
    ( ( ( sK3_SY12 @ c0 )
      = $true )
    | ( ( sK2_SY10 @ sK1_SV1 )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(60,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY19: ( $i > $o ) > $o] :
                      ( ~ ( SV5 @ SY19 )
                      | ( SV5 @ ( cS @ SY19 ) ) )
                | ~ ( SV5 @ c0 ) )
          | ( SV5 @ sK1_SV1 ) )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(61,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY18: ( $i > $o ) > $o] :
                      ( ~ ( SV4 @ SY18 )
                      | ( SV4 @ ( cS @ SY18 ) ) )
                | ~ ( SV4 @ c0 ) ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[54]) ).

thf(62,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ! [SY12: ( ( $i > $o ) > $o ) > $o] :
              ( ~ ~ ( ~ ! [SX2: ( $i > $o ) > $o] :
                          ( ~ ( SY12 @ SX2 )
                          | ( SY12 @ ( cS @ SX2 ) ) )
                    | ~ ( SY12 @ c0 ) )
              | ( SY12 @ sK1_SV1 ) ) )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(63,plain,
    ( ( ( ~ ( ~ ! [SY17: ( $i > $o ) > $o] :
                  ( ~ ( sK5_SY12 @ SY17 )
                  | ( sK5_SY12 @ ( cS @ SY17 ) ) )
            | ~ ( sK5_SY12 @ c0 ) ) )
      = $true )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(64,plain,
    ! [SV6: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK3_SY12 @ SV6 )
          | ( sK3_SY12 @ ( cS @ SV6 ) ) )
        = $true )
      | ( ( sK2_SY10 @ sK1_SV1 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(65,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY19: ( $i > $o ) > $o] :
                      ( ~ ( SV5 @ SY19 )
                      | ( SV5 @ ( cS @ SY19 ) ) )
                | ~ ( SV5 @ c0 ) ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(66,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( ~ ! [SY18: ( $i > $o ) > $o] :
                    ( ~ ( SV4 @ SY18 )
                    | ( SV4 @ ( cS @ SY18 ) ) )
              | ~ ( SV4 @ c0 ) ) )
        = $false )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(67,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY20: ( $i > $o ) > $o] :
                      ( ~ ( sK6_SY12 @ SV3 @ SY20 )
                      | ( sK6_SY12 @ SV3 @ ( cS @ SY20 ) ) )
                | ~ ( sK6_SY12 @ SV3 @ c0 ) )
          | ( sK6_SY12 @ SV3 @ sK1_SV1 ) )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[62]) ).

thf(68,plain,
    ( ( ( ~ ! [SY17: ( $i > $o ) > $o] :
              ( ~ ( sK5_SY12 @ SY17 )
              | ( sK5_SY12 @ ( cS @ SY17 ) ) )
        | ~ ( sK5_SY12 @ c0 ) )
      = $false )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(69,plain,
    ! [SV6: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK3_SY12 @ SV6 ) )
        = $true )
      | ( ( sK3_SY12 @ ( cS @ SV6 ) )
        = $true )
      | ( ( sK2_SY10 @ sK1_SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(70,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( ~ ! [SY19: ( $i > $o ) > $o] :
                    ( ~ ( SV5 @ SY19 )
                    | ( SV5 @ ( cS @ SY19 ) ) )
              | ~ ( SV5 @ c0 ) ) )
        = $false )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(71,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ! [SY18: ( $i > $o ) > $o] :
                ( ~ ( SV4 @ SY18 )
                | ( SV4 @ ( cS @ SY18 ) ) )
          | ~ ( SV4 @ c0 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[66]) ).

thf(72,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ~ ( ~ ! [SY20: ( $i > $o ) > $o] :
                      ( ~ ( sK6_SY12 @ SV3 @ SY20 )
                      | ( sK6_SY12 @ SV3 @ ( cS @ SY20 ) ) )
                | ~ ( sK6_SY12 @ SV3 @ c0 ) ) )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(73,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( sK6_SY12 @ SV3 @ sK1_SV1 )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(74,plain,
    ( ( ( ~ ! [SY17: ( $i > $o ) > $o] :
              ( ~ ( sK5_SY12 @ SY17 )
              | ( sK5_SY12 @ ( cS @ SY17 ) ) ) )
      = $false )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[68]) ).

thf(75,plain,
    ( ( ( ~ ( sK5_SY12 @ c0 ) )
      = $false )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[68]) ).

