TSTP Solution File: SYN504+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYN504+1 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 12:29:07 EDT 2023
% Result : Theorem 8.10s 3.18s
% Output : Refutation 8.19s
% 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 : 2320 ( 0 equ; 0 cnn)
% Maximal formula atoms : 773 ( 580 avg)
% Number of connectives : 4556 ( 818 ~;1317 |; 621 &;1422 @)
% ( 0 <=>; 378 =>; 0 <=; 0 <~>)
% Maximal formula depth : 116 ( 87 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 : 378 ( 0 ^; 378 !; 0 ?; 378 :)
% 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(a353_type,type,
a353: $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(a355_type,type,
a355: $i ).
thf(c3_1_type,type,
c3_1: $i > $o ).
thf(hskp2_type,type,
hskp2: $o ).
thf(a356_type,type,
a356: $i ).
thf(hskp3_type,type,
hskp3: $o ).
thf(a357_type,type,
a357: $i ).
thf(hskp4_type,type,
hskp4: $o ).
thf(a358_type,type,
a358: $i ).
thf(hskp5_type,type,
hskp5: $o ).
thf(a359_type,type,
a359: $i ).
thf(hskp6_type,type,
hskp6: $o ).
thf(a360_type,type,
a360: $i ).
thf(hskp7_type,type,
hskp7: $o ).
thf(a361_type,type,
a361: $i ).
thf(hskp8_type,type,
hskp8: $o ).
thf(a363_type,type,
a363: $i ).
thf(hskp9_type,type,
hskp9: $o ).
thf(a364_type,type,
a364: $i ).
thf(hskp10_type,type,
hskp10: $o ).
thf(a366_type,type,
a366: $i ).
thf(hskp11_type,type,
hskp11: $o ).
thf(a368_type,type,
a368: $i ).
thf(hskp12_type,type,
hskp12: $o ).
thf(a369_type,type,
a369: $i ).
thf(hskp13_type,type,
hskp13: $o ).
thf(a370_type,type,
a370: $i ).
thf(hskp14_type,type,
hskp14: $o ).
thf(a375_type,type,
a375: $i ).
thf(hskp15_type,type,
hskp15: $o ).
thf(a376_type,type,
a376: $i ).
thf(hskp16_type,type,
hskp16: $o ).
thf(a379_type,type,
a379: $i ).
thf(hskp17_type,type,
hskp17: $o ).
thf(a380_type,type,
a380: $i ).
thf(hskp18_type,type,
hskp18: $o ).
thf(a382_type,type,
a382: $i ).
thf(hskp19_type,type,
hskp19: $o ).
thf(a387_type,type,
a387: $i ).
thf(hskp20_type,type,
hskp20: $o ).
thf(a388_type,type,
a388: $i ).
thf(hskp21_type,type,
hskp21: $o ).
thf(a395_type,type,
a395: $i ).
thf(hskp22_type,type,
hskp22: $o ).
thf(a397_type,type,
a397: $i ).
thf(hskp23_type,type,
hskp23: $o ).
thf(a398_type,type,
a398: $i ).
thf(hskp24_type,type,
hskp24: $o ).
thf(a399_type,type,
a399: $i ).
thf(hskp25_type,type,
hskp25: $o ).
thf(a417_type,type,
a417: $i ).
thf(hskp26_type,type,
hskp26: $o ).
thf(a418_type,type,
a418: $i ).
thf(hskp27_type,type,
hskp27: $o ).
thf(a446_type,type,
a446: $i ).
thf(hskp28_type,type,
hskp28: $o ).
thf(a365_type,type,
a365: $i ).
thf(hskp29_type,type,
hskp29: $o ).
thf(a372_type,type,
a372: $i ).
thf(hskp30_type,type,
hskp30: $o ).
thf(a373_type,type,
a373: $i ).
thf(hskp31_type,type,
hskp31: $o ).
thf(a410_type,type,
a410: $i ).
