TSTP Solution File: SYN502+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYN502+1 : TPTP v8.2.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:12:31 EDT 2024
% Result : Theorem 8.89s 3.44s
% Output : Refutation 8.89s
% 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 : 2242 ( 0 equ; 0 cnn)
% Maximal formula atoms : 747 ( 560 avg)
% Number of connectives : 4301 ( 722 ~;1266 |; 621 &;1341 @)
% ( 0 <=>; 351 =>; 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 : 351 ( 0 ^ 351 !; 0 ?; 351 :)
% Comments :
%------------------------------------------------------------------------------
thf(hskp0_type,type,
hskp0: $o ).
thf(ndr1_0_type,type,
ndr1_0: $o ).
thf(c1_1_type,type,
c1_1: $i > $o ).
thf(a234_type,type,
a234: $i ).
thf(c0_1_type,type,
c0_1: $i > $o ).
thf(c2_1_type,type,
c2_1: $i > $o ).
thf(hskp1_type,type,
hskp1: $o ).
thf(a235_type,type,
a235: $i ).
thf(hskp2_type,type,
hskp2: $o ).
thf(a236_type,type,
a236: $i ).
thf(c3_1_type,type,
c3_1: $i > $o ).
thf(hskp3_type,type,
hskp3: $o ).
thf(a238_type,type,
a238: $i ).
thf(hskp4_type,type,
hskp4: $o ).
thf(a239_type,type,
a239: $i ).
thf(hskp5_type,type,
hskp5: $o ).
thf(a241_type,type,
a241: $i ).
thf(hskp6_type,type,
hskp6: $o ).
thf(a242_type,type,
a242: $i ).
thf(hskp7_type,type,
hskp7: $o ).
thf(a244_type,type,
a244: $i ).
thf(hskp8_type,type,
hskp8: $o ).
thf(a245_type,type,
a245: $i ).
thf(hskp9_type,type,
hskp9: $o ).
thf(a248_type,type,
a248: $i ).
thf(hskp10_type,type,
hskp10: $o ).
thf(a249_type,type,
a249: $i ).
thf(hskp11_type,type,
hskp11: $o ).
thf(a251_type,type,
a251: $i ).
thf(hskp12_type,type,
hskp12: $o ).
thf(a252_type,type,
a252: $i ).
thf(hskp13_type,type,
hskp13: $o ).
thf(a253_type,type,
a253: $i ).
thf(hskp14_type,type,
hskp14: $o ).
thf(a257_type,type,
a257: $i ).
thf(hskp15_type,type,
hskp15: $o ).
thf(a258_type,type,
a258: $i ).
thf(hskp16_type,type,
hskp16: $o ).
thf(a259_type,type,
a259: $i ).
thf(hskp17_type,type,
hskp17: $o ).
thf(a263_type,type,
a263: $i ).
thf(hskp18_type,type,
hskp18: $o ).
thf(a265_type,type,
a265: $i ).
thf(hskp19_type,type,
hskp19: $o ).
thf(a269_type,type,
a269: $i ).
thf(hskp20_type,type,
hskp20: $o ).
thf(a271_type,type,
a271: $i ).
thf(hskp21_type,type,
hskp21: $o ).
thf(a274_type,type,
a274: $i ).
thf(hskp22_type,type,
hskp22: $o ).
thf(a276_type,type,
a276: $i ).
thf(hskp23_type,type,
hskp23: $o ).
thf(a281_type,type,
a281: $i ).
thf(hskp24_type,type,
hskp24: $o ).
thf(a282_type,type,
a282: $i ).
thf(hskp25_type,type,
hskp25: $o ).
thf(a294_type,type,
a294: $i ).
thf(hskp26_type,type,
hskp26: $o ).
thf(a314_type,type,
a314: $i ).
thf(hskp27_type,type,
hskp27: $o ).
thf(a322_type,type,
a322: $i ).
thf(hskp28_type,type,
hskp28: $o ).
thf(a237_type,type,
a237: $i ).
thf(hskp29_type,type,
hskp29: $o ).
thf(a240_type,type,
a240: $i ).
