%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 5 06:58:56 PM UTC 2026
% Result : Theorem 2.14s 1.72s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 88
% Number of leaves : 17
% Syntax : Number of formulae : 374 ( 17 unt; 0 typ; 14 def)
% Number of atoms : 7393 (1744 equ; 0 cnn)
% Maximal formula atoms : 33 ( 19 avg)
% Number of connectives : 24945 (3190 ~;4055 |; 301 &;14480 @)
% ( 14 <=>; 175 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 8 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 2533 (2533 >; 0 *; 0 +; 0 <<)
% Number of symbols : 135 ( 131 usr; 21 con; 0-4 aty)
% (2730 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 4683 (3119 ^;1557 !; 7 ?;4683 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
d_unsorted: $tType ).
thf(func_def_0,type,
unsorted: $tType ).
thf(func_def_1,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
d_unsorted: $tType ).
thf(func_def_31,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_32,type,
d_unsorted_0: d_unsorted ).
thf(func_def_53,type,
sK0: $i > d_unsorted ).
thf(func_def_55,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
sK3: $i > $i > $o ).
thf(func_def_58,type,
sK5: $i > $o ).
thf(func_def_59,type,
sK6: $i > $o ).
thf(func_def_60,type,
sK7: $i > $i ).
thf(func_def_61,type,
sK8: ( $i > $i > $o ) > $i ).
thf(func_def_62,type,
sK9: ( $i > $i > $o ) > $i ).
thf(func_def_63,type,
sK10: ( $i > $i > $o ) > $i ).
thf(func_def_64,type,
sK11: ( $i > $i > $o ) > $i ).
thf(func_def_65,type,
sK12: ( $i > $i > $o ) > $i ).
thf(func_def_67,type,
sK14: $i > $o ).
thf(func_def_68,type,
sK15: $i > $i ).
thf(func_def_69,type,
sK16: $i > $i ).
thf(func_def_70,type,
sK17: ( $i > $i > $o ) > $i ).
thf(func_def_71,type,
sK18: ( $i > $i > $o ) > $i ).
thf(func_def_72,type,
sK19: ( $i > $i > $o ) > $i ).
thf(func_def_73,type,
sK20: ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK21: ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK23: ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK24: ( $i > $i > $o ) > $i ).
thf(func_def_78,type,
sK25: ( $i > $i > $o ) > $i ).
thf(func_def_79,type,
sK26: $i > $i ).
thf(func_def_80,type,
sK27: ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK28: ( $i > $i > $o ) > $i ).
thf(func_def_82,type,
sK29: ( $i > $i > $o ) > $i ).
thf(func_def_83,type,
sK30: ( $i > $i > $o ) > $i ).
thf(func_def_84,type,
sK31: ( $i > $i > $o ) > $i ).
thf(func_def_85,type,
sK32: ( $i > $i > $o ) > $i ).
thf(func_def_86,type,
sK33: ( $i > $i > $o ) > $i ).
thf(func_def_87,type,
sK34: ( $i > $i > $o ) > $i ).
thf(func_def_88,type,
sK35: ( $i > $i > $o ) > $i ).
thf(func_def_89,type,
sK36: ( $i > $i > $o ) > $i ).
thf(func_def_90,type,
sK37: ( $i > $i > $o ) > $i ).
thf(func_def_91,type,
sK38: ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
sK39: ( $i > $i > $o ) > $i ).
thf(func_def_93,type,
sK40: ( $i > $i > $o ) > $i ).
thf(func_def_94,type,
sK41: ( $i > $i > $o ) > $i ).
thf(func_def_95,type,
sK42: ( $i > $i > $o ) > $i ).
thf(func_def_96,type,
sK43: ( $i > $i > $o ) > $i ).
thf(func_def_97,type,
sK44: ( $i > $i > $o ) > $i ).
thf(func_def_98,type,
sK45: ( $i > $i > $o ) > $i ).
thf(func_def_99,type,
sK46: ( $i > $i > $o ) > $i ).
thf(func_def_100,type,
sK47: ( $i > $i > $o ) > $i ).
thf(func_def_101,type,
sK48: ( $i > $i > $o ) > $i ).
thf(func_def_102,type,
sK49: ( $i > $i > $o ) > $i ).
thf(func_def_103,type,
sK50: ( $i > $i > $o ) > $i ).
thf(func_def_104,type,
sK51: ( $i > $i > $o ) > $i ).
thf(func_def_105,type,
sK52: ( $i > $i > $o ) > $i ).
thf(func_def_106,type,
sK53: ( $i > $i > $o ) > $i ).
thf(func_def_107,type,
sK54: ( $i > $i > $o ) > $i ).