thf(1,conjecture,
~ ( ( ~ hskp0
| ( ndr1_0
& ( c0_1 @ a353 )
& ( c1_1 @ a353 )
& ~ ( c2_1 @ a353 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a355 )
& ( c3_1 @ a355 )
& ~ ( c1_1 @ a355 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c0_1 @ a356 )
& ( c2_1 @ a356 )
& ~ ( c1_1 @ a356 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c1_1 @ a357 )
& ( c3_1 @ a357 )
& ~ ( c0_1 @ a357 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c2_1 @ a358 )
& ~ ( c0_1 @ a358 )
& ~ ( c3_1 @ a358 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ ( c0_1 @ a359 )
& ~ ( c1_1 @ a359 )
& ~ ( c3_1 @ a359 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ~ ( c1_1 @ a360 )
& ~ ( c2_1 @ a360 )
& ~ ( c3_1 @ a360 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c3_1 @ a361 )
& ~ ( c1_1 @ a361 )
& ~ ( c2_1 @ a361 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c1_1 @ a363 )
& ( c2_1 @ a363 )
& ~ ( c3_1 @ a363 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c2_1 @ a364 )
& ~ ( c0_1 @ a364 )
& ~ ( c1_1 @ a364 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ~ ( c0_1 @ a366 )
& ~ ( c2_1 @ a366 )
& ~ ( c3_1 @ a366 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c2_1 @ a368 )
& ( c3_1 @ a368 )
& ~ ( c1_1 @ a368 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a369 )
& ( c3_1 @ a369 )
& ~ ( c2_1 @ a369 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a370 )
& ( c2_1 @ a370 )
& ~ ( c3_1 @ a370 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c3_1 @ a375 )
& ~ ( c0_1 @ a375 )
& ~ ( c1_1 @ a375 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ( c0_1 @ a376 )
& ~ ( c1_1 @ a376 )
& ~ ( c2_1 @ a376 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c2_1 @ a379 )
& ~ ( c1_1 @ a379 )
& ~ ( c3_1 @ a379 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c0_1 @ a380 )
& ( c1_1 @ a380 )
& ~ ( c3_1 @ a380 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c3_1 @ a382 )
& ~ ( c0_1 @ a382 )
& ~ ( c2_1 @ a382 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ~ ( c0_1 @ a387 )
& ~ ( c1_1 @ a387 )
& ~ ( c2_1 @ a387 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c1_1 @ a388 )
& ~ ( c2_1 @ a388 )
& ~ ( c3_1 @ a388 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c1_1 @ a395 )
& ~ ( c0_1 @ a395 )
& ~ ( c2_1 @ a395 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c1_1 @ a397 )
& ( c2_1 @ a397 )
& ~ ( c0_1 @ a397 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a398 )
& ( c3_1 @ a398 )
& ~ ( c2_1 @ a398 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c1_1 @ a399 )
& ~ ( c0_1 @ a399 )
& ~ ( c3_1 @ a399 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c0_1 @ a417 )
& ~ ( c1_1 @ a417 )
& ~ ( c3_1 @ a417 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c0_1 @ a418 )
& ~ ( c2_1 @ a418 )
& ~ ( c3_1 @ a418 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c2_1 @ a446 )
& ( c3_1 @ a446 )
& ~ ( c0_1 @ a446 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c1_1 @ a365 )
& ( c2_1 @ a365 )
& ( c3_1 @ a365 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c0_1 @ a372 )
& ( c1_1 @ a372 )
& ( c2_1 @ a372 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a373 )
& ( c1_1 @ a373 )
& ( c3_1 @ a373 ) ) )
& ( ~ hskp31
| ( ndr1_0
& ( c0_1 @ a410 )
& ( c2_1 @ a410 )
& ( c3_1 @ a410 ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp0 )
& ( ! [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
=> ( ( c2_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
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp0 )
& ( ! [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 ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| 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 )
| ( c2_1 @ A ) ) )
| hskp5
| hskp6 )
& ( ! [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 ) ) )
| hskp7 )
& ( ! [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
=> ( ( c2_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
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_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 ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9 )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8
| hskp11 )
& ( ! [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 ) ) )
| hskp12 )
& ( ! [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 ) ) )
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_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 )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp30 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp1
| hskp14 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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 ) ) )
| hskp5 )
& ( ! [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 ) ) )
| ! [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
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4 )
& ( ! [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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp3 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28
| hskp19 )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_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 ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp15 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp21
