TSTP Solution File: SYN501+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYN501+1 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 12:29:06 EDT 2023
% Result : Theorem 7.17s 3.07s
% Output : Refutation 8.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 66
% Syntax : Number of formulae : 69 ( 1 unt; 65 typ; 0 def)
% Number of atoms : 2251 ( 0 equ; 0 cnn)
% Maximal formula atoms : 750 ( 562 avg)
% Number of connectives : 4376 ( 770 ~;1287 |; 597 &;1359 @)
% ( 0 <=>; 363 =>; 0 <=; 0 <~>)
% Maximal formula depth : 114 ( 86 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 65 usr; 62 con; 0-1 aty)
% Number of variables : 363 ( 0 ^; 363 !; 0 ?; 363 :)
% 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(a97_type,type,
a97: $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(a98_type,type,
a98: $i ).
thf(c1_1_type,type,
c1_1: $i > $o ).
thf(hskp2_type,type,
hskp2: $o ).
thf(a99_type,type,
a99: $i ).
thf(hskp3_type,type,
hskp3: $o ).
thf(a100_type,type,
a100: $i ).
thf(hskp4_type,type,
hskp4: $o ).
thf(a103_type,type,
a103: $i ).
thf(hskp5_type,type,
hskp5: $o ).
thf(a104_type,type,
a104: $i ).
thf(hskp6_type,type,
hskp6: $o ).
thf(a105_type,type,
a105: $i ).
thf(hskp7_type,type,
hskp7: $o ).
thf(a106_type,type,
a106: $i ).
thf(hskp8_type,type,
hskp8: $o ).
thf(a107_type,type,
a107: $i ).
thf(hskp9_type,type,
hskp9: $o ).
thf(a108_type,type,
a108: $i ).
thf(hskp10_type,type,
hskp10: $o ).
thf(a110_type,type,
a110: $i ).
thf(hskp11_type,type,
hskp11: $o ).
thf(a112_type,type,
a112: $i ).
thf(hskp12_type,type,
hskp12: $o ).
thf(a113_type,type,
a113: $i ).
thf(hskp13_type,type,
hskp13: $o ).
thf(a116_type,type,
a116: $i ).
thf(hskp14_type,type,
hskp14: $o ).
thf(a120_type,type,
a120: $i ).
thf(hskp15_type,type,
hskp15: $o ).
thf(a121_type,type,
a121: $i ).
thf(hskp16_type,type,
hskp16: $o ).
thf(a122_type,type,
a122: $i ).
thf(hskp17_type,type,
hskp17: $o ).
thf(a124_type,type,
a124: $i ).
thf(hskp18_type,type,
hskp18: $o ).
thf(a129_type,type,
a129: $i ).
thf(hskp19_type,type,
hskp19: $o ).
thf(a130_type,type,
a130: $i ).
thf(hskp20_type,type,
hskp20: $o ).
thf(a132_type,type,
a132: $i ).
thf(hskp21_type,type,
hskp21: $o ).
thf(a136_type,type,
a136: $i ).
thf(hskp22_type,type,
hskp22: $o ).
thf(a138_type,type,
a138: $i ).
thf(hskp23_type,type,
hskp23: $o ).
thf(a145_type,type,
a145: $i ).
thf(hskp24_type,type,
hskp24: $o ).
thf(a147_type,type,
a147: $i ).
thf(hskp25_type,type,
hskp25: $o ).
thf(a173_type,type,
a173: $i ).
thf(hskp26_type,type,
hskp26: $o ).
thf(a195_type,type,
a195: $i ).
thf(hskp27_type,type,
hskp27: $o ).
thf(a101_type,type,
a101: $i ).
thf(hskp28_type,type,
hskp28: $o ).
thf(a137_type,type,
a137: $i ).
thf(hskp29_type,type,
hskp29: $o ).
thf(a166_type,type,
a166: $i ).