thf(func_def_108,type,
sK55: ( $i > $i > $o ) > $i ).
thf(func_def_109,type,
sK56: ( $i > $i > $o ) > $i ).
thf(func_def_110,type,
sK57: ( $i > $i > $o ) > $i ).
thf(func_def_111,type,
sK58: ( $i > $i > $o ) > $i ).
thf(func_def_112,type,
sK59: ( $i > $i > $o ) > $i ).
thf(func_def_113,type,
sK60: ( $i > $i > $o ) > $i ).
thf(func_def_114,type,
sK61: ( $i > $i > $o ) > $i ).
thf(func_def_115,type,
sK62: ( $i > $i > $o ) > $i ).
thf(func_def_116,type,
sK63: ( $i > $i > $o ) > $i ).
thf(func_def_117,type,
sK64: ( $i > $i > $o ) > $i ).
thf(func_def_118,type,
sK65: ( $i > $i > $o ) > $i ).
thf(func_def_119,type,
sK66: ( $i > $i > $o ) > $i ).
thf(func_def_120,type,
sK67: ( $i > $i > $o ) > $i ).
thf(func_def_121,type,
sK68: ( $i > $i > $o ) > $i ).
thf(func_def_122,type,
sK69: ( $i > $i > $o ) > $i ).
thf(func_def_123,type,
sK70: ( $i > $i > $o ) > $i ).
thf(func_def_125,type,
sK72: ( $i > $i > $o ) > $i ).
thf(func_def_126,type,
sK73: ( $i > $i > $o ) > $i ).
thf(func_def_127,type,
sK74: ( $i > $i > $o ) > $i ).
thf(func_def_128,type,
sK75: ( $i > $i > $o ) > $i ).
thf(func_def_129,type,
sK76: ( $i > $i > $o ) > $i ).
thf(func_def_130,type,
sK77: ( $i > $i > $o ) > $i ).
thf(func_def_131,type,
sK78: ( $i > $i > $o ) > $i ).
thf(func_def_132,type,
sK79: ( $i > $o ) > $i ).
thf(func_def_133,type,
sK80: ( $i > $o ) > $i ).
thf(func_def_134,type,
sK81: $i > ( $i > $o ) > $i > $i > $o ).
thf(func_def_135,type,
sK82: $i > ( $i > $o ) > $i > $i > $o ).
thf(func_def_136,type,
sK83: ( $i > $o ) > $i > $i > $i > $o ).
thf(func_def_137,type,
sK84: ( $i > $o ) > $i > $i > $i > $o ).
thf(func_def_138,type,
sK85: ( $i > $o ) > $i > $i > $i > $o ).
thf(func_def_139,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_140,type,
sK87: ( $i > $o ) > $i > $i > $i > $o ).
thf(f2994,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f681,f689,f695,f707,f712,f777,f969,f1245,f1270,f1639,f1666,f2212,f2253,f2349,f2381,f2563,f2869,f2975]) ).
thf(f2975,plain,
( ~ spl1_35
| ~ spl1_38 ),
inference(avatar_contradiction_clause,[status(thm)],[f2974]) ).
thf(f2974,plain,
( $false
| ~ spl1_35
| ~ spl1_38 ),
inference(subsumption_resolution,[status(thm)],[f2970,f1310]) ).
thf(f1310,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f50,f50]) ).
thf(f50,plain,
! [X0: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X0 ),
inference(backward_demodulation,[status(thm)],[f45,f44]) ).
thf(f44,plain,
! [X2: d_unsorted] : ( d_unsorted_0 = X2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ! [X0: $i] :
( ( d2unsorted @ ( sK0 @ X0 ) )
= X0 )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y5 != Y4 ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) )
| ( Y1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ( Y3 @ Y8 @ Y7 )
| ~ ( Y3 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y6 ) ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( Y3 @ Y1 @ Y2 )
| ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) )
| ( X3 = X4 ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) )
| ( Y2 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y6 )
| ~ ( Y2 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 = Y1 ) ) ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y8 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y1 @ Y2 @ Y3 )
| ~ ( Y0 @ Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ( Y2 @ Y8 @ Y7 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).