| hskp4 )
& ( ! [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 )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp3
| hskp19 )
& ( ! [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
=> ( ( c3_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 )
| ~ ( 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 )
| ~ ( c2_1 @ A ) ) )
| hskp12
| hskp8 )
& ( ! [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 ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp30
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp2
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp26 )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp17
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp22
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp30
| hskp22 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp29
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp31
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( hskp29
| hskp13
| hskp15 )
& ( hskp17
| hskp1
| hskp11 )
& ( hskp13
| hskp27
| hskp4 )
& ( hskp15
| hskp11
| hskp16 )
& ( hskp25
| hskp8
| hskp11 )
& ( hskp21
| hskp18
| hskp6 )
& ( hskp24
| hskp11
| hskp4 )
& ( hskp4
| hskp6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c0_1 @ a353 )
& ( c1_1 @ a353 )
& ~ ( c2_1 @ a353 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a355 )
& ( c3_1 @ a355 )
& ~ ( c1_1 @ a355 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c0_1 @ a356 )
& ( c2_1 @ a356 )
& ~ ( c1_1 @ a356 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c1_1 @ a357 )
& ( c3_1 @ a357 )
& ~ ( c0_1 @ a357 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c2_1 @ a358 )
& ~ ( c0_1 @ a358 )
& ~ ( c3_1 @ a358 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ ( c0_1 @ a359 )
& ~ ( c1_1 @ a359 )
& ~ ( c3_1 @ a359 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ~ ( c1_1 @ a360 )
& ~ ( c2_1 @ a360 )
& ~ ( c3_1 @ a360 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c3_1 @ a361 )
& ~ ( c1_1 @ a361 )
& ~ ( c2_1 @ a361 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c1_1 @ a363 )
& ( c2_1 @ a363 )
& ~ ( c3_1 @ a363 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c2_1 @ a364 )
& ~ ( c0_1 @ a364 )
& ~ ( c1_1 @ a364 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ~ ( c0_1 @ a366 )
& ~ ( c2_1 @ a366 )
& ~ ( c3_1 @ a366 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c2_1 @ a368 )
& ( c3_1 @ a368 )
& ~ ( c1_1 @ a368 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a369 )
& ( c3_1 @ a369 )
& ~ ( c2_1 @ a369 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a370 )
& ( c2_1 @ a370 )
& ~ ( c3_1 @ a370 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c3_1 @ a375 )
& ~ ( c0_1 @ a375 )
& ~ ( c1_1 @ a375 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ( c0_1 @ a376 )
& ~ ( c1_1 @ a376 )
& ~ ( c2_1 @ a376 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c2_1 @ a379 )
& ~ ( c1_1 @ a379 )
& ~ ( c3_1 @ a379 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c0_1 @ a380 )
& ( c1_1 @ a380 )
& ~ ( c3_1 @ a380 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c3_1 @ a382 )
& ~ ( c0_1 @ a382 )
& ~ ( c2_1 @ a382 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ~ ( c0_1 @ a387 )
& ~ ( c1_1 @ a387 )
& ~ ( c2_1 @ a387 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c1_1 @ a388 )
& ~ ( c2_1 @ a388 )
& ~ ( c3_1 @ a388 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c1_1 @ a395 )
& ~ ( c0_1 @ a395 )
& ~ ( c2_1 @ a395 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c1_1 @ a397 )
& ( c2_1 @ a397 )
& ~ ( c0_1 @ a397 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a398 )
& ( c3_1 @ a398 )
& ~ ( c2_1 @ a398 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c1_1 @ a399 )
& ~ ( c0_1 @ a399 )
& ~ ( c3_1 @ a399 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c0_1 @ a417 )
& ~ ( c1_1 @ a417 )
& ~ ( c3_1 @ a417 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c0_1 @ a418 )
& ~ ( c2_1 @ a418 )
& ~ ( c3_1 @ a418 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c2_1 @ a446 )
& ( c3_1 @ a446 )
& ~ ( c0_1 @ a446 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c1_1 @ a365 )
& ( c2_1 @ a365 )
& ( c3_1 @ a365 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c0_1 @ a372 )
& ( c1_1 @ a372 )
& ( c2_1 @ a372 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a373 )
& ( c1_1 @ a373 )
& ( c3_1 @ a373 ) ) )
& ( ~ hskp31
| ( ndr1_0
& ( c0_1 @ a410 )
& ( c2_1 @ a410 )
& ( c3_1 @ a410 ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp0 )
& ( ! [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
=> ( ( c2_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
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp0 )
& ( ! [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 ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| 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 )
| ( c2_1 @ A ) ) )
| hskp5
| hskp6 )
& ( ! [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 ) ) )
| hskp7 )
& ( ! [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
=> ( ( c2_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
