TSTP Solution File: SYN474+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYN474+1 : TPTP v8.2.0. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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  : 300s
% DateTime : Tue May 21 08:12:19 EDT 2024

% Result   : Theorem 9.17s 3.33s
% Output   : Refutation 9.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   70
% Syntax   : Number of formulae    :   73 (   1 unt;  69 typ;   0 def)
%            Number of atoms       : 2143 (   0 equ;   0 cnn)
%            Maximal formula atoms :  714 ( 535 avg)
%            Number of connectives : 4193 ( 749   ~;1203   |; 597   &;1305   @)
%                                         (   0 <=>; 339  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  108 (  81 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   70 (  69 usr;  66 con; 0-1 aty)
%            Number of variables   :  339 (   0   ^ 339   !;   0   ?; 339   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hskp0_type,type,
    hskp0: $o ).

thf(ndr1_0_type,type,
    ndr1_0: $o ).

thf(c0_1_type,type,
    c0_1: $i > $o ).

thf(a898_type,type,
    a898: $i ).

thf(c1_1_type,type,
    c1_1: $i > $o ).

thf(c2_1_type,type,
    c2_1: $i > $o ).

thf(hskp1_type,type,
    hskp1: $o ).

thf(a899_type,type,
    a899: $i ).

thf(hskp2_type,type,
    hskp2: $o ).

thf(a901_type,type,
    a901: $i ).

thf(c3_1_type,type,
    c3_1: $i > $o ).

thf(hskp3_type,type,
    hskp3: $o ).

thf(a903_type,type,
    a903: $i ).

thf(hskp4_type,type,
    hskp4: $o ).

thf(a904_type,type,
    a904: $i ).

thf(hskp5_type,type,
    hskp5: $o ).

thf(a905_type,type,
    a905: $i ).

thf(hskp6_type,type,
    hskp6: $o ).

thf(a906_type,type,
    a906: $i ).

thf(hskp7_type,type,
    hskp7: $o ).

thf(a907_type,type,
    a907: $i ).

thf(hskp8_type,type,
    hskp8: $o ).

thf(a908_type,type,
    a908: $i ).

thf(hskp9_type,type,
    hskp9: $o ).

thf(a909_type,type,
    a909: $i ).

thf(hskp10_type,type,
    hskp10: $o ).

thf(a910_type,type,
    a910: $i ).

thf(hskp11_type,type,
    hskp11: $o ).

thf(a912_type,type,
    a912: $i ).

thf(hskp12_type,type,
    hskp12: $o ).

thf(a913_type,type,
    a913: $i ).

thf(hskp13_type,type,
    hskp13: $o ).

thf(a914_type,type,
    a914: $i ).

thf(hskp14_type,type,
    hskp14: $o ).

thf(a918_type,type,
    a918: $i ).

thf(hskp15_type,type,
    hskp15: $o ).

thf(a921_type,type,
    a921: $i ).

thf(hskp16_type,type,
    hskp16: $o ).

thf(a923_type,type,
    a923: $i ).

thf(hskp17_type,type,
    hskp17: $o ).

thf(a928_type,type,
    a928: $i ).

thf(hskp18_type,type,
    hskp18: $o ).

thf(a929_type,type,
    a929: $i ).

thf(hskp19_type,type,
    hskp19: $o ).

thf(a930_type,type,
    a930: $i ).

thf(hskp20_type,type,
    hskp20: $o ).

thf(a937_type,type,
    a937: $i ).

thf(hskp21_type,type,
    hskp21: $o ).

thf(a938_type,type,
    a938: $i ).

thf(hskp22_type,type,
    hskp22: $o ).

thf(a939_type,type,
    a939: $i ).

thf(hskp23_type,type,
    hskp23: $o ).

thf(a950_type,type,
    a950: $i ).

thf(hskp24_type,type,
    hskp24: $o ).

thf(a953_type,type,
    a953: $i ).

thf(hskp25_type,type,
    hskp25: $o ).

thf(a958_type,type,
    a958: $i ).

thf(hskp26_type,type,
    hskp26: $o ).

thf(a969_type,type,
    a969: $i ).

thf(hskp27_type,type,
    hskp27: $o ).

thf(a978_type,type,
    a978: $i ).

thf(hskp28_type,type,
    hskp28: $o ).

thf(a900_type,type,
    a900: $i ).

