TSTP Solution File: SYN511+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYN511+1 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Fri May 19 12:29:10 EDT 2023
% Result : Theorem 8.72s 3.21s
% Output : Refutation 8.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 68
% Syntax : Number of formulae : 71 ( 1 unt; 67 typ; 0 def)
% Number of atoms : 2323 ( 0 equ; 0 cnn)
% Maximal formula atoms : 774 ( 580 avg)
% Number of connectives : 4595 ( 854 ~;1329 |; 609 &;1422 @)
% ( 0 <=>; 381 =>; 0 <=; 0 <~>)
% Maximal formula depth : 115 ( 86 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 67 usr; 64 con; 0-1 aty)
% Number of variables : 381 ( 0 ^; 381 !; 0 ?; 381 :)
% Comments :
%------------------------------------------------------------------------------
thf(hskp0_type,type,
hskp0: $o ).
thf(ndr1_0_type,type,
ndr1_0: $o ).
thf(c1_1_type,type,
c1_1: $i > $o ).
thf(a668_type,type,
a668: $i ).
thf(c2_1_type,type,
c2_1: $i > $o ).
thf(c3_1_type,type,
c3_1: $i > $o ).
thf(hskp1_type,type,
hskp1: $o ).
thf(c0_1_type,type,
c0_1: $i > $o ).
thf(a669_type,type,
a669: $i ).
thf(hskp2_type,type,
hskp2: $o ).
thf(a670_type,type,
a670: $i ).
thf(hskp3_type,type,
hskp3: $o ).
thf(a671_type,type,
a671: $i ).
thf(hskp4_type,type,
hskp4: $o ).
thf(a672_type,type,
a672: $i ).
thf(hskp5_type,type,
hskp5: $o ).
thf(a673_type,type,
a673: $i ).
thf(hskp6_type,type,
hskp6: $o ).
thf(a674_type,type,
a674: $i ).
thf(hskp7_type,type,
hskp7: $o ).
thf(a675_type,type,
a675: $i ).
thf(hskp8_type,type,
hskp8: $o ).
thf(a679_type,type,
a679: $i ).
thf(hskp9_type,type,
hskp9: $o ).
thf(a680_type,type,
a680: $i ).
thf(hskp10_type,type,
hskp10: $o ).
thf(a681_type,type,
a681: $i ).
thf(hskp11_type,type,
hskp11: $o ).
thf(a683_type,type,
a683: $i ).
thf(hskp12_type,type,
hskp12: $o ).
thf(a684_type,type,
a684: $i ).
thf(hskp13_type,type,
hskp13: $o ).
thf(a688_type,type,
a688: $i ).
thf(hskp14_type,type,
hskp14: $o ).
thf(a696_type,type,
a696: $i ).
thf(hskp15_type,type,
hskp15: $o ).
thf(a700_type,type,
a700: $i ).
thf(hskp16_type,type,
hskp16: $o ).
thf(a702_type,type,
a702: $i ).
thf(hskp17_type,type,
hskp17: $o ).
thf(a703_type,type,
a703: $i ).
thf(hskp18_type,type,
hskp18: $o ).
thf(a708_type,type,
a708: $i ).
thf(hskp19_type,type,
hskp19: $o ).
thf(a710_type,type,
a710: $i ).
thf(hskp20_type,type,
hskp20: $o ).
thf(a711_type,type,
a711: $i ).
thf(hskp21_type,type,
hskp21: $o ).
thf(a715_type,type,
a715: $i ).
thf(hskp22_type,type,
hskp22: $o ).
thf(a716_type,type,
a716: $i ).
thf(hskp23_type,type,
hskp23: $o ).
thf(a730_type,type,
a730: $i ).
thf(hskp24_type,type,
hskp24: $o ).
thf(a731_type,type,
a731: $i ).
thf(hskp25_type,type,
hskp25: $o ).
thf(a760_type,type,
a760: $i ).
thf(hskp26_type,type,
hskp26: $o ).
thf(a762_type,type,
a762: $i ).
thf(hskp27_type,type,
hskp27: $o ).
thf(a676_type,type,
a676: $i ).
thf(hskp28_type,type,
hskp28: $o ).
thf(a678_type,type,
a678: $i ).
thf(hskp29_type,type,
hskp29: $o ).
thf(a725_type,type,
a725: $i ).
thf(hskp30_type,type,
hskp30: $o ).
thf(a753_type,type,
a753: $i ).