thf(1,conjecture,
~ ( ( ~ hskp0
| ( ndr1_0
& ( c0_1 @ a97 )
& ~ ( c2_1 @ a97 )
& ~ ( c3_1 @ a97 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a98 )
& ~ ( c1_1 @ a98 )
& ~ ( c3_1 @ a98 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c2_1 @ a99 )
& ~ ( c0_1 @ a99 )
& ~ ( c1_1 @ a99 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c2_1 @ a100 )
& ( c3_1 @ a100 )
& ~ ( c1_1 @ a100 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c0_1 @ a103 )
& ( c2_1 @ a103 )
& ~ ( c3_1 @ a103 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ( c2_1 @ a104 )
& ~ ( c0_1 @ a104 )
& ~ ( c3_1 @ a104 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c1_1 @ a105 )
& ( c2_1 @ a105 )
& ~ ( c3_1 @ a105 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c2_1 @ a106 )
& ( c3_1 @ a106 )
& ~ ( c0_1 @ a106 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c3_1 @ a107 )
& ~ ( c0_1 @ a107 )
& ~ ( c2_1 @ a107 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c1_1 @ a108 )
& ( c2_1 @ a108 )
& ~ ( c0_1 @ a108 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c1_1 @ a110 )
& ~ ( c2_1 @ a110 )
& ~ ( c3_1 @ a110 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c3_1 @ a112 )
& ~ ( c0_1 @ a112 )
& ~ ( c1_1 @ a112 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a113 )
& ( c1_1 @ a113 )
& ~ ( c2_1 @ a113 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a116 )
& ( c1_1 @ a116 )
& ~ ( c3_1 @ a116 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ~ ( c0_1 @ a120 )
& ~ ( c1_1 @ a120 )
& ~ ( c2_1 @ a120 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ~ ( c0_1 @ a121 )
& ~ ( c2_1 @ a121 )
& ~ ( c3_1 @ a121 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c0_1 @ a122 )
& ~ ( c1_1 @ a122 )
& ~ ( c2_1 @ a122 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c2_1 @ a124 )
& ~ ( c1_1 @ a124 )
& ~ ( c3_1 @ a124 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c0_1 @ a129 )
& ( c2_1 @ a129 )
& ~ ( c1_1 @ a129 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c1_1 @ a130 )
& ( c3_1 @ a130 )
& ~ ( c2_1 @ a130 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ~ ( c1_1 @ a132 )
& ~ ( c2_1 @ a132 )
& ~ ( c3_1 @ a132 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c3_1 @ a136 )
& ~ ( c1_1 @ a136 )
& ~ ( c2_1 @ a136 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c0_1 @ a138 )
& ( c3_1 @ a138 )
& ~ ( c2_1 @ a138 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a145 )
& ( c3_1 @ a145 )
& ~ ( c0_1 @ a145 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ~ ( c0_1 @ a147 )
& ~ ( c1_1 @ a147 )
& ~ ( c3_1 @ a147 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c1_1 @ a173 )
& ~ ( c0_1 @ a173 )
& ~ ( c3_1 @ a173 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c0_1 @ a195 )
& ( c3_1 @ a195 )
& ~ ( c1_1 @ a195 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c0_1 @ a101 )
& ( c1_1 @ a101 )
& ( c3_1 @ a101 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a137 )
& ( c1_1 @ a137 )
& ( c2_1 @ a137 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c0_1 @ a166 )
& ( c2_1 @ a166 )
& ( c3_1 @ a166 ) ) )
& ( ! [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 )
| ( c3_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 )
| ( c2_1 @ A )
| ~ ( c3_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 )
| ( 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 )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_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
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp3 )
& ( ! [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 )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp6
| 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 ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp6 )
& ( ! [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
=> ( ( c1_1 @ A )
| ~ ( c0_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 )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp5
| hskp11 )
& ( ! [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 ) ) )
| hskp12 )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [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
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp13
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp14 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp0 )
& ( ! [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 ) ) )
| hskp17 )
& ( ! [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 ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_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 )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp18
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_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 )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp6
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp2
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp22
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp22
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp23
| hskp17 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp3