thf(76,plain,
    ! [SV6: ( $i > $o ) > $o] :
      ( ( ( sK3_SY12 @ SV6 )
        = $false )
      | ( ( sK3_SY12 @ ( cS @ SV6 ) )
        = $true )
      | ( ( sK2_SY10 @ sK1_SV1 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(77,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ! [SY19: ( $i > $o ) > $o] :
                ( ~ ( SV5 @ SY19 )
                | ( SV5 @ ( cS @ SY19 ) ) )
          | ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(78,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ! [SY18: ( $i > $o ) > $o] :
                ( ~ ( SV4 @ SY18 )
                | ( SV4 @ ( cS @ SY18 ) ) ) )
        = $true )
      | ( ( ~ ( SV4 @ c0 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(79,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ( ~ ! [SY20: ( $i > $o ) > $o] :
                    ( ~ ( sK6_SY12 @ SV3 @ SY20 )
                    | ( sK6_SY12 @ SV3 @ ( cS @ SY20 ) ) )
              | ~ ( sK6_SY12 @ SV3 @ c0 ) ) )
        = $true )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[72]) ).

thf(80,plain,
    ( ( ( ! [SY17: ( $i > $o ) > $o] :
            ( ~ ( sK5_SY12 @ SY17 )
            | ( sK5_SY12 @ ( cS @ SY17 ) ) ) )
      = $true )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[74]) ).

thf(81,plain,
    ( ( ( sK5_SY12 @ c0 )
      = $true )
    | ( ( sK2_SY10 @ c0 )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(82,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ! [SY19: ( $i > $o ) > $o] :
                ( ~ ( SV5 @ SY19 )
                | ( SV5 @ ( cS @ SY19 ) ) ) )
        = $true )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[77]) ).

thf(83,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ! [SY18: ( $i > $o ) > $o] :
              ( ~ ( SV4 @ SY18 )
              | ( SV4 @ ( cS @ SY18 ) ) ) )
        = $false )
      | ( ( ~ ( SV4 @ c0 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[78]) ).

thf(84,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ! [SY20: ( $i > $o ) > $o] :
                ( ~ ( sK6_SY12 @ SV3 @ SY20 )
                | ( sK6_SY12 @ SV3 @ ( cS @ SY20 ) ) )
          | ~ ( sK6_SY12 @ SV3 @ c0 ) )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(85,plain,
    ! [SV7: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK5_SY12 @ SV7 )
          | ( sK5_SY12 @ ( cS @ SV7 ) ) )
        = $true )
      | ( ( sK2_SY10 @ c0 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(86,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ! [SY19: ( $i > $o ) > $o] :
              ( ~ ( SV5 @ SY19 )
              | ( SV5 @ ( cS @ SY19 ) ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(87,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( SV4 @ ( sK7_SY18 @ SV2 @ SV4 ) )
          | ( SV4 @ ( cS @ ( sK7_SY18 @ SV2 @ SV4 ) ) ) )
        = $false )
      | ( ( ~ ( SV4 @ c0 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[83]) ).

thf(88,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ! [SY20: ( $i > $o ) > $o] :
                ( ~ ( sK6_SY12 @ SV3 @ SY20 )
                | ( sK6_SY12 @ SV3 @ ( cS @ SY20 ) ) ) )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[84]) ).

thf(89,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK6_SY12 @ SV3 @ c0 ) )
        = $false )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[84]) ).

thf(90,plain,
    ! [SV7: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK5_SY12 @ SV7 ) )
        = $true )
      | ( ( sK5_SY12 @ ( cS @ SV7 ) )
        = $true )
      | ( ( sK2_SY10 @ c0 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(91,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( SV5 @ ( sK8_SY19 @ SV2 @ SV5 ) )
          | ( SV5 @ ( cS @ ( sK8_SY19 @ SV2 @ SV5 ) ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[86]) ).

thf(92,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( SV4 @ ( sK7_SY18 @ SV2 @ SV4 ) ) )
        = $false )
      | ( ( ~ ( SV4 @ c0 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[87]) ).

thf(93,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV4 @ ( cS @ ( sK7_SY18 @ SV2 @ SV4 ) ) )
        = $false )
      | ( ( ~ ( SV4 @ c0 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[87]) ).