thf(1,conjecture,
~ ( ( ~ hskp0
| ( ndr1_0
& ( c1_1 @ a668 )
& ~ ( c2_1 @ a668 )
& ~ ( c3_1 @ a668 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a669 )
& ~ ( c1_1 @ a669 )
& ~ ( c2_1 @ a669 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c3_1 @ a670 )
& ~ ( c0_1 @ a670 )
& ~ ( c1_1 @ a670 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c2_1 @ a671 )
& ~ ( c0_1 @ a671 )
& ~ ( c1_1 @ a671 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ~ ( c0_1 @ a672 )
& ~ ( c1_1 @ a672 )
& ~ ( c2_1 @ a672 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ ( c0_1 @ a673 )
& ~ ( c2_1 @ a673 )
& ~ ( c3_1 @ a673 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c0_1 @ a674 )
& ( c3_1 @ a674 )
& ~ ( c1_1 @ a674 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c1_1 @ a675 )
& ( c3_1 @ a675 )
& ~ ( c2_1 @ a675 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c1_1 @ a679 )
& ( c3_1 @ a679 )
& ~ ( c0_1 @ a679 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c2_1 @ a680 )
& ~ ( c1_1 @ a680 )
& ~ ( c3_1 @ a680 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c2_1 @ a681 )
& ( c3_1 @ a681 )
& ~ ( c0_1 @ a681 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c0_1 @ a683 )
& ( c3_1 @ a683 )
& ~ ( c2_1 @ a683 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c3_1 @ a684 )
& ~ ( c0_1 @ a684 )
& ~ ( c2_1 @ a684 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a688 )
& ( c1_1 @ a688 )
& ~ ( c3_1 @ a688 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c0_1 @ a696 )
& ( c2_1 @ a696 )
& ~ ( c3_1 @ a696 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ( c2_1 @ a700 )
& ~ ( c0_1 @ a700 )
& ~ ( c3_1 @ a700 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c2_1 @ a702 )
& ( c3_1 @ a702 )
& ~ ( c1_1 @ a702 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c1_1 @ a703 )
& ~ ( c0_1 @ a703 )
& ~ ( c2_1 @ a703 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c3_1 @ a708 )
& ~ ( c1_1 @ a708 )
& ~ ( c2_1 @ a708 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c1_1 @ a710 )
& ( c2_1 @ a710 )
& ~ ( c0_1 @ a710 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c0_1 @ a711 )
& ( c1_1 @ a711 )
& ~ ( c2_1 @ a711 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c0_1 @ a715 )
& ~ ( c2_1 @ a715 )
& ~ ( c3_1 @ a715 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c1_1 @ a716 )
& ( c2_1 @ a716 )
& ~ ( c3_1 @ a716 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c0_1 @ a730 )
& ( c2_1 @ a730 )
& ~ ( c1_1 @ a730 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c0_1 @ a731 )
& ~ ( c1_1 @ a731 )
& ~ ( c3_1 @ a731 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ~ ( c0_1 @ a760 )
& ~ ( c1_1 @ a760 )
& ~ ( c3_1 @ a760 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c1_1 @ a762 )
& ~ ( c0_1 @ a762 )
& ~ ( c3_1 @ a762 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c0_1 @ a676 )
& ( c1_1 @ a676 )
& ( c2_1 @ a676 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a678 )
& ( c1_1 @ a678 )
& ( c3_1 @ a678 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c1_1 @ a725 )
& ( c2_1 @ a725 )
& ( c3_1 @ a725 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a753 )
& ( c2_1 @ a753 )
& ( c3_1 @ a753 ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp1
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp3
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| hskp6
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp27 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_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
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp8
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_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
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp28
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp13
| hskp9 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_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
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp14
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_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 )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp27 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp16 )
& ( ! [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 ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6 )
& ( ! [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 ) ) )
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp20
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp1
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp21
| hskp22 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp9
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp20
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp27
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp24
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp15
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp28
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp14
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp14
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9
| hskp5 )
& ( ! [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
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23
| hskp16 )
& ( hskp27
| hskp24
| hskp18 )
& ( hskp28
| hskp30
| hskp11 )
& ( hskp28
| hskp19
| hskp9 )
& ( hskp13
| hskp12
| hskp25 )
& ( hskp30
| hskp26
| hskp12 )
& ( hskp11
| hskp21
| hskp2 )
& ( hskp24
| hskp18
| hskp4 )
& ( hskp29
| hskp0
| hskp16 )
& ( hskp22
| hskp8
| hskp0 )
& ( hskp7
| hskp25
| hskp5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c1_1 @ a668 )
& ~ ( c2_1 @ a668 )
& ~ ( c3_1 @ a668 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a669 )
& ~ ( c1_1 @ a669 )
& ~ ( c2_1 @ a669 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c3_1 @ a670 )
& ~ ( c0_1 @ a670 )
& ~ ( c1_1 @ a670 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c2_1 @ a671 )
& ~ ( c0_1 @ a671 )
& ~ ( c1_1 @ a671 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ~ ( c0_1 @ a672 )