thf(hskp30_type,type,
hskp30: $o ).
thf(a243_type,type,
a243: $i ).
thf(hskp31_type,type,
hskp31: $o ).
thf(a246_type,type,
a246: $i ).
thf(1,conjecture,
~ ( ( ~ hskp0
| ( ndr1_0
& ( c1_1 @ a234 )
& ~ ( c0_1 @ a234 )
& ~ ( c2_1 @ a234 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ~ ( c0_1 @ a235 )
& ~ ( c1_1 @ a235 )
& ~ ( c2_1 @ a235 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c1_1 @ a236 )
& ( c3_1 @ a236 )
& ~ ( c0_1 @ a236 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c0_1 @ a238 )
& ~ ( c2_1 @ a238 )
& ~ ( c3_1 @ a238 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c3_1 @ a239 )
& ~ ( c1_1 @ a239 )
& ~ ( c2_1 @ a239 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ( c2_1 @ a241 )
& ( c3_1 @ a241 )
& ~ ( c0_1 @ a241 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c2_1 @ a242 )
& ~ ( c0_1 @ a242 )
& ~ ( c1_1 @ a242 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c0_1 @ a244 )
& ~ ( c1_1 @ a244 )
& ~ ( c2_1 @ a244 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c0_1 @ a245 )
& ( c2_1 @ a245 )
& ~ ( c1_1 @ a245 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c3_1 @ a248 )
& ~ ( c0_1 @ a248 )
& ~ ( c1_1 @ a248 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c0_1 @ a249 )
& ( c3_1 @ a249 )
& ~ ( c2_1 @ a249 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c2_1 @ a251 )
& ~ ( c1_1 @ a251 )
& ~ ( c3_1 @ a251 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a252 )
& ~ ( c1_1 @ a252 )
& ~ ( c3_1 @ a252 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c1_1 @ a253 )
& ~ ( c0_1 @ a253 )
& ~ ( c3_1 @ a253 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c2_1 @ a257 )
& ( c3_1 @ a257 )
& ~ ( c1_1 @ a257 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ~ ( c0_1 @ a258 )
& ~ ( c2_1 @ a258 )
& ~ ( c3_1 @ a258 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c1_1 @ a259 )
& ~ ( c2_1 @ a259 )
& ~ ( c3_1 @ a259 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ~ ( c0_1 @ a263 )
& ~ ( c1_1 @ a263 )
& ~ ( c3_1 @ a263 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c1_1 @ a265 )
& ( c2_1 @ a265 )
& ~ ( c0_1 @ a265 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c0_1 @ a269 )
& ( c3_1 @ a269 )
& ~ ( c1_1 @ a269 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c0_1 @ a271 )
& ( c1_1 @ a271 )
& ~ ( c2_1 @ a271 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c0_1 @ a274 )
& ( c2_1 @ a274 )
& ~ ( c3_1 @ a274 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c0_1 @ a276 )
& ( c1_1 @ a276 )
& ~ ( c3_1 @ a276 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a281 )
& ( c3_1 @ a281 )
& ~ ( c2_1 @ a281 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c3_1 @ a282 )
& ~ ( c0_1 @ a282 )
& ~ ( c2_1 @ a282 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c1_1 @ a294 )
& ( c2_1 @ a294 )
& ~ ( c3_1 @ a294 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c2_1 @ a314 )
& ~ ( c0_1 @ a314 )
& ~ ( c3_1 @ a314 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ~ ( c1_1 @ a322 )
& ~ ( c2_1 @ a322 )
& ~ ( c3_1 @ a322 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a237 )
& ( c1_1 @ a237 )
& ( c2_1 @ a237 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c1_1 @ a240 )
& ( c2_1 @ a240 )
& ( c3_1 @ a240 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a243 )
& ( c1_1 @ a243 )
& ( c3_1 @ a243 ) ) )
& ( ~ hskp31
| ( ndr1_0
& ( c0_1 @ a246 )
& ( c2_1 @ a246 )
& ( c3_1 @ a246 ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp1 )
& ( ! [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
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( 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 )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp2 )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp29
| hskp5 )
& ( ! [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 ) ) )
| hskp6 )
& ( ! [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 ) ) )
| hskp30 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp7 )
& ( ! [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 ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp7
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp30
| hskp9 )
& ( ! [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 ) ) )
| ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp14 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp31