thf(f13,plain,
! [X0: $i] :
( ? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
=> ( ( d2unsorted @ ( sK0 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ! [X2: d_unsorted] : ( d_unsorted_0 = X2 )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y5 != Y4 ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) )
| ( Y1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ( Y3 @ Y8 @ Y7 )
| ~ ( Y3 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y6 ) ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( Y3 @ Y1 @ Y2 )
| ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ! [X3: d_unsorted,X4: d_unsorted] :
( ( ( d2unsorted @ X3 )
!= ( d2unsorted @ X4 ) )
| ( X3 = X4 ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) )
| ( Y2 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y6 )
| ~ ( Y2 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 = Y1 ) ) ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y8 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y1 @ Y2 @ Y3 )
| ~ ( Y0 @ Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ( Y2 @ Y8 @ Y7 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
( ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y5 != Y4 ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) )
| ( Y1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ( Y3 @ Y8 @ Y7 )
| ~ ( Y3 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y6 ) ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( Y3 @ Y1 @ Y2 )
| ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
!= ( d2unsorted @ X0 ) )
| ( X0 = X1 ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) )
| ( Y2 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y6 )
| ~ ( Y2 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 = Y1 ) ) ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y8 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y1 @ Y2 @ Y3 )
| ~ ( Y0 @ Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ( Y2 @ Y8 @ Y7 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ! [X2: $i] :
? [X3: d_unsorted] :
( ( d2unsorted @ X3 )
= X2 )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y1 @ Y2 @ Y3 )
| ~ ( Y0 @ Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) )
| ( Y2 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y6 )
| ~ ( Y2 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 = Y1 ) ) ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y8 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( Y3 @ Y1 @ Y2 )
| ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ! [X0: d_unsorted,X1: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X0 ) )
=> ( X0 = X1 ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ( Y2 @ Y8 @ Y7 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y5 != Y4 ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) )
| ( Y1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ( Y3 @ Y8 @ Y7 )
| ~ ( Y3 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y6 ) ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ! [X4: d_unsorted] : ( d_unsorted_0 = X4 )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ( Y2 @ Y8 @ Y7 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ! [X53: d_unsorted,X54: d_unsorted] :