thf(hskp29_type,type,
    hskp29: $o ).

thf(a911_type,type,
    a911: $i ).

thf(hskp30_type,type,
    hskp30: $o ).

thf(a919_type,type,
    a919: $i ).

thf(hskp31_type,type,
    hskp31: $o ).

thf(a957_type,type,
    a957: $i ).

thf(1,conjecture,
    ~ ( ( ~ hskp0
        | ( ndr1_0
          & ( c0_1 @ a898 )
          & ( c1_1 @ a898 )
          & ~ ( c2_1 @ a898 ) ) )
      & ( ~ hskp1
        | ( ndr1_0
          & ( c1_1 @ a899 )
          & ( c2_1 @ a899 )
          & ~ ( c0_1 @ a899 ) ) )
      & ( ~ hskp2
        | ( ndr1_0
          & ~ ( c0_1 @ a901 )
          & ~ ( c2_1 @ a901 )
          & ~ ( c3_1 @ a901 ) ) )
      & ( ~ hskp3
        | ( ndr1_0
          & ( c0_1 @ a903 )
          & ( c2_1 @ a903 )
          & ~ ( c3_1 @ a903 ) ) )
      & ( ~ hskp4
        | ( ndr1_0
          & ( c2_1 @ a904 )
          & ~ ( c1_1 @ a904 )
          & ~ ( c3_1 @ a904 ) ) )
      & ( ~ hskp5
        | ( ndr1_0
          & ( c1_1 @ a905 )
          & ( c3_1 @ a905 )
          & ~ ( c0_1 @ a905 ) ) )
      & ( ~ hskp6
        | ( ndr1_0
          & ( c2_1 @ a906 )
          & ( c3_1 @ a906 )
          & ~ ( c1_1 @ a906 ) ) )
      & ( ~ hskp7
        | ( ndr1_0
          & ( c3_1 @ a907 )
          & ~ ( c0_1 @ a907 )
          & ~ ( c1_1 @ a907 ) ) )
      & ( ~ hskp8
        | ( ndr1_0
          & ( c3_1 @ a908 )
          & ~ ( c0_1 @ a908 )
          & ~ ( c2_1 @ a908 ) ) )
      & ( ~ hskp9
        | ( ndr1_0
          & ~ ( c0_1 @ a909 )
          & ~ ( c1_1 @ a909 )
          & ~ ( c2_1 @ a909 ) ) )
      & ( ~ hskp10
        | ( ndr1_0
          & ( c1_1 @ a910 )
          & ~ ( c0_1 @ a910 )
          & ~ ( c2_1 @ a910 ) ) )
      & ( ~ hskp11
        | ( ndr1_0
          & ~ ( c1_1 @ a912 )
          & ~ ( c2_1 @ a912 )
          & ~ ( c3_1 @ a912 ) ) )
      & ( ~ hskp12
        | ( ndr1_0
          & ( c0_1 @ a913 )
          & ~ ( c1_1 @ a913 )
          & ~ ( c3_1 @ a913 ) ) )
      & ( ~ hskp13
        | ( ndr1_0
          & ( c3_1 @ a914 )
          & ~ ( c1_1 @ a914 )
          & ~ ( c2_1 @ a914 ) ) )
      & ( ~ hskp14
        | ( ndr1_0
          & ( c0_1 @ a918 )
          & ( c3_1 @ a918 )
          & ~ ( c1_1 @ a918 ) ) )
      & ( ~ hskp15
        | ( ndr1_0
          & ( c0_1 @ a921 )
          & ( c1_1 @ a921 )
          & ~ ( c3_1 @ a921 ) ) )
      & ( ~ hskp16
        | ( ndr1_0
          & ( c1_1 @ a923 )
          & ( c2_1 @ a923 )
          & ~ ( c3_1 @ a923 ) ) )
      & ( ~ hskp17
        | ( ndr1_0
          & ( c1_1 @ a928 )
          & ~ ( c2_1 @ a928 )
          & ~ ( c3_1 @ a928 ) ) )
      & ( ~ hskp18
        | ( ndr1_0
          & ( c0_1 @ a929 )
          & ( c2_1 @ a929 )
          & ~ ( c1_1 @ a929 ) ) )
      & ( ~ hskp19
        | ( ndr1_0
          & ( c2_1 @ a930 )
          & ~ ( c0_1 @ a930 )
          & ~ ( c1_1 @ a930 ) ) )
      & ( ~ hskp20
        | ( ndr1_0
          & ( c2_1 @ a937 )
          & ~ ( c0_1 @ a937 )
          & ~ ( c3_1 @ a937 ) ) )
      & ( ~ hskp21
        | ( ndr1_0
          & ( c0_1 @ a938 )
          & ~ ( c2_1 @ a938 )
          & ~ ( c3_1 @ a938 ) ) )
      & ( ~ hskp22
        | ( ndr1_0
          & ( c1_1 @ a939 )
          & ~ ( c0_1 @ a939 )
          & ~ ( c3_1 @ a939 ) ) )
      & ( ~ hskp23
        | ( ndr1_0
          & ( c0_1 @ a950 )
          & ( c3_1 @ a950 )
          & ~ ( c2_1 @ a950 ) ) )
      & ( ~ hskp24
        | ( ndr1_0
          & ( c1_1 @ a953 )
          & ( c3_1 @ a953 )
          & ~ ( c2_1 @ a953 ) ) )
      & ( ~ hskp25
        | ( ndr1_0
          & ~ ( c0_1 @ a958 )
          & ~ ( c1_1 @ a958 )
          & ~ ( c3_1 @ a958 ) ) )
      & ( ~ hskp26
        | ( ndr1_0
          & ( c0_1 @ a969 )
          & ~ ( c1_1 @ a969 )
          & ~ ( c2_1 @ a969 ) ) )
      & ( ~ hskp27
        | ( ndr1_0
          & ( c2_1 @ a978 )
          & ( c3_1 @ a978 )
          & ~ ( c0_1 @ a978 ) ) )
      & ( ~ hskp28
        | ( ndr1_0
          & ( c0_1 @ a900 )
          & ( c2_1 @ a900 )
          & ( c3_1 @ a900 ) ) )
      & ( ~ hskp29
        | ( ndr1_0
          & ( c0_1 @ a911 )
          & ( c1_1 @ a911 )
          & ( c3_1 @ a911 ) ) )
      & ( ~ hskp30
        | ( ndr1_0
          & ( c0_1 @ a919 )
          & ( c1_1 @ a919 )
          & ( c2_1 @ a919 ) ) )
      & ( ~ hskp31
        | ( ndr1_0
          & ( c1_1 @ a957 )
          & ( c2_1 @ a957 )
          & ( c3_1 @ a957 ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ( c2_1 @ A ) ) )
        | hskp0
        | hskp1 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ( c3_1 @ A ) ) )
        | hskp28