| hskp14 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp29
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp18
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp19
| hskp16 )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp8
| hskp13 )
& ( ! [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 ) ) )
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp22
| hskp18 )
& ( ! [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 ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp19
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_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 ) ) ) )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| 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 ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp16
| hskp11 )
& ( ! [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
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp29 )
& ( ! [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 ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12
| hskp3 )
& ( ! [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 ) ) )
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp25
| hskp5 )
& ( ! [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
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp22
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp20
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp31
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp19
| hskp15 )
& ( ! [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 ) ) )
| hskp26 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp19
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31
| hskp21 )
& ( ! [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 ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp27 )
& ( hskp28
| hskp22
| hskp2 )
& ( hskp22
| hskp18
| hskp5 )
& ( hskp8
| hskp19
| hskp9 )
& ( hskp8
| hskp7
| hskp15 )
& ( hskp8
| hskp13
| hskp11 )
& ( hskp8
| hskp13
| hskp24 )
& ( hskp19
| hskp18
| hskp11 )
& ( hskp2
| hskp13
| hskp14 )
& ( hskp23
| hskp13
| hskp24 )
& ( hskp5
| hskp11
| hskp9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c1_1 @ a234 )
& ~ ( c0_1 @ a234 )
& ~ ( c2_1 @ a234 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ~ ( c0_1 @ a235 )
& ~ ( c1_1 @ a235 )
& ~ ( c2_1 @ a235 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c1_1 @ a236 )
& ( c3_1 @ a236 )
& ~ ( c0_1 @ a236 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c0_1 @ a238 )
& ~ ( c2_1 @ a238 )
& ~ ( c3_1 @ a238 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c3_1 @ a239 )
& ~ ( c1_1 @ a239 )
& ~ ( c2_1 @ a239 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ( c2_1 @ a241 )
& ( c3_1 @ a241 )
& ~ ( c0_1 @ a241 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c2_1 @ a242 )
& ~ ( c0_1 @ a242 )
& ~ ( c1_1 @ a242 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c0_1 @ a244 )
& ~ ( c1_1 @ a244 )
& ~ ( c2_1 @ a244 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c0_1 @ a245 )
& ( c2_1 @ a245 )
& ~ ( c1_1 @ a245 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c3_1 @ a248 )
& ~ ( c0_1 @ a248 )
& ~ ( c1_1 @ a248 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c0_1 @ a249 )
& ( c3_1 @ a249 )
& ~ ( c2_1 @ a249 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c2_1 @ a251 )
& ~ ( c1_1 @ a251 )
& ~ ( c3_1 @ a251 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a252 )
& ~ ( c1_1 @ a252 )
& ~ ( c3_1 @ a252 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c1_1 @ a253 )
& ~ ( c0_1 @ a253 )
& ~ ( c3_1 @ a253 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c2_1 @ a257 )
& ( c3_1 @ a257 )
& ~ ( c1_1 @ a257 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ~ ( c0_1 @ a258 )
& ~ ( c2_1 @ a258 )
& ~ ( c3_1 @ a258 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c1_1 @ a259 )
& ~ ( c2_1 @ a259 )
& ~ ( c3_1 @ a259 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ~ ( c0_1 @ a263 )
& ~ ( c1_1 @ a263 )
& ~ ( c3_1 @ a263 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c1_1 @ a265 )
& ( c2_1 @ a265 )
& ~ ( c0_1 @ a265 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c0_1 @ a269 )
& ( c3_1 @ a269 )
& ~ ( c1_1 @ a269 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c0_1 @ a271 )
& ( c1_1 @ a271 )
& ~ ( c2_1 @ a271 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c0_1 @ a274 )