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_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 ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9 )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8
| hskp11 )
& ( ! [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 ) ) )
| hskp12 )
& ( ! [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 ) ) )
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_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 )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp30 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp1
| hskp14 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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 ) ) )
| hskp5 )
& ( ! [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 ) ) )
| ! [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
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4 )
& ( ! [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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp3 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28
| hskp19 )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_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 ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp15 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp21
| hskp4 )
& ( ! [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 )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp3
| hskp19 )
& ( ! [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
=> ( ( c3_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 )
| ~ ( 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 )
| ~ ( c2_1 @ A ) ) )
| hskp12
| hskp8 )
& ( ! [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 ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp30
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp2
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp26 )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp17
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp22
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp30
| hskp22 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp29
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp31
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( hskp29
| hskp13
| hskp15 )
& ( hskp17
| hskp1
| hskp11 )
& ( hskp13
| hskp27
| hskp4 )
& ( hskp15
| hskp11
| hskp16 )
& ( hskp25
| hskp8
| hskp11 )
& ( hskp21
| hskp18
| hskp6 )
& ( hskp24
| hskp11
| hskp4 )
& ( hskp4
| hskp6 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c0_1 @ a353 )
& ( c1_1 @ a353 )
& ~ ( c2_1 @ a353 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a355 )
& ( c3_1 @ a355 )
& ~ ( c1_1 @ a355 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c0_1 @ a356 )
& ( c2_1 @ a356 )
& ~ ( c1_1 @ a356 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c1_1 @ a357 )
& ( c3_1 @ a357 )
& ~ ( c0_1 @ a357 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c2_1 @ a358 )
& ~ ( c0_1 @ a358 )
& ~ ( c3_1 @ a358 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ~ ( c0_1 @ a359 )
& ~ ( c1_1 @ a359 )
& ~ ( c3_1 @ a359 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ~ ( c1_1 @ a360 )
& ~ ( c2_1 @ a360 )
& ~ ( c3_1 @ a360 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c3_1 @ a361 )
& ~ ( c1_1 @ a361 )
& ~ ( c2_1 @ a361 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c1_1 @ a363 )
& ( c2_1 @ a363 )
& ~ ( c3_1 @ a363 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c2_1 @ a364 )
& ~ ( c0_1 @ a364 )
& ~ ( c1_1 @ a364 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ~ ( c0_1 @ a366 )
& ~ ( c2_1 @ a366 )
& ~ ( c3_1 @ a366 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c2_1 @ a368 )
& ( c3_1 @ a368 )
& ~ ( c1_1 @ a368 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a369 )
& ( c3_1 @ a369 )
& ~ ( c2_1 @ a369 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a370 )
& ( c2_1 @ a370 )
& ~ ( c3_1 @ a370 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c3_1 @ a375 )
& ~ ( c0_1 @ a375 )
& ~ ( c1_1 @ a375 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ( c0_1 @ a376 )
& ~ ( c1_1 @ a376 )
& ~ ( c2_1 @ a376 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c2_1 @ a379 )
& ~ ( c1_1 @ a379 )
& ~ ( c3_1 @ a379 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c0_1 @ a380 )
& ( c1_1 @ a380 )
& ~ ( c3_1 @ a380 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c3_1 @ a382 )
& ~ ( c0_1 @ a382 )
& ~ ( c2_1 @ a382 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ~ ( c0_1 @ a387 )
& ~ ( c1_1 @ a387 )
& ~ ( c2_1 @ a387 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c1_1 @ a388 )
& ~ ( c2_1 @ a388 )
& ~ ( c3_1 @ a388 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c1_1 @ a395 )
& ~ ( c0_1 @ a395 )
& ~ ( c2_1 @ a395 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c1_1 @ a397 )
& ( c2_1 @ a397 )
& ~ ( c0_1 @ a397 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a398 )
& ( c3_1 @ a398 )
& ~ ( c2_1 @ a398 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c1_1 @ a399 )
& ~ ( c0_1 @ a399 )
& ~ ( c3_1 @ a399 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c0_1 @ a417 )
& ~ ( c1_1 @ a417 )
& ~ ( c3_1 @ a417 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c0_1 @ a418 )