        | hskp2 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp1 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp3 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp4 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp5
        | hskp6 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp7
        | hskp8 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ( c3_1 @ A ) ) )
        | hskp9 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ( c3_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ( c3_1 @ A ) ) )
        | hskp10 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp29 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp11 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp12
        | hskp13 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp8 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp4 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp12 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp14 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp30
        | hskp1 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp15
        | hskp5 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp16
        | hskp9 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp4
        | hskp7 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp0
        | hskp17 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp18
        | hskp19 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | hskp14 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp15 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp9 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp14 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp12
        | hskp10 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c1_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp20 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp21 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp22 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp22 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c1_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp1 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp12 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp18 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | hskp18
        | hskp12 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp21 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp29
        | hskp15 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) ) )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp7 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp23 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | hskp18 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp28 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c1_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp24
        | hskp17 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c0_1 @ A ) ) )
        | hskp10
        | hskp7 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp31 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ( c3_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp25 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp1
        | hskp20 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp0 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp1
        | hskp5 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp12
        | hskp6 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c2_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp1
        | hskp13 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp21 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A ) ) )
        | hskp26
        | hskp17 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c1_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp9 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ( c3_1 @ A )
              | ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A ) ) )
        | hskp16
        | hskp10 )
      & ( ! [A: $i] :
            ( ndr1_0
           => ( ~ ( c0_1 @ A )
              | ~ ( c2_1 @ A )
              | ~ ( c3_1 @ A ) ) )
        | hskp13
        | hskp2 )
      & ( hskp29
        | hskp31
        | hskp27 )
      & ( hskp0
        | hskp12
        | hskp9 )
      & ( hskp0
        | hskp21
        | hskp25 )
      & ( hskp15
        | hskp22
        | hskp19 )
      & ( hskp28
        | hskp22
        | hskp17 )
      & ( hskp3
        | hskp24
        | hskp25 )
      & ( hskp23
        | hskp26
        | hskp22 )
      & ( hskp27
        | hskp7
        | hskp9 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ~ ( ( ~ hskp0
          | ( ndr1_0
            & ( c0_1 @ a898 )