& ( c2_1 @ a274 )
& ~ ( c3_1 @ a274 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c0_1 @ a276 )
& ( c1_1 @ a276 )
& ~ ( c3_1 @ a276 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a281 )
& ( c3_1 @ a281 )
& ~ ( c2_1 @ a281 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c3_1 @ a282 )
& ~ ( c0_1 @ a282 )
& ~ ( c2_1 @ a282 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c1_1 @ a294 )
& ( c2_1 @ a294 )
& ~ ( c3_1 @ a294 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c2_1 @ a314 )
& ~ ( c0_1 @ a314 )
& ~ ( c3_1 @ a314 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ~ ( c1_1 @ a322 )
& ~ ( c2_1 @ a322 )
& ~ ( c3_1 @ a322 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a237 )
& ( c1_1 @ a237 )
& ( c2_1 @ a237 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c1_1 @ a240 )
& ( c2_1 @ a240 )
& ( c3_1 @ a240 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a243 )
& ( c1_1 @ a243 )
& ( c3_1 @ a243 ) ) )
& ( ~ hskp31
| ( ndr1_0
& ( c0_1 @ a246 )
& ( c2_1 @ a246 )
& ( c3_1 @ a246 ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp1 )
& ( ! [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
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( 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 )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp2 )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp29
| hskp5 )
& ( ! [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 ) ) )
| hskp6 )
& ( ! [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 ) ) )
| hskp30 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp7 )
& ( ! [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 ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp7
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp30
| hskp9 )
& ( ! [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 ) ) )
| ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp14 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp31
| hskp14 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp29
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp18
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp19
| hskp16 )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp8
| hskp13 )
& ( ! [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 ) ) )
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp22
| hskp18 )
& ( ! [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 ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp19
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_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 ) ) ) )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| 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 ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp16
| hskp11 )
& ( ! [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
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp29 )
& ( ! [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 ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12
| hskp3 )
& ( ! [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 ) ) )
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp25
| hskp5 )
& ( ! [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
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp22
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp20
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp31
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp19
| hskp15 )
& ( ! [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 ) ) )
| hskp26 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp19
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31
| hskp21 )
& ( ! [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 ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp27 )
& ( hskp28
| hskp22
| hskp2 )
& ( hskp22
| hskp18
| hskp5 )
& ( hskp8
| hskp19
| hskp9 )
& ( hskp8
| hskp7
| hskp15 )
& ( hskp8
| hskp13
| hskp11 )
& ( hskp8
| hskp13
| hskp24 )
& ( hskp19
| hskp18
| hskp11 )
& ( hskp2
| hskp13
| hskp14 )
& ( hskp23
| hskp13
| hskp24 )
& ( hskp5
| hskp11
| hskp9 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( ~ hskp0
| ( ndr1_0
& ( c1_1 @ a234 )
& ~ ( c0_1 @ a234 )
& ~ ( c2_1 @ a234 ) ) )
& ( ~ hskp1
| ( ndr1_0
& ~ ( c0_1 @ a235 )
& ~ ( c1_1 @ a235 )
& ~ ( c2_1 @ a235 ) ) )
& ( ~ hskp2
| ( ndr1_0
& ( c1_1 @ a236 )
& ( c3_1 @ a236 )
& ~ ( c0_1 @ a236 ) ) )