( ( ( d2unsorted @ X54 )
= ( d2unsorted @ X53 ) )
=> ( X53 = X54 ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( Y3 @ Y1 @ Y2 )
| ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y8 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
& ( inv
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y1 @ Y2 @ Y3 )
| ~ ( Y0 @ Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ! [X160: $i] :
? [X161: d_unsorted] :
( ( d2unsorted @ X161 )
= X160 )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) )
| ( Y2 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y6 )
| ~ ( Y2 @ Y5 @ Y7 )
| ( Y2 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 = Y1 ) ) ) ) ) ) ) )
& ! [X202: d_unsorted] : ( d_unsorted_0 = X202 )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) )
& ( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y5 != Y4 ) )
| ( ( Y5 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ( Y6 @ Y5 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y3 @ Y6 @ Y7 ) ) ) )
| ( Y1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ( Y3 @ Y8 @ Y7 )
| ~ ( Y3 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y6 ) ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( irrefl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
~ ( X0 @ X1 @ X1 ) ) )
& ( tc
= ( ^ [X2: $i > $i > $o,X3: $i,X4: $i] :
! [X5: $i > $i > $o] :
( ( X5 @ X3 @ X4 )
| ~ ! [X6: $i,X7: $i] :
( ~ ( X2 @ X6 @ X7 )
| ( X5 @ X6 @ X7 ) )
| ~ ! [X8: $i,X9: $i,X10: $i] :
( ~ ( X5 @ X10 @ X8 )
| ( X5 @ X10 @ X9 )
| ~ ( X5 @ X8 @ X9 ) ) ) ) )
& ( lconfl
= ( ^ [X11: $i > $i > $o] :
! [X12: $i > $i > $o,X13: $i,X14: $i,X15: $i > $i > $o,X16: $i] :
( ~ ! [X17: $i,X18: $i,X19: $i] :
( ~ ( X12 @ X17 @ X18 )
| ( X12 @ X19 @ X18 )
| ~ ( X12 @ X19 @ X17 ) )
| ( X12 @ X16 @ X13 )
| ~ ! [X20: $i,X21: $i,X22: $i] :
( ( X15 @ X20 @ X21 )
| ~ ( X15 @ X20 @ X22 )
| ~ ( X15 @ X22 @ X21 ) )
| ~ ! [X23: $i,X24: $i] :
( ~ ( X11 @ X24 @ X23 )
| ( X12 @ X24 @ X23 ) )
| ~ ( X11 @ X14 @ X16 )
| ( X15 @ X13 @ X16 )
| ( X13 = X16 )
| ~ ! [X25: $i,X26: $i] :
( ~ ( X11 @ X26 @ X25 )
| ( X15 @ X26 @ X25 ) )
| ~ ( X11 @ X14 @ X13 )
| ~ ! [X27: $i] :
( ~ ! [X28: $i > $i > $o] :
( ~ ! [X29: $i,X30: $i] :
( ( X28 @ X29 @ X30 )
| ~ ( X11 @ X29 @ X30 ) )
| ~ ! [X31: $i,X32: $i,X33: $i] :
( ~ ( X28 @ X32 @ X31 )
| ~ ( X28 @ X33 @ X32 )
| ( X28 @ X33 @ X31 ) )
| ( X28 @ X13 @ X27 ) )
| ~ ! [X34: $i > $i > $o] :
( ~ ! [X35: $i,X36: $i] :
( ~ ( X11 @ X36 @ X35 )
| ( X34 @ X36 @ X35 ) )
| ~ ! [X37: $i,X38: $i,X39: $i] :
( ~ ( X34 @ X37 @ X39 )
| ~ ( X34 @ X39 @ X38 )
| ( X34 @ X37 @ X38 ) )
| ( X34 @ X16 @ X27 ) ) ) ) ) )
& ( ( ^ [X40: $i > $i > $o] :
! [X41: $i,X42: $i] :
( ~ ( X40 @ X41 @ X42 )
| ( X40 @ X42 @ X41 ) ) )
= symm )
& ( ( ^ [X43: $i > $i > $o] :
! [X44: $i,X45: $i,X46: $i] :
( ~ ( X43 @ X44 @ X45 )
| ( X43 @ X46 @ X45 )
| ~ ( X43 @ X46 @ X44 ) ) )
= trans )
& ( ( ^ [X47: $i > $i > $o] :