            & ( c1_1 @ a898 )
            & ~ ( c2_1 @ a898 ) ) )
        & ( ~ hskp1
          | ( ndr1_0
            & ( c1_1 @ a899 )
            & ( c2_1 @ a899 )
            & ~ ( c0_1 @ a899 ) ) )
        & ( ~ hskp2
          | ( ndr1_0
            & ~ ( c0_1 @ a901 )
            & ~ ( c2_1 @ a901 )
            & ~ ( c3_1 @ a901 ) ) )
        & ( ~ hskp3
          | ( ndr1_0
            & ( c0_1 @ a903 )
            & ( c2_1 @ a903 )
            & ~ ( c3_1 @ a903 ) ) )
        & ( ~ hskp4
          | ( ndr1_0
            & ( c2_1 @ a904 )
            & ~ ( c1_1 @ a904 )
            & ~ ( c3_1 @ a904 ) ) )
        & ( ~ hskp5
          | ( ndr1_0
            & ( c1_1 @ a905 )
            & ( c3_1 @ a905 )
            & ~ ( c0_1 @ a905 ) ) )
        & ( ~ hskp6
          | ( ndr1_0
            & ( c2_1 @ a906 )
            & ( c3_1 @ a906 )
            & ~ ( c1_1 @ a906 ) ) )
        & ( ~ hskp7
          | ( ndr1_0
            & ( c3_1 @ a907 )
            & ~ ( c0_1 @ a907 )
            & ~ ( c1_1 @ a907 ) ) )
        & ( ~ hskp8
          | ( ndr1_0
            & ( c3_1 @ a908 )
            & ~ ( c0_1 @ a908 )
            & ~ ( c2_1 @ a908 ) ) )
        & ( ~ hskp9
          | ( ndr1_0
            & ~ ( c0_1 @ a909 )
            & ~ ( c1_1 @ a909 )
            & ~ ( c2_1 @ a909 ) ) )
        & ( ~ hskp10
          | ( ndr1_0
            & ( c1_1 @ a910 )
            & ~ ( c0_1 @ a910 )
            & ~ ( c2_1 @ a910 ) ) )
        & ( ~ hskp11
          | ( ndr1_0
            & ~ ( c1_1 @ a912 )
            & ~ ( c2_1 @ a912 )
            & ~ ( c3_1 @ a912 ) ) )
        & ( ~ hskp12
          | ( ndr1_0
            & ( c0_1 @ a913 )
            & ~ ( c1_1 @ a913 )
            & ~ ( c3_1 @ a913 ) ) )
        & ( ~ hskp13
          | ( ndr1_0
            & ( c3_1 @ a914 )
            & ~ ( c1_1 @ a914 )
            & ~ ( c2_1 @ a914 ) ) )
        & ( ~ hskp14
          | ( ndr1_0
            & ( c0_1 @ a918 )
            & ( c3_1 @ a918 )
            & ~ ( c1_1 @ a918 ) ) )
        & ( ~ hskp15
          | ( ndr1_0
            & ( c0_1 @ a921 )
            & ( c1_1 @ a921 )
            & ~ ( c3_1 @ a921 ) ) )
        & ( ~ hskp16
          | ( ndr1_0
            & ( c1_1 @ a923 )
            & ( c2_1 @ a923 )
            & ~ ( c3_1 @ a923 ) ) )
        & ( ~ hskp17
          | ( ndr1_0
            & ( c1_1 @ a928 )
            & ~ ( c2_1 @ a928 )
            & ~ ( c3_1 @ a928 ) ) )
        & ( ~ hskp18
          | ( ndr1_0
            & ( c0_1 @ a929 )
            & ( c2_1 @ a929 )
            & ~ ( c1_1 @ a929 ) ) )
        & ( ~ hskp19
          | ( ndr1_0
            & ( c2_1 @ a930 )
            & ~ ( c0_1 @ a930 )
            & ~ ( c1_1 @ a930 ) ) )
        & ( ~ hskp20
          | ( ndr1_0
            & ( c2_1 @ a937 )
            & ~ ( c0_1 @ a937 )
            & ~ ( c3_1 @ a937 ) ) )
        & ( ~ hskp21
          | ( ndr1_0
            & ( c0_1 @ a938 )
            & ~ ( c2_1 @ a938 )
            & ~ ( c3_1 @ a938 ) ) )
        & ( ~ hskp22
          | ( ndr1_0
            & ( c1_1 @ a939 )
            & ~ ( c0_1 @ a939 )
            & ~ ( c3_1 @ a939 ) ) )
        & ( ~ hskp23
          | ( ndr1_0
            & ( c0_1 @ a950 )
            & ( c3_1 @ a950 )
            & ~ ( c2_1 @ a950 ) ) )
        & ( ~ hskp24
          | ( ndr1_0
            & ( c1_1 @ a953 )
            & ( c3_1 @ a953 )
            & ~ ( c2_1 @ a953 ) ) )
        & ( ~ hskp25
          | ( ndr1_0
            & ~ ( c0_1 @ a958 )
            & ~ ( c1_1 @ a958 )
            & ~ ( c3_1 @ a958 ) ) )
        & ( ~ hskp26
          | ( ndr1_0
            & ( c0_1 @ a969 )
            & ~ ( c1_1 @ a969 )
            & ~ ( c2_1 @ a969 ) ) )
        & ( ~ hskp27
          | ( ndr1_0
            & ( c2_1 @ a978 )
            & ( c3_1 @ a978 )
            & ~ ( c0_1 @ a978 ) ) )
        & ( ~ hskp28
          | ( ndr1_0
            & ( c0_1 @ a900 )
            & ( c2_1 @ a900 )
            & ( c3_1 @ a900 ) ) )
        & ( ~ hskp29
          | ( ndr1_0
            & ( c0_1 @ a911 )
            & ( c1_1 @ a911 )
            & ( c3_1 @ a911 ) ) )
        & ( ~ hskp30
          | ( ndr1_0
            & ( c0_1 @ a919 )
            & ( c1_1 @ a919 )
            & ( c2_1 @ a919 ) ) )
        & ( ~ hskp31
          | ( ndr1_0
            & ( c1_1 @ a957 )
            & ( c2_1 @ a957 )
            & ( c3_1 @ a957 ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c2_1 @ A ) ) )
          | hskp0
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c3_1 @ A ) ) )
          | hskp28