& ( ~ hskp3
| ( ndr1_0
& ( c0_1 @ a238 )
& ~ ( c2_1 @ a238 )
& ~ ( c3_1 @ a238 ) ) )
& ( ~ hskp4
| ( ndr1_0
& ( c3_1 @ a239 )
& ~ ( c1_1 @ a239 )
& ~ ( c2_1 @ a239 ) ) )
& ( ~ hskp5
| ( ndr1_0
& ( c2_1 @ a241 )
& ( c3_1 @ a241 )
& ~ ( c0_1 @ a241 ) ) )
& ( ~ hskp6
| ( ndr1_0
& ( c2_1 @ a242 )
& ~ ( c0_1 @ a242 )
& ~ ( c1_1 @ a242 ) ) )
& ( ~ hskp7
| ( ndr1_0
& ( c0_1 @ a244 )
& ~ ( c1_1 @ a244 )
& ~ ( c2_1 @ a244 ) ) )
& ( ~ hskp8
| ( ndr1_0
& ( c0_1 @ a245 )
& ( c2_1 @ a245 )
& ~ ( c1_1 @ a245 ) ) )
& ( ~ hskp9
| ( ndr1_0
& ( c3_1 @ a248 )
& ~ ( c0_1 @ a248 )
& ~ ( c1_1 @ a248 ) ) )
& ( ~ hskp10
| ( ndr1_0
& ( c0_1 @ a249 )
& ( c3_1 @ a249 )
& ~ ( c2_1 @ a249 ) ) )
& ( ~ hskp11
| ( ndr1_0
& ( c2_1 @ a251 )
& ~ ( c1_1 @ a251 )
& ~ ( c3_1 @ a251 ) ) )
& ( ~ hskp12
| ( ndr1_0
& ( c0_1 @ a252 )
& ~ ( c1_1 @ a252 )
& ~ ( c3_1 @ a252 ) ) )
& ( ~ hskp13
| ( ndr1_0
& ( c1_1 @ a253 )
& ~ ( c0_1 @ a253 )
& ~ ( c3_1 @ a253 ) ) )
& ( ~ hskp14
| ( ndr1_0
& ( c2_1 @ a257 )
& ( c3_1 @ a257 )
& ~ ( c1_1 @ a257 ) ) )
& ( ~ hskp15
| ( ndr1_0
& ~ ( c0_1 @ a258 )
& ~ ( c2_1 @ a258 )
& ~ ( c3_1 @ a258 ) ) )
& ( ~ hskp16
| ( ndr1_0
& ( c1_1 @ a259 )
& ~ ( c2_1 @ a259 )
& ~ ( c3_1 @ a259 ) ) )
& ( ~ hskp17
| ( ndr1_0
& ~ ( c0_1 @ a263 )
& ~ ( c1_1 @ a263 )
& ~ ( c3_1 @ a263 ) ) )
& ( ~ hskp18
| ( ndr1_0
& ( c1_1 @ a265 )
& ( c2_1 @ a265 )
& ~ ( c0_1 @ a265 ) ) )
& ( ~ hskp19
| ( ndr1_0
& ( c0_1 @ a269 )
& ( c3_1 @ a269 )
& ~ ( c1_1 @ a269 ) ) )
& ( ~ hskp20
| ( ndr1_0
& ( c0_1 @ a271 )
& ( c1_1 @ a271 )
& ~ ( c2_1 @ a271 ) ) )
& ( ~ hskp21
| ( ndr1_0
& ( c0_1 @ a274 )
& ( c2_1 @ a274 )
& ~ ( c3_1 @ a274 ) ) )
& ( ~ hskp22
| ( ndr1_0
& ( c0_1 @ a276 )
& ( c1_1 @ a276 )
& ~ ( c3_1 @ a276 ) ) )
& ( ~ hskp23
| ( ndr1_0
& ( c1_1 @ a281 )
& ( c3_1 @ a281 )
& ~ ( c2_1 @ a281 ) ) )
& ( ~ hskp24
| ( ndr1_0
& ( c3_1 @ a282 )
& ~ ( c0_1 @ a282 )
& ~ ( c2_1 @ a282 ) ) )
& ( ~ hskp25
| ( ndr1_0
& ( c1_1 @ a294 )
& ( c2_1 @ a294 )
& ~ ( c3_1 @ a294 ) ) )
& ( ~ hskp26
| ( ndr1_0
& ( c2_1 @ a314 )
& ~ ( c0_1 @ a314 )
& ~ ( c3_1 @ a314 ) ) )
& ( ~ hskp27
| ( ndr1_0
& ~ ( c1_1 @ a322 )
& ~ ( c2_1 @ a322 )
& ~ ( c3_1 @ a322 ) ) )
& ( ~ hskp28
| ( ndr1_0
& ( c0_1 @ a237 )
& ( c1_1 @ a237 )
& ( c2_1 @ a237 ) ) )
& ( ~ hskp29
| ( ndr1_0
& ( c1_1 @ a240 )
& ( c2_1 @ a240 )
& ( c3_1 @ a240 ) ) )
& ( ~ hskp30
| ( ndr1_0
& ( c0_1 @ a243 )
& ( c1_1 @ a243 )
& ( c3_1 @ a243 ) ) )
& ( ~ hskp31
| ( ndr1_0
& ( c0_1 @ a246 )
& ( c2_1 @ a246 )
& ( c3_1 @ a246 ) ) )
& ( ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp1 )
& ( ! [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
=> ( ( c2_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( 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 )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp2 )
& ( ! [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 ) ) )
| hskp28 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c2_1 @ A ) ) )
| hskp29
| hskp5 )
& ( ! [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 ) ) )
| hskp6 )
& ( ! [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 ) ) )
| hskp30 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp7 )
& ( ! [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 ) ) )
| hskp8 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp7
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12
| hskp13 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [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 ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| hskp30
| hskp9 )
& ( ! [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 ) ) )
| ! [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 ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp14 )
& ( ! [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 ) ) )
| 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 ) ) )
| hskp16 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp31
| hskp14 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp29
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp18
| hskp9 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp28
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp19
| hskp16 )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp8
| hskp13 )
& ( ! [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 ) ) )
| hskp21 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp22
| hskp18 )