! [X48: $i,X49: $i] :
( ~ ( X47 @ X49 @ X48 )
| ( X48 = X49 )
| ~ ( X47 @ X48 @ X49 ) ) )
= antisymm )
& ( total
= ( ^ [X50: $i > $i > $o] :
! [X51: $i,X52: $i] :
( ( X50 @ X51 @ X52 )
| ( X50 @ X52 @ X51 )
| ( X51 = X52 ) ) ) )
& ! [X53: d_unsorted,X54: d_unsorted] :
( ( ( d2unsorted @ X54 )
= ( d2unsorted @ X53 ) )
=> ( X53 = X54 ) )
& ( ( ^ [X55: ( $i > $i > $o ) > $i > $i > $o] :
! [X56: $i > $i > $o,X57: $i,X58: $i] :
( ( X55 @ X56 @ X58 @ X57 )
| ~ ( X56 @ X58 @ X57 ) ) )
= infl )
& ( sconfl
= ( ^ [X59: $i > $i > $o] :
! [X60: $i > $i > $o,X61: $i,X62: $i > $i > $o,X63: $i,X64: $i] :
( ~ ! [X65: $i,X66: $i] :
( ( X62 @ X66 @ X65 )
| ~ ( X59 @ X66 @ X65 ) )
| ~ ! [X67: $i,X68: $i,X69: $i] :
( ( X62 @ X69 @ X68 )
| ~ ( X62 @ X67 @ X68 )
| ~ ( X62 @ X69 @ X67 ) )
| ( X61 = X63 )
| ( ( X61 != X64 )
& ~ ! [X70: $i > $i > $o] :
( ~ ! [X71: $i,X72: $i,X73: $i] :
( ~ ( X70 @ X72 @ X73 )
| ( X70 @ X71 @ X73 )
| ~ ( X70 @ X71 @ X72 ) )
| ~ ! [X74: $i,X75: $i] :
( ( X70 @ X75 @ X74 )
| ~ ( X59 @ X75 @ X74 ) )
| ( X70 @ X64 @ X61 ) ) )
| ~ ! [X76: $i,X77: $i] :
( ( X60 @ X76 @ X77 )
| ~ ( X59 @ X76 @ X77 ) )
| ~ ! [X78: $i,X79: $i,X80: $i] :
( ( X60 @ X80 @ X78 )
| ~ ( X60 @ X80 @ X79 )
| ~ ( X60 @ X79 @ X78 ) )
| ( X60 @ X63 @ X61 )
| ~ ( X59 @ X64 @ X63 )
| ~ ! [X81: $i] :
( ~ ! [X82: $i > $i > $o] :
( ~ ! [X83: $i,X84: $i] :
( ( X82 @ X83 @ X84 )
| ~ ( X59 @ X83 @ X84 ) )
| ~ ! [X85: $i,X86: $i,X87: $i] :
( ~ ( X82 @ X86 @ X85 )
| ( X82 @ X87 @ X85 )
| ~ ( X82 @ X87 @ X86 ) )
| ( X82 @ X61 @ X81 ) )
| ~ ! [X88: $i > $i > $o] :
( ~ ! [X89: $i,X90: $i] :
( ( X88 @ X90 @ X89 )
| ~ ( X59 @ X90 @ X89 ) )
| ( X88 @ X63 @ X81 )
| ~ ! [X91: $i,X92: $i,X93: $i] :
( ~ ( X88 @ X92 @ X93 )
| ( X88 @ X91 @ X93 )
| ~ ( X88 @ X91 @ X92 ) ) ) )
| ( X62 @ X61 @ X63 ) ) ) )
& ( inv
= ( ^ [X94: $i > $i > $o,X95: $i,X96: $i] : ( X94 @ X96 @ X95 ) ) )
& ( norm
= ( ^ [X97: $i > $i > $o] :
! [X98: $i,X99: $i] :
( ~ ( X97 @ X99 @ X98 )
| ~ ! [X100: $i] :
( ~ ! [X101: $i] :
~ ( X97 @ X100 @ X101 )
| ~ ! [X102: $i > $i > $o] :
( ~ ! [X103: $i,X104: $i] :
( ~ ( X97 @ X104 @ X103 )
| ( X102 @ X104 @ X103 ) )
| ~ ! [X105: $i,X106: $i,X107: $i] :
( ~ ( X102 @ X105 @ X107 )
| ~ ( X102 @ X107 @ X106 )
| ( X102 @ X105 @ X106 ) )
| ( X102 @ X99 @ X100 ) ) ) ) ) )
& ( ( ^ [X108: $i > $i > $o,X109: $i,X110: $i] :
( ( X108 @ X110 @ X109 )
| ( X108 @ X109 @ X110 ) ) )
= sc )
& ( join
= ( ^ [X111: $i > $i > $o,X112: $i,X113: $i] :
~ ( ~ ! [X114: $i > $i > $o] :
( ~ ! [X115: $i,X116: $i] :
( ( X114 @ X115 @ X116 )
| ~ ( X111 @ X115 @ X116 ) )
| ( X114 @ X112 @ X113 )
| ~ ! [X117: $i,X118: $i,X119: $i] :
( ~ ( X114 @ X117 @ X119 )
| ~ ( X114 @ X118 @ X117 )
| ( X114 @ X118 @ X119 ) ) )
& ( X112 != X113 )
& ! [X120: $i] :
( ~ ! [X121: $i > $i > $o] :
( ( X121 @ X112 @ X120 )
| ~ ! [X122: $i,X123: $i] :
( ( X121 @ X122 @ X123 )
| ~ ( X111 @ X122 @ X123 ) )
| ~ ! [X124: $i,X125: $i,X126: $i] :
( ( X121 @ X126 @ X125 )
| ~ ( X121 @ X124 @ X125 )
| ~ ( X121 @ X126 @ X124 ) ) )
| ~ ! [X127: $i > $i > $o] :
( ~ ! [X128: $i,X129: $i,X130: $i] :