          | hskp2 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp3 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp4 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp5
          | hskp6 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp7
          | hskp8 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | hskp10 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp29 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp11 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp12
          | hskp13 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp8 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp4 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp12 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp14 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp30
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp15
          | hskp5 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp16
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp4
          | hskp7 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp0
          | hskp17 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp18
          | hskp19 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp14 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp15 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp14 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp12
          | hskp10 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp20 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp21 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp22 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp22 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp12 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp18 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp18
          | hskp12 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp21 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp29
          | hskp15 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp7 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp23 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp18 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp28 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp24
          | hskp17 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp10
          | hskp7 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp31 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp25 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp1
          | hskp20 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp0 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp1
          | hskp5 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp12
          | hskp6 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp1
          | hskp13 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp21 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp26
          | hskp17 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp16
          | hskp10 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp13
          | hskp2 )
        & ( hskp29
          | hskp31
          | hskp27 )
        & ( hskp0
          | hskp12
          | hskp9 )
        & ( hskp0
          | hskp21
          | hskp25 )
        & ( hskp15
          | hskp22
          | hskp19 )
        & ( hskp28
          | hskp22
          | hskp17 )
        & ( hskp3
          | hskp24
          | hskp25 )
        & ( hskp23
          | hskp26
          | hskp22 )
        & ( hskp27
          | hskp7
          | hskp9 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ~ ( ( ~ hskp0
          | ( ndr1_0
            & ( c0_1 @ a898 )
            & ( c1_1 @ a898 )
            & ~ ( c2_1 @ a898 ) ) )
        & ( ~ hskp1
          | ( ndr1_0
            & ( c1_1 @ a899 )
            & ( c2_1 @ a899 )
            & ~ ( c0_1 @ a899 ) ) )
        & ( ~ hskp2
          | ( ndr1_0
            & ~ ( c0_1 @ a901 )
            & ~ ( c2_1 @ a901 )
            & ~ ( c3_1 @ a901 ) ) )
        & ( ~ hskp3
          | ( ndr1_0
            & ( c0_1 @ a903 )
            & ( c2_1 @ a903 )
            & ~ ( c3_1 @ a903 ) ) )
        & ( ~ hskp4
          | ( ndr1_0
            & ( c2_1 @ a904 )
            & ~ ( c1_1 @ a904 )
            & ~ ( c3_1 @ a904 ) ) )
        & ( ~ hskp5
          | ( ndr1_0
            & ( c1_1 @ a905 )
            & ( c3_1 @ a905 )
            & ~ ( c0_1 @ a905 ) ) )
        & ( ~ hskp6
          | ( ndr1_0
            & ( c2_1 @ a906 )
            & ( c3_1 @ a906 )
            & ~ ( c1_1 @ a906 ) ) )
        & ( ~ hskp7
          | ( ndr1_0
            & ( c3_1 @ a907 )
            & ~ ( c0_1 @ a907 )