& ( ! [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 ) ) )
| hskp31 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp19
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp23
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c0_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp11
| hskp24 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_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 ) ) ) )
& ( ! [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 ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| 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 ) ) )
| hskp18 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c2_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp16
| hskp11 )
& ( ! [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
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp10 )
& ( ! [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 ) ) )
| hskp29 )
& ( ! [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 ) ) )
| hskp11 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp25 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ( c3_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp9
| hskp17 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp10
| hskp5 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp12
| hskp3 )
& ( ! [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 ) ) )
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp25
| hskp5 )
& ( ! [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
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) ) )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c0_1 @ A ) ) )
| hskp22
| hskp7 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp20 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp20
| hskp2 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp31
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c2_1 @ A )
| ( c3_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp19
| hskp15 )
& ( ! [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 ) ) )
| hskp26 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c0_1 @ A )
| ~ ( c1_1 @ A ) ) )
| hskp19
| hskp29 )
& ( ! [A: $i] :
( ndr1_0
=> ( ( c3_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c2_1 @ A ) ) )
| hskp31
| hskp21 )
& ( ! [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 ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c0_1 @ A )
| ~ ( c1_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp4 )
& ( ! [A: $i] :
( ndr1_0
=> ( ~ ( c1_1 @ A )
| ~ ( c2_1 @ A )
| ~ ( c3_1 @ A ) ) )
| hskp24
| hskp27 )
& ( hskp28
| hskp22
| hskp2 )
& ( hskp22
| hskp18
| hskp5 )
& ( hskp8
| hskp19
| hskp9 )
& ( hskp8
| hskp7
| hskp15 )
& ( hskp8
| hskp13
| hskp11 )
& ( hskp8
| hskp13
| hskp24 )
& ( hskp19
| hskp18
| hskp11 )
& ( hskp2
| hskp13
| hskp14 )
& ( hskp23
| hskp13
| hskp24 )
& ( hskp5
| hskp11
| hskp9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(304,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN502+1 : TPTP v8.2.0. Released v2.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n008.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 14:28:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.92/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.55/1.09 % [INFO] Parsing done (160ms).
% 1.55/1.10 % [INFO] Running in sequential loop mode.
% 1.92/1.31 % [INFO] eprover registered as external prover.
% 1.92/1.31 % [INFO] cvc4 registered as external prover.
% 1.92/1.32 % [INFO] Scanning for conjecture ...
% 2.66/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.87/1.71 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.87/1.71 % [INFO] Problem is first-order (TPTP FOF).
% 2.87/1.73 % [INFO] Type checking passed.
% 2.87/1.73 % [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 ...
% 8.89/3.43 % External prover 'cvc4' found a proof!
% 8.89/3.43 % [INFO] Killing All external provers ...
% 8.89/3.44 % Time passed: 2879ms (effective reasoning time: 2336ms)
% 8.89/3.44 % 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)>
% 8.89/3.44 % Axioms used in derivation (0):
% 8.89/3.44 % No. of inferences in proof: 4
% 8.89/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2879 ms resp. 2336 ms w/o parsing
% 8.89/3.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.89/3.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------