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp18
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp16
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp7
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp11 )
& ( ! [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 ) ) )
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp27
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp18
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp27
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp1
| hskp9 )
& ( hskp28
| hskp4
| hskp22 )
& ( hskp27
| hskp9
| hskp2 )
& ( hskp12
| hskp13 )
& ( hskp13
| hskp18
| hskp8 )
& ( hskp18
| hskp4
| hskp20 )
& ( hskp18
| hskp19
| hskp17 )
& ( hskp26
| hskp25
| hskp5 )
& ( hskp22
| hskp0
| hskp11 )
& ( hskp22
| hskp8
| hskp15 )
& ( hskp16
| hskp6
| hskp15 )
& ( hskp16
| hskp10
| hskp8 )
& ( hskp19
| hskp8
| hskp15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c0_1 @ a97 )
& ~ ( c2_1 @ a97 )
& ~ ( c3_1 @ a97 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a98 )
& ~ ( c1_1 @ a98 )
& ~ ( c3_1 @ a98 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c2_1 @ a99 )
& ~ ( c0_1 @ a99 )
& ~ ( c1_1 @ a99 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c2_1 @ a100 )
& ( c3_1 @ a100 )
& ~ ( c1_1 @ a100 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c0_1 @ a103 )
& ( c2_1 @ a103 )
& ~ ( c3_1 @ a103 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ( c2_1 @ a104 )
& ~ ( c0_1 @ a104 )
& ~ ( c3_1 @ a104 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c1_1 @ a105 )
& ( c2_1 @ a105 )
& ~ ( c3_1 @ a105 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c2_1 @ a106 )
& ( c3_1 @ a106 )
& ~ ( c0_1 @ a106 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c3_1 @ a107 )
& ~ ( c0_1 @ a107 )
& ~ ( c2_1 @ a107 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c1_1 @ a108 )
& ( c2_1 @ a108 )
& ~ ( c0_1 @ a108 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c1_1 @ a110 )
& ~ ( c2_1 @ a110 )
& ~ ( c3_1 @ a110 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c3_1 @ a112 )
& ~ ( c0_1 @ a112 )
& ~ ( c1_1 @ a112 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a113 )
& ( c1_1 @ a113 )
& ~ ( c2_1 @ a113 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a116 )
& ( c1_1 @ a116 )
& ~ ( c3_1 @ a116 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ~ ( c0_1 @ a120 )
& ~ ( c1_1 @ a120 )
& ~ ( c2_1 @ a120 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ~ ( c0_1 @ a121 )
& ~ ( c2_1 @ a121 )
& ~ ( c3_1 @ a121 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c0_1 @ a122 )
& ~ ( c1_1 @ a122 )
& ~ ( c2_1 @ a122 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c2_1 @ a124 )
& ~ ( c1_1 @ a124 )
& ~ ( c3_1 @ a124 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c0_1 @ a129 )
& ( c2_1 @ a129 )
& ~ ( c1_1 @ a129 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c1_1 @ a130 )
& ( c3_1 @ a130 )
& ~ ( c2_1 @ a130 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ~ ( c1_1 @ a132 )
& ~ ( c2_1 @ a132 )
& ~ ( c3_1 @ a132 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c3_1 @ a136 )
& ~ ( c1_1 @ a136 )
& ~ ( c2_1 @ a136 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c0_1 @ a138 )
& ( c3_1 @ a138 )
& ~ ( c2_1 @ a138 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a145 )
& ( c3_1 @ a145 )
& ~ ( c0_1 @ a145 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ~ ( c0_1 @ a147 )
& ~ ( c1_1 @ a147 )
& ~ ( c3_1 @ a147 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c1_1 @ a173 )
& ~ ( c0_1 @ a173 )
& ~ ( c3_1 @ a173 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c0_1 @ a195 )
& ( c3_1 @ a195 )
& ~ ( c1_1 @ a195 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c0_1 @ a101 )
& ( c1_1 @ a101 )
& ( c3_1 @ a101 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a137 )
& ( c1_1 @ a137 )
& ( c2_1 @ a137 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c0_1 @ a166 )
& ( c2_1 @ a166 )
& ( c3_1 @ a166 ) ) )
& ( ! [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 )
| ( c3_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 )
| ( c2_1 @ A )
| ~ ( c3_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 )
| ( 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 )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_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
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp3 )
& ( ! [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 )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp6
| 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 ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp6 )
& ( ! [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
=> ( ( c1_1 @ A )
| ~ ( c0_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 )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp5
| hskp11 )
& ( ! [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 ) ) )
| hskp12 )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [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