            & ~ ( c1_1 @ a907 ) ) )
        & ( ~ hskp8
          | ( ndr1_0
            & ( c3_1 @ a908 )
            & ~ ( c0_1 @ a908 )
            & ~ ( c2_1 @ a908 ) ) )
        & ( ~ hskp9
          | ( ndr1_0
            & ~ ( c0_1 @ a909 )
            & ~ ( c1_1 @ a909 )
            & ~ ( c2_1 @ a909 ) ) )
        & ( ~ hskp10
          | ( ndr1_0
            & ( c1_1 @ a910 )
            & ~ ( c0_1 @ a910 )
            & ~ ( c2_1 @ a910 ) ) )
        & ( ~ hskp11
          | ( ndr1_0
            & ~ ( c1_1 @ a912 )
            & ~ ( c2_1 @ a912 )
            & ~ ( c3_1 @ a912 ) ) )
        & ( ~ hskp12
          | ( ndr1_0
            & ( c0_1 @ a913 )
            & ~ ( c1_1 @ a913 )
            & ~ ( c3_1 @ a913 ) ) )
        & ( ~ hskp13
          | ( ndr1_0
            & ( c3_1 @ a914 )
            & ~ ( c1_1 @ a914 )
            & ~ ( c2_1 @ a914 ) ) )
        & ( ~ hskp14
          | ( ndr1_0
            & ( c0_1 @ a918 )
            & ( c3_1 @ a918 )
            & ~ ( c1_1 @ a918 ) ) )
        & ( ~ hskp15
          | ( ndr1_0
            & ( c0_1 @ a921 )
            & ( c1_1 @ a921 )
            & ~ ( c3_1 @ a921 ) ) )
        & ( ~ hskp16
          | ( ndr1_0
            & ( c1_1 @ a923 )
            & ( c2_1 @ a923 )
            & ~ ( c3_1 @ a923 ) ) )
        & ( ~ hskp17
          | ( ndr1_0
            & ( c1_1 @ a928 )
            & ~ ( c2_1 @ a928 )
            & ~ ( c3_1 @ a928 ) ) )
        & ( ~ hskp18
          | ( ndr1_0
            & ( c0_1 @ a929 )
            & ( c2_1 @ a929 )
            & ~ ( c1_1 @ a929 ) ) )
        & ( ~ hskp19
          | ( ndr1_0
            & ( c2_1 @ a930 )
            & ~ ( c0_1 @ a930 )
            & ~ ( c1_1 @ a930 ) ) )
        & ( ~ hskp20
          | ( ndr1_0
            & ( c2_1 @ a937 )
            & ~ ( c0_1 @ a937 )
            & ~ ( c3_1 @ a937 ) ) )
        & ( ~ hskp21
          | ( ndr1_0
            & ( c0_1 @ a938 )
            & ~ ( c2_1 @ a938 )
            & ~ ( c3_1 @ a938 ) ) )
        & ( ~ hskp22
          | ( ndr1_0
            & ( c1_1 @ a939 )
            & ~ ( c0_1 @ a939 )
            & ~ ( c3_1 @ a939 ) ) )
        & ( ~ hskp23
          | ( ndr1_0
            & ( c0_1 @ a950 )
            & ( c3_1 @ a950 )
            & ~ ( c2_1 @ a950 ) ) )
        & ( ~ hskp24
          | ( ndr1_0
            & ( c1_1 @ a953 )
            & ( c3_1 @ a953 )
            & ~ ( c2_1 @ a953 ) ) )
        & ( ~ hskp25
          | ( ndr1_0
            & ~ ( c0_1 @ a958 )
            & ~ ( c1_1 @ a958 )
            & ~ ( c3_1 @ a958 ) ) )
        & ( ~ hskp26
          | ( ndr1_0
            & ( c0_1 @ a969 )
            & ~ ( c1_1 @ a969 )
            & ~ ( c2_1 @ a969 ) ) )
        & ( ~ hskp27
          | ( ndr1_0
            & ( c2_1 @ a978 )
            & ( c3_1 @ a978 )
            & ~ ( c0_1 @ a978 ) ) )
        & ( ~ hskp28
          | ( ndr1_0
            & ( c0_1 @ a900 )
            & ( c2_1 @ a900 )
            & ( c3_1 @ a900 ) ) )
        & ( ~ hskp29
          | ( ndr1_0
            & ( c0_1 @ a911 )
            & ( c1_1 @ a911 )
            & ( c3_1 @ a911 ) ) )
        & ( ~ hskp30
          | ( ndr1_0
            & ( c0_1 @ a919 )
            & ( c1_1 @ a919 )
            & ( c2_1 @ a919 ) ) )
        & ( ~ hskp31
          | ( ndr1_0
            & ( c1_1 @ a957 )
            & ( c2_1 @ a957 )
            & ( c3_1 @ a957 ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c2_1 @ A ) ) )
          | hskp0
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ( c3_1 @ A ) ) )
          | hskp28
          | hskp2 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp3 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp4 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp5
          | hskp6 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp7
          | hskp8 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | hskp10 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp29 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp11 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp12
          | hskp13 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp8 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp4 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp12 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp14 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp30
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp15
          | hskp5 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp16
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp4
          | hskp7 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp0