& ~ ( c2_1 @ a418 )
& ~ ( c3_1 @ a418 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c2_1 @ a446 )
& ( c3_1 @ a446 )
& ~ ( c0_1 @ a446 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c1_1 @ a365 )
& ( c2_1 @ a365 )
& ( c3_1 @ a365 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c0_1 @ a372 )
& ( c1_1 @ a372 )
& ( c2_1 @ a372 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a373 )
& ( c1_1 @ a373 )
& ( c3_1 @ a373 ) ) )
& ( ~ hskp31
| ( ndr1_0
& ( c0_1 @ a410 )
& ( c2_1 @ a410 )
& ( c3_1 @ a410 ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp0 )
& ( ! [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
=> ( ( c2_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
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp0 )
& ( ! [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 ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| 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 )
| ( c2_1 @ A ) ) )
| hskp5
| hskp6 )
& ( ! [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 ) ) )
| hskp7 )
& ( ! [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
=> ( ( c2_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
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_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 ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9 )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp8
| hskp11 )
& ( ! [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 ) ) )
| hskp12 )
& ( ! [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 ) ) )
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_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 )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp30 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp1
| hskp14 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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 ) ) )
| hskp5 )
& ( ! [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 ) ) )
| ! [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
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4 )
& ( ! [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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp3 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28
| hskp19 )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_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 ) ) )
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp15 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp21
| hskp4 )
& ( ! [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 )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp3
| hskp19 )
& ( ! [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
=> ( ( c3_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 )
| ~ ( 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 )
| ~ ( c2_1 @ A ) ) )
| hskp12
| hskp8 )
& ( ! [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 ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp30
| hskp23 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp2
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp26 )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp2
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp12 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp17
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp22
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp30
| hskp22 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp29
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp31
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( hskp29
| hskp13
| hskp15 )
& ( hskp17
| hskp1
| hskp11 )
& ( hskp13
| hskp27
| hskp4 )
& ( hskp15
| hskp11
| hskp16 )
& ( hskp25
| hskp8
| hskp11 )
& ( hskp21
| hskp18
| hskp6 )
& ( hskp24
| hskp11
| hskp4 )
& ( hskp4
| hskp6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(362,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN504+1 : TPTP v8.1.2. Released v2.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 19:40:09 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.00 % [INFO] Parsing done (155ms).
% 1.18/1.00 % [INFO] Running in sequential loop mode.
% 1.85/1.20 % [INFO] eprover registered as external prover.
% 1.85/1.20 % [INFO] cvc4 registered as external prover.
% 1.92/1.21 % [INFO] Scanning for conjecture ...
% 2.53/1.50 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.65/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.65/1.58 % [INFO] Problem is first-order (TPTP FOF).
% 2.65/1.59 % [INFO] Type checking passed.
% 2.65/1.60 % [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 ...
% 8.10/3.17 % External prover 'cvc4' found a proof!
% 8.10/3.18 % [INFO] Killing All external provers ...
% 8.10/3.18 % Time passed: 2657ms (effective reasoning time: 2168ms)
% 8.10/3.18 % 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)>
% 8.10/3.18 % Axioms used in derivation (0):
% 8.10/3.18 % No. of inferences in proof: 4
% 8.10/3.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2657 ms resp. 2168 ms w/o parsing
% 8.19/3.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.19/3.24 % [INFO] Killing All external provers ...
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