& ~ ( c1_1 @ a672 )
& ~ ( c2_1 @ a672 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ ( c0_1 @ a673 )
& ~ ( c2_1 @ a673 )
& ~ ( c3_1 @ a673 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c0_1 @ a674 )
& ( c3_1 @ a674 )
& ~ ( c1_1 @ a674 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c1_1 @ a675 )
& ( c3_1 @ a675 )
& ~ ( c2_1 @ a675 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c1_1 @ a679 )
& ( c3_1 @ a679 )
& ~ ( c0_1 @ a679 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c2_1 @ a680 )
& ~ ( c1_1 @ a680 )
& ~ ( c3_1 @ a680 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c2_1 @ a681 )
& ( c3_1 @ a681 )
& ~ ( c0_1 @ a681 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c0_1 @ a683 )
& ( c3_1 @ a683 )
& ~ ( c2_1 @ a683 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c3_1 @ a684 )
& ~ ( c0_1 @ a684 )
& ~ ( c2_1 @ a684 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a688 )
& ( c1_1 @ a688 )
& ~ ( c3_1 @ a688 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c0_1 @ a696 )
& ( c2_1 @ a696 )
& ~ ( c3_1 @ a696 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ( c2_1 @ a700 )
& ~ ( c0_1 @ a700 )
& ~ ( c3_1 @ a700 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c2_1 @ a702 )
& ( c3_1 @ a702 )
& ~ ( c1_1 @ a702 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c1_1 @ a703 )
& ~ ( c0_1 @ a703 )
& ~ ( c2_1 @ a703 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c3_1 @ a708 )
& ~ ( c1_1 @ a708 )
& ~ ( c2_1 @ a708 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c1_1 @ a710 )
& ( c2_1 @ a710 )
& ~ ( c0_1 @ a710 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c0_1 @ a711 )
& ( c1_1 @ a711 )
& ~ ( c2_1 @ a711 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c0_1 @ a715 )
& ~ ( c2_1 @ a715 )
& ~ ( c3_1 @ a715 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c1_1 @ a716 )
& ( c2_1 @ a716 )
& ~ ( c3_1 @ a716 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c0_1 @ a730 )
& ( c2_1 @ a730 )
& ~ ( c1_1 @ a730 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c0_1 @ a731 )
& ~ ( c1_1 @ a731 )
& ~ ( c3_1 @ a731 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ~ ( c0_1 @ a760 )
& ~ ( c1_1 @ a760 )
& ~ ( c3_1 @ a760 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c1_1 @ a762 )
& ~ ( c0_1 @ a762 )
& ~ ( c3_1 @ a762 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c0_1 @ a676 )
& ( c1_1 @ a676 )
& ( c2_1 @ a676 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a678 )
& ( c1_1 @ a678 )
& ( c3_1 @ a678 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c1_1 @ a725 )
& ( c2_1 @ a725 )
& ( c3_1 @ a725 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a753 )
& ( c2_1 @ a753 )
& ( c3_1 @ a753 ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp1
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp3
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| hskp6
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp27 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_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
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp8
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_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
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp28
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp13
| hskp9 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_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
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp14
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_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 )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp27 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp16 )
& ( ! [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 ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6 )
& ( ! [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 ) ) )
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp20
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp1
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp21
| hskp22 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp9
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp20
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp27
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp24
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp15
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp28
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp14
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp14
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9
| hskp5 )
& ( ! [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
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23
| hskp16 )
& ( hskp27
| hskp24
| hskp18 )
& ( hskp28
| hskp30
| hskp11 )
& ( hskp28
| hskp19
| hskp9 )
& ( hskp13
| hskp12
| hskp25 )
& ( hskp30
| hskp26
| hskp12 )
& ( hskp11
| hskp21
| hskp2 )
& ( hskp24
| hskp18
| hskp4 )
& ( hskp29
| hskp0
| hskp16 )
& ( hskp22
| hskp8
| hskp0 )
& ( hskp7
| hskp25
| hskp5 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c1_1 @ a668 )
& ~ ( c2_1 @ a668 )
& ~ ( c3_1 @ a668 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a669 )
& ~ ( c1_1 @ a669 )
& ~ ( c2_1 @ a669 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c3_1 @ a670 )
& ~ ( c0_1 @ a670 )
& ~ ( c1_1 @ a670 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c2_1 @ a671 )
& ~ ( c0_1 @ a671 )
& ~ ( c1_1 @ a671 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ~ ( c0_1 @ a672 )
& ~ ( c1_1 @ a672 )
& ~ ( c2_1 @ a672 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ ( c0_1 @ a673 )
& ~ ( c2_1 @ a673 )
& ~ ( c3_1 @ a673 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c0_1 @ a674 )
& ( c3_1 @ a674 )
& ~ ( c1_1 @ a674 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c1_1 @ a675 )
& ( c3_1 @ a675 )
& ~ ( c2_1 @ a675 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c1_1 @ a679 )
& ( c3_1 @ a679 )
& ~ ( c0_1 @ a679 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c2_1 @ a680 )