          | hskp17 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp18
          | hskp19 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp14 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp15 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp14 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp12
          | hskp10 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp20 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp21 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp22 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp22 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp1 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp12 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp18 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp18
          | hskp12 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp21 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp29
          | hskp15 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) ) )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp7 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp23 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp18 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp28 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c1_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp24
          | hskp17 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c0_1 @ A ) ) )
          | hskp10
          | hskp7 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp31 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ( c3_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp25 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp1
          | hskp20 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp0 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp1
          | hskp5 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp12
          | hskp6 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c2_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp1
          | hskp13 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp21 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A ) ) )
          | hskp26
          | hskp17 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c1_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp9 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ( c3_1 @ A )
                | ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A ) ) )
          | hskp16
          | hskp10 )
        & ( ! [A: $i] :
              ( ndr1_0
             => ( ~ ( c0_1 @ A )
                | ~ ( c2_1 @ A )
                | ~ ( c3_1 @ A ) ) )
          | hskp13
          | hskp2 )
        & ( hskp29
          | hskp31
          | hskp27 )
        & ( hskp0
          | hskp12
          | hskp9 )
        & ( hskp0
          | hskp21
          | hskp25 )
        & ( hskp15
          | hskp22
          | hskp19 )
        & ( hskp28
          | hskp22
          | hskp17 )
        & ( hskp3
          | hskp24
          | hskp25 )
        & ( hskp23
          | hskp26
          | hskp22 )
        & ( hskp27
          | hskp7
          | hskp9 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(478,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN474+1 : TPTP v8.2.0. Released v2.1.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n017.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 14:31:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.34/1.02  % [INFO] 	 Parsing done (146ms). 
% 1.34/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.93/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.93/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.93/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.64/1.57  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.94/1.65  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.94/1.65  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.94/1.67  % [INFO] 	 Type checking passed. 
% 2.94/1.67  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 9.17/3.33  % External prover 'cvc4' found a proof!
% 9.17/3.33  % [INFO] 	 Killing All external provers ... 
% 9.17/3.33  % Time passed: 2796ms (effective reasoning time: 2298ms)
% 9.17/3.33  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.17/3.33  % Axioms used in derivation (0): 
% 9.17/3.33  % No. of inferences in proof: 4
% 9.17/3.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2796 ms resp. 2298 ms w/o parsing
% 9.17/3.40  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.17/3.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------