thf(94,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( ! [SY20: ( $i > $o ) > $o] :
              ( ~ ( sK6_SY12 @ SV3 @ SY20 )
              | ( sK6_SY12 @ SV3 @ ( cS @ SY20 ) ) ) )
        = $true )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[88]) ).

thf(95,plain,
    ! [SV3: ( $i > $o ) > $o] :
      ( ( ( sK6_SY12 @ SV3 @ c0 )
        = $true )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(96,plain,
    ! [SV7: ( $i > $o ) > $o] :
      ( ( ( sK5_SY12 @ SV7 )
        = $false )
      | ( ( sK5_SY12 @ ( cS @ SV7 ) )
        = $true )
      | ( ( sK2_SY10 @ c0 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(97,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( ~ ( SV5 @ ( sK8_SY19 @ SV2 @ SV5 ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(98,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV5 @ ( cS @ ( sK8_SY19 @ SV2 @ SV5 ) ) )
        = $false )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[91]) ).

thf(99,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV4 @ ( sK7_SY18 @ SV2 @ SV4 ) )
        = $true )
      | ( ( ~ ( SV4 @ c0 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[92]) ).

thf(100,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV4 @ c0 )
        = $false )
      | ( ( SV4 @ ( cS @ ( sK7_SY18 @ SV2 @ SV4 ) ) )
        = $false )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[93]) ).

thf(101,plain,
    ! [SV8: ( $i > $o ) > $o,SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK6_SY12 @ SV3 @ SV8 )
          | ( sK6_SY12 @ SV3 @ ( cS @ SV8 ) ) )
        = $true )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(102,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV5 @ ( sK8_SY19 @ SV2 @ SV5 ) )
        = $true )
      | ( ( ~ ( SV5 @ c0 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[97]) ).

thf(103,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV5 @ c0 )
        = $false )
      | ( ( SV5 @ ( cS @ ( sK8_SY19 @ SV2 @ SV5 ) ) )
        = $false )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(104,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV4 @ c0 )
        = $false )
      | ( ( SV4 @ ( sK7_SY18 @ SV2 @ SV4 ) )
        = $true )
      | ( ( SV4 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( cS @ ( sK4_SY14 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(105,plain,
    ! [SV8: ( $i > $o ) > $o,SV3: ( $i > $o ) > $o] :
      ( ( ( ~ ( sK6_SY12 @ SV3 @ SV8 ) )
        = $true )
      | ( ( sK6_SY12 @ SV3 @ ( cS @ SV8 ) )
        = $true )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(106,plain,
    ! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
      ( ( ( SV5 @ c0 )
        = $false )
      | ( ( SV5 @ ( sK8_SY19 @ SV2 @ SV5 ) )
        = $true )
      | ( ( SV5 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ sK1_SV1 )
        = $true )
      | ( ( SV2 @ ( sK4_SY14 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[102]) ).

thf(107,plain,
    ! [SV8: ( $i > $o ) > $o,SV3: ( $i > $o ) > $o] :
      ( ( ( sK6_SY12 @ SV3 @ SV8 )
        = $false )
      | ( ( sK6_SY12 @ SV3 @ ( cS @ SV8 ) )
        = $true )
      | ( ( sK2_SY10 @ ( cS @ SV3 ) )
        = $true )
      | ( ( sK2_SY10 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(108,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[10,107,106,104,103,100,96,95,81,76,73,59,57,37,13]) ).

thf(109,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[108]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEV232^5 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.10  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 600
% 0.10/0.29  % DateTime : Tue Jun 28 14:41:27 EDT 2022
% 0.10/0.29  % CPUTime  : 
% 0.10/0.30  
% 0.10/0.30   No.of.Axioms: 0
% 0.10/0.30  
% 0.10/0.30   Length.of.Defs: 0
% 0.10/0.30  
% 0.10/0.30   Contains.Choice.Funs: false
% 0.10/0.30  (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.14/0.35  
% 0.14/0.35  ********************************
% 0.14/0.35  *   All subproblems solved!    *
% 0.14/0.35  ********************************
% 0.14/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:108,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.14/0.36  
% 0.14/0.36  %**** Beginning of derivation protocol ****
% 0.14/0.36  % SZS output start CNFRefutation
% See solution above
% 0.14/0.36  
% 0.14/0.36  %**** End of derivation protocol ****
% 0.14/0.36  %**** no. of clauses in derivation: 109 ****
% 0.14/0.36  %**** clause counter: 108 ****
% 0.14/0.36  
% 0.14/0.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:108,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------