( ( X127 @ X130 @ X128 )
| ~ ( X127 @ X130 @ X129 )
| ~ ( X127 @ X129 @ X128 ) )
| ( X127 @ X113 @ X120 )
| ~ ! [X131: $i,X132: $i] :
( ( X127 @ X132 @ X131 )
| ~ ( X111 @ X132 @ X131 ) ) ) )
& ~ ! [X133: $i > $i > $o] :
( ~ ! [X134: $i,X135: $i] :
( ~ ( X111 @ X135 @ X134 )
| ( X133 @ X135 @ X134 ) )
| ~ ! [X136: $i,X137: $i,X138: $i] :
( ( X133 @ X138 @ X136 )
| ~ ( X133 @ X137 @ X136 )
| ~ ( X133 @ X138 @ X137 ) )
| ( X133 @ X113 @ X112 ) ) ) ) )
& ( mono
= ( ^ [X139: ( $i > $i > $o ) > $i > $i > $o] :
! [X140: $i > $i > $o,X141: $i,X142: $i,X143: $i > $i > $o] :
( ~ ! [X144: $i,X145: $i] :
( ~ ( X140 @ X145 @ X144 )
| ( X143 @ X145 @ X144 ) )
| ~ ( X139 @ X140 @ X142 @ X141 )
| ( X139 @ X143 @ X142 @ X141 ) ) ) )
& ( ind
= ( ^ [X146: $i > $i > $o] :
! [X147: $i > $o,X148: $i] :
( ~ ! [X149: $i] :
( ~ ! [X150: $i] :
( ~ ! [X151: $i > $i > $o] :
( ~ ! [X152: $i,X153: $i] :
( ~ ( X146 @ X152 @ X153 )
| ( X151 @ X152 @ X153 ) )
| ( X151 @ X149 @ X150 )
| ~ ! [X154: $i,X155: $i,X156: $i] :
( ( X151 @ X154 @ X156 )
| ~ ( X151 @ X155 @ X156 )
| ~ ( X151 @ X154 @ X155 ) ) )
| ( X147 @ X150 ) )
| ( X147 @ X149 ) )
| ( X147 @ X148 ) ) ) )
& ( ( ^ [X157: $i > $i > $o] :
! [X158: $i,X159: $i] :
( ~ ( X157 @ X159 @ X158 )
| ~ ( X157 @ X158 @ X159 ) ) )
= asymm )
& ! [X160: $i] :
? [X161: d_unsorted] :
( ( d2unsorted @ X161 )
= X160 )
& ( cr
= ( ^ [X162: $i > $i > $o] :
! [X163: $i,X164: $i > $i > $o,X165: $i > $i > $o,X166: $i] :
( ( X163 = X166 )
| ~ ! [X167: $i,X168: $i,X169: $i] :
( ( X165 @ X169 @ X168 )
| ~ ( X165 @ X169 @ X167 )
| ~ ( X165 @ X167 @ X168 ) )
| ~ ! [X170: $i] :
( ~ ! [X171: $i > $i > $o] :
( ~ ! [X172: $i,X173: $i] :
( ~ ( X162 @ X172 @ X173 )
| ( X171 @ X172 @ X173 ) )
| ~ ! [X174: $i,X175: $i,X176: $i] :
( ~ ( X171 @ X174 @ X175 )
| ~ ( X171 @ X175 @ X176 )
| ( X171 @ X174 @ X176 ) )
| ( X171 @ X163 @ X170 ) )
| ~ ! [X177: $i > $i > $o] :
( ( X177 @ X166 @ X170 )
| ~ ! [X178: $i,X179: $i] :
( ~ ( X162 @ X178 @ X179 )
| ( X177 @ X178 @ X179 ) )
| ~ ! [X180: $i,X181: $i,X182: $i] :
( ( X177 @ X181 @ X180 )
| ~ ( X177 @ X182 @ X180 )
| ~ ( X177 @ X181 @ X182 ) ) ) )
| ( X165 @ X166 @ X163 )
| ~ ! [X183: $i,X184: $i] :
( ( X164 @ X184 @ X183 )
| ~ ( X162 @ X184 @ X183 ) )
| ( X164 @ X163 @ X166 )
| ~ ! [X185: $i,X186: $i] :
( ( X165 @ X186 @ X185 )
| ~ ( X162 @ X186 @ X185 ) )
| ( ~ ! [X187: $i > $i > $o] :
( ~ ! [X188: $i,X189: $i,X190: $i] :
( ~ ( X187 @ X190 @ X189 )
| ( X187 @ X188 @ X189 )
| ~ ( X187 @ X188 @ X190 ) )
| ~ ! [X191: $i,X192: $i] :
( ( X187 @ X192 @ X191 )
| ~ ( X162 @ X192 @ X191 ) )
| ( X187 @ X163 @ X166 ) )
& ( X163 != X166 )
& ~ ! [X193: $i > $i > $o] :
( ( X193 @ X166 @ X163 )
| ~ ! [X194: $i,X195: $i,X196: $i] :
( ( X193 @ X195 @ X196 )
| ~ ( X193 @ X195 @ X194 )
| ~ ( X193 @ X194 @ X196 ) )
| ~ ! [X197: $i,X198: $i] :
( ~ ( X162 @ X198 @ X197 )
| ( X193 @ X198 @ X197 ) ) ) )
| ~ ! [X199: $i,X200: $i,X201: $i] :
( ~ ( X164 @ X199 @ X200 )
| ( X164 @ X201 @ X200 )
| ~ ( X164 @ X201 @ X199 ) ) ) ) )
& ! [X202: d_unsorted] : ( d_unsorted_0 = X202 )
& ( nfof