& ~ ( c1_1 @ a680 )
& ~ ( c3_1 @ a680 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c2_1 @ a681 )
& ( c3_1 @ a681 )
& ~ ( c0_1 @ a681 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c0_1 @ a683 )
& ( c3_1 @ a683 )
& ~ ( c2_1 @ a683 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c3_1 @ a684 )
& ~ ( c0_1 @ a684 )
& ~ ( c2_1 @ a684 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a688 )
& ( c1_1 @ a688 )
& ~ ( c3_1 @ a688 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c0_1 @ a696 )
& ( c2_1 @ a696 )
& ~ ( c3_1 @ a696 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ( c2_1 @ a700 )
& ~ ( c0_1 @ a700 )
& ~ ( c3_1 @ a700 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c2_1 @ a702 )
& ( c3_1 @ a702 )
& ~ ( c1_1 @ a702 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c1_1 @ a703 )
& ~ ( c0_1 @ a703 )
& ~ ( c2_1 @ a703 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c3_1 @ a708 )
& ~ ( c1_1 @ a708 )
& ~ ( c2_1 @ a708 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c1_1 @ a710 )
& ( c2_1 @ a710 )
& ~ ( c0_1 @ a710 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c0_1 @ a711 )
& ( c1_1 @ a711 )
& ~ ( c2_1 @ a711 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c0_1 @ a715 )
& ~ ( c2_1 @ a715 )
& ~ ( c3_1 @ a715 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c1_1 @ a716 )
& ( c2_1 @ a716 )
& ~ ( c3_1 @ a716 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c0_1 @ a730 )
& ( c2_1 @ a730 )
& ~ ( c1_1 @ a730 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c0_1 @ a731 )
& ~ ( c1_1 @ a731 )
& ~ ( c3_1 @ a731 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ~ ( c0_1 @ a760 )
& ~ ( c1_1 @ a760 )
& ~ ( c3_1 @ a760 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c1_1 @ a762 )
& ~ ( c0_1 @ a762 )
& ~ ( c3_1 @ a762 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c0_1 @ a676 )
& ( c1_1 @ a676 )
& ( c2_1 @ a676 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a678 )
& ( c1_1 @ a678 )
& ( c3_1 @ a678 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c1_1 @ a725 )
& ( c2_1 @ a725 )
& ( c3_1 @ a725 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a753 )
& ( c2_1 @ a753 )
& ( c3_1 @ a753 ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp1
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp3
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| hskp6
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp27 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_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
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp8
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_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
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp28
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp13
| hskp9 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_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
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp14
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_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 )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp27 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp16 )
& ( ! [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 ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6 )
& ( ! [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 ) ) )
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp20
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp1
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp21
| hskp22 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp9
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp20
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp27
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp24
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp15
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp28
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp14
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp14
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9
| hskp5 )
& ( ! [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
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23
| hskp16 )
& ( hskp27
| hskp24
| hskp18 )
& ( hskp28
| hskp30
| hskp11 )
& ( hskp28
| hskp19
| hskp9 )
& ( hskp13
| hskp12
| hskp25 )
& ( hskp30
| hskp26
| hskp12 )
& ( hskp11
| hskp21
| hskp2 )
& ( hskp24
| hskp18
| hskp4 )
& ( hskp29
| hskp0
| hskp16 )
& ( hskp22
| hskp8
| hskp0 )
& ( hskp7
| hskp25
| hskp5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(346,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN511+1 : TPTP v8.1.2. Released v2.1.0.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 20:23:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.83/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.99 % [INFO] Parsing done (164ms).
% 1.27/1.00 % [INFO] Running in sequential loop mode.
% 1.87/1.19 % [INFO] eprover registered as external prover.
% 1.87/1.20 % [INFO] cvc4 registered as external prover.
% 1.87/1.20 % [INFO] Scanning for conjecture ...
% 2.54/1.50 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.66/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.66/1.57 % [INFO] Problem is first-order (TPTP FOF).
% 2.66/1.59 % [INFO] Type checking passed.
% 2.66/1.59 % [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 ...
% 8.72/3.20 % External prover 'cvc4' found a proof!
% 8.72/3.20 % [INFO] Killing All external provers ...
% 8.72/3.20 % Time passed: 2698ms (effective reasoning time: 2202ms)
% 8.72/3.20 % 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)>
% 8.72/3.21 % Axioms used in derivation (0):
% 8.72/3.21 % No. of inferences in proof: 4
% 8.72/3.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2698 ms resp. 2202 ms w/o parsing
% 8.72/3.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.72/3.27 % [INFO] Killing All external provers ...
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