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp13
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp14 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp0 )
& ( ! [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 ) ) )
| hskp17 )
& ( ! [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 ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_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 )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp18
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_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 )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp6
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp2
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp22
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp22
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp23
| hskp17 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp3
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp18
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp16
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp7
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp11 )
& ( ! [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 ) ) )
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp27
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp18
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp27
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp1
| hskp9 )
& ( hskp28
| hskp4
| hskp22 )
& ( hskp27
| hskp9
| hskp2 )
& ( hskp12
| hskp13 )
& ( hskp13
| hskp18
| hskp8 )
& ( hskp18
| hskp4
| hskp20 )
& ( hskp18
| hskp19
| hskp17 )
& ( hskp26
| hskp25
| hskp5 )
& ( hskp22
| hskp0
| hskp11 )
& ( hskp22
| hskp8
| hskp15 )
& ( hskp16
| hskp6
| hskp15 )
& ( hskp16
| hskp10
| hskp8 )
& ( hskp19
| hskp8
| hskp15 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c0_1 @ a97 )
& ~ ( c2_1 @ a97 )
& ~ ( c3_1 @ a97 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ( c0_1 @ a98 )
& ~ ( c1_1 @ a98 )
& ~ ( c3_1 @ a98 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c2_1 @ a99 )
& ~ ( c0_1 @ a99 )
& ~ ( c1_1 @ a99 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c2_1 @ a100 )
& ( c3_1 @ a100 )
& ~ ( c1_1 @ a100 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c0_1 @ a103 )
& ( c2_1 @ a103 )
& ~ ( c3_1 @ a103 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ( c2_1 @ a104 )
& ~ ( c0_1 @ a104 )
& ~ ( c3_1 @ a104 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c1_1 @ a105 )
& ( c2_1 @ a105 )
& ~ ( c3_1 @ a105 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c2_1 @ a106 )
& ( c3_1 @ a106 )
& ~ ( c0_1 @ a106 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c3_1 @ a107 )
& ~ ( c0_1 @ a107 )
& ~ ( c2_1 @ a107 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c1_1 @ a108 )
& ( c2_1 @ a108 )
& ~ ( c0_1 @ a108 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c1_1 @ a110 )
& ~ ( c2_1 @ a110 )
& ~ ( c3_1 @ a110 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c3_1 @ a112 )
& ~ ( c0_1 @ a112 )
& ~ ( c1_1 @ a112 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a113 )
& ( c1_1 @ a113 )
& ~ ( c2_1 @ a113 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c0_1 @ a116 )
& ( c1_1 @ a116 )
& ~ ( c3_1 @ a116 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ~ ( c0_1 @ a120 )
& ~ ( c1_1 @ a120 )
& ~ ( c2_1 @ a120 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ~ ( c0_1 @ a121 )
& ~ ( c2_1 @ a121 )
& ~ ( c3_1 @ a121 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c0_1 @ a122 )
& ~ ( c1_1 @ a122 )
& ~ ( c2_1 @ a122 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ( c2_1 @ a124 )
& ~ ( c1_1 @ a124 )
& ~ ( c3_1 @ a124 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c0_1 @ a129 )
& ( c2_1 @ a129 )
& ~ ( c1_1 @ a129 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c1_1 @ a130 )
& ( c3_1 @ a130 )
& ~ ( c2_1 @ a130 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ~ ( c1_1 @ a132 )
& ~ ( c2_1 @ a132 )
& ~ ( c3_1 @ a132 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c3_1 @ a136 )
& ~ ( c1_1 @ a136 )
& ~ ( c2_1 @ a136 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c0_1 @ a138 )
& ( c3_1 @ a138 )
& ~ ( c2_1 @ a138 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a145 )
& ( c3_1 @ a145 )
& ~ ( c0_1 @ a145 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ~ ( c0_1 @ a147 )
& ~ ( c1_1 @ a147 )
& ~ ( c3_1 @ a147 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c1_1 @ a173 )
& ~ ( c0_1 @ a173 )
& ~ ( c3_1 @ a173 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c0_1 @ a195 )
& ( c3_1 @ a195 )
& ~ ( c1_1 @ a195 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ( c0_1 @ a101 )
& ( c1_1 @ a101 )
& ( c3_1 @ a101 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a137 )
& ( c1_1 @ a137 )
& ( c2_1 @ a137 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c0_1 @ a166 )
& ( c2_1 @ a166 )
& ( c3_1 @ a166 ) ) )
& ( ! [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 )
| ( c3_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 )
| ( c2_1 @ A )