= ( ^ [X203: $i > $i > $o,X204: $i,X205: $i] :
( ! [X206: $i] :
~ ( X203 @ X204 @ X206 )
& ( ( X204 = X205 )
| ! [X207: $i > $i > $o] :
( ( X207 @ X205 @ X204 )
| ~ ! [X208: $i,X209: $i,X210: $i] :
( ~ ( X207 @ X209 @ X210 )
| ( X207 @ X209 @ X208 )
| ~ ( X207 @ X210 @ X208 ) )
| ~ ! [X211: $i,X212: $i] :
( ~ ( X203 @ X211 @ X212 )
| ( X207 @ X211 @ X212 ) ) ) ) ) ) )
& ( po
= ( ^ [X213: $i > $i > $o] :
( ! [X214: $i,X215: $i] :
( ( X214 = X215 )
| ~ ( X213 @ X215 @ X214 )
| ~ ( X213 @ X214 @ X215 ) )
& ! [X216: $i,X217: $i,X218: $i] :
( ( X213 @ X217 @ X218 )
| ~ ( X213 @ X216 @ X218 )
| ~ ( X213 @ X217 @ X216 ) )
& ! [X219: $i] : ( X213 @ X219 @ X219 ) ) ) )
& ( subrel
= ( ^ [X220: $i > $i > $o,X221: $i > $i > $o] :
! [X222: $i,X223: $i] :
( ( X221 @ X223 @ X222 )
| ~ ( X220 @ X223 @ X222 ) ) ) )
& ( trc
= ( ^ [X224: $i > $i > $o,X225: $i,X226: $i] :
( ( X225 = X226 )
| ! [X227: $i > $i > $o] :
( ( X227 @ X225 @ X226 )
| ~ ! [X228: $i,X229: $i] :
( ( X227 @ X229 @ X228 )
| ~ ( X224 @ X229 @ X228 ) )
| ~ ! [X230: $i,X231: $i,X232: $i] :
( ( X227 @ X232 @ X230 )
| ~ ( X227 @ X231 @ X230 )
| ~ ( X227 @ X232 @ X231 ) ) ) ) ) )
& ( rc
= ( ^ [X233: $i > $i > $o,X234: $i,X235: $i] :
( ( X234 = X235 )
| ( X233 @ X234 @ X235 ) ) ) )
& ( ( ^ [X236: $i > $i > $o,X237: $i,X238: $i] :
( ! [X239: $i > $i > $o] :
( ( X239 @ X237 @ X238 )
| ~ ! [X240: $i,X241: $i] :
( ~ ( X236 @ X240 @ X241 )
| ( X239 @ X240 @ X241 ) )
| ~ ! [X242: $i,X243: $i,X244: $i] :
( ~ ( X239 @ X244 @ X242 )
| ( X239 @ X243 @ X242 )
| ~ ( X239 @ X243 @ X244 ) ) )
| ( X237 = X238 )
| ! [X245: $i > $i > $o] :
( ~ ! [X246: $i,X247: $i] :
( ( X245 @ X246 @ X247 )
| ~ ( X236 @ X246 @ X247 ) )
| ~ ! [X248: $i,X249: $i,X250: $i] :
( ~ ( X245 @ X249 @ X250 )
| ~ ( X245 @ X248 @ X249 )
| ( X245 @ X248 @ X250 ) )
| ( X245 @ X238 @ X237 ) ) ) )
= trsc )
& ( ( ^ [X251: $i > $i > $o] :
! [X252: $i] : ( X251 @ X252 @ X252 ) )
= refl )
& ( idem
= ( ^ [X253: ( $i > $i > $o ) > $i > $i > $o] :
! [X254: $i > $i > $o] :
( ( X253 @ ( X253 @ X254 ) )
= ( X253 @ X254 ) ) ) )
& ( ( ^ [X255: $i > $i > $o,X256: $i] :
! [X257: $i] :
~ ( X255 @ X256 @ X257 ) )
= innf )
& ( ( ^ [X258: $i > $i > $o] :
( ! [X259: $i,X260: $i,X261: $i] :
( ~ ( X258 @ X259 @ X261 )
| ( X258 @ X260 @ X261 )
| ~ ( X258 @ X260 @ X259 ) )
& ! [X262: $i,X263: $i] :
( ~ ( X258 @ X263 @ X262 )
| ~ ( X258 @ X262 @ X263 ) ) ) )
= so )
& ( term
= ( ^ [X264: $i > $i > $o] :
! [X265: $i > $o,X266: $i] :
( ~ ( X265 @ X266 )
| ~ ! [X267: $i] :
( ~ ! [X268: $i] :
( ~ ( X264 @ X267 @ X268 )
| ~ ( X265 @ X268 ) )
| ~ ( X265 @ X267 ) ) ) ) )
& ( confl
= ( ^ [X269: $i > $i > $o] :
! [X270: $i,X271: $i,X272: $i > $i > $o,X273: $i,X274: $i > $i > $o] :
( ~ ! [X275: $i] :
( ~ ! [X276: $i > $i > $o] :
( ~ ! [X277: $i,X278: $i] :
( ~ ( X269 @ X278 @ X277 )
| ( X276 @ X278 @ X277 ) )
| ( X276 @ X271 @ X275 )
| ~ ! [X279: $i,X280: $i,X281: $i] :
( ( X276 @ X279 @ X280 )
| ~ ( X276 @ X279 @ X281 )
| ~ ( X276 @ X281 @ X280 ) ) )
| ~ ! [X282: $i > $i > $o] :
( ( X282 @ X273 @ X275 )
| ~ ! [X283: $i,X284: $i] :
( ~ ( X269 @ X284 @ X283 )