| ~ ( c3_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 )
| ( 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 )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_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
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp3 )
& ( ! [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 )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp6
| 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 ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp6 )
& ( ! [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
=> ( ( c1_1 @ A )
| ~ ( c0_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 )
| ~ ( c1_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp5
| hskp11 )
& ( ! [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 ) ) )
| hskp12 )
& ( ! [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 ) ) )
| hskp10 )
& ( ! [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
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp13
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp14 )
& ( ! [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 ) ) )
| hskp15 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp0 )
& ( ! [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 ) ) )
| hskp17 )
& ( ! [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 ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp9
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_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 )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp15 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp18
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_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 )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp6
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp2
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp28 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp22
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [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 ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp22
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp1
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp23
| hskp17 )
& ( ! [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 ) ) )
| ! [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
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp1 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp4
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp3
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp18
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp16
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp7
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp11 )
& ( ! [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 ) ) )
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp27
| hskp19 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp29
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp18
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp0 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp6 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp16
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp27
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp1
| hskp9 )
& ( hskp28
| hskp4
| hskp22 )
& ( hskp27
| hskp9
| hskp2 )
& ( hskp12
| hskp13 )
& ( hskp13
| hskp18
| hskp8 )
& ( hskp18
| hskp4
| hskp20 )
& ( hskp18
| hskp19
| hskp17 )
& ( hskp26
| hskp25
| hskp5 )
& ( hskp22
| hskp0
| hskp11 )
& ( hskp22
| hskp8
| hskp15 )
& ( hskp16
| hskp6
| hskp15 )
& ( hskp16
| hskp10
| hskp8 )
& ( hskp19
| hskp8
| hskp15 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(284,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN501+1 : TPTP v8.1.2. Released v2.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 19:45:48 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.02/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.07 % [INFO] Parsing done (177ms).
% 1.29/1.08 % [INFO] Running in sequential loop mode.
% 1.89/1.27 % [INFO] eprover registered as external prover.
% 1.89/1.27 % [INFO] cvc4 registered as external prover.
% 1.89/1.27 % [INFO] Scanning for conjecture ...
% 2.61/1.54 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.61/1.61 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.61/1.61 % [INFO] Problem is first-order (TPTP FOF).
% 2.88/1.63 % [INFO] Type checking passed.
% 2.88/1.63 % [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 ...
% 7.17/3.06 % External prover 'cvc4' found a proof!
% 7.17/3.06 % [INFO] Killing All external provers ...
% 7.17/3.07 % Time passed: 2542ms (effective reasoning time: 1980ms)
% 7.17/3.07 % 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)>
% 7.17/3.07 % Axioms used in derivation (0):
% 7.17/3.07 % No. of inferences in proof: 4
% 7.17/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2542 ms resp. 1980 ms w/o parsing
% 8.08/3.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.08/3.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------