| ( X282 @ X284 @ X283 ) )
| ~ ! [X285: $i,X286: $i,X287: $i] :
( ~ ( X282 @ X286 @ X285 )
| ( X282 @ X287 @ X285 )
| ~ ( X282 @ X287 @ X286 ) ) ) )
| ~ ! [X288: $i,X289: $i] :
( ( X274 @ X288 @ X289 )
| ~ ( X269 @ X288 @ X289 ) )
| ( X271 = X273 )
| ~ ! [X290: $i,X291: $i,X292: $i] :
( ( X274 @ X290 @ X292 )
| ~ ( X274 @ X290 @ X291 )
| ~ ( X274 @ X291 @ X292 ) )
| ~ ! [X293: $i,X294: $i,X295: $i] :
( ~ ( X272 @ X293 @ X295 )
| ( X272 @ X293 @ X294 )
| ~ ( X272 @ X295 @ X294 ) )
| ( X274 @ X271 @ X273 )
| ~ ! [X296: $i,X297: $i] :
( ( X272 @ X297 @ X296 )
| ~ ( X269 @ X297 @ X296 ) )
| ( ~ ! [X298: $i > $i > $o] :
( ( X298 @ X270 @ X273 )
| ~ ! [X299: $i,X300: $i,X301: $i] :
( ~ ( X298 @ X299 @ X300 )
| ~ ( X298 @ X301 @ X299 )
| ( X298 @ X301 @ X300 ) )
| ~ ! [X302: $i,X303: $i] :
( ( X298 @ X302 @ X303 )
| ~ ( X269 @ X302 @ X303 ) ) )
& ( X270 != X273 ) )
| ( ( X270 != X271 )
& ~ ! [X304: $i > $i > $o] :
( ~ ! [X305: $i,X306: $i] :
( ( X304 @ X306 @ X305 )
| ~ ( X269 @ X306 @ X305 ) )
| ( X304 @ X270 @ X271 )
| ~ ! [X307: $i,X308: $i,X309: $i] :
( ~ ( X304 @ X307 @ X308 )
| ~ ( X304 @ X308 @ X309 )
| ( X304 @ X307 @ X309 ) ) ) )
| ( X272 @ X273 @ X271 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( irrefl
= ( ^ [X4: $i > $i > $o] :
! [X6: $i] :
~ ( X4 @ X6 @ X6 ) ) )
& ( tc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X7 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X13: $i,X11: $i,X12: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 ) ) ) ) )
& ( lconfl
= ( ^ [X4: $i > $i > $o] :
! [X29: $i > $i > $o,X7: $i,X6: $i,X28: $i > $i > $o,X11: $i] :
( ~ ! [X13: $i,X26: $i,X12: $i] :
( ~ ( X29 @ X13 @ X26 )
| ( X29 @ X12 @ X26 )
| ~ ( X29 @ X12 @ X13 ) )
| ( X29 @ X11 @ X7 )
| ~ ! [X12: $i,X25: $i,X13: $i] :
( ( X28 @ X12 @ X25 )
| ~ ( X28 @ X12 @ X13 )
| ~ ( X28 @ X13 @ X25 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X29 @ X14 @ X15 ) )
| ~ ( X4 @ X6 @ X11 )
| ( X28 @ X7 @ X11 )
| ( X7 = X11 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X28 @ X14 @ X15 ) )
| ~ ( X4 @ X6 @ X7 )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 ) )
| ( X5 @ X7 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 ) )
| ( X5 @ X11 @ X27 ) ) ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X4 @ X7 @ X6 ) ) )
= symm )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X11: $i,X6: $i] :
( ~ ( X4 @ X7 @ X11 )
| ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 ) ) )
= trans )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ~ ( X4 @ X7 @ X6 )
| ( X6 = X7 )
| ~ ( X4 @ X6 @ X7 ) ) )
= antisymm )
& ( total
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X4 @ X7 @ X6 )
| ( X4 @ X6 @ X7 )
| ( X6 = X7 ) ) ) )
& ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o,X7: $i,X6: $i] :
( ( X8 @ X4 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) )
= infl )
& ( sconfl
= ( ^ [X4: $i > $i > $o] :
! [X31: $i > $i > $o,X7: $i,X30: $i > $i > $o,X11: $i,X6: $i] :
( ~ ! [X15: $i,X14: $i] :
( ( X30 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X25: $i,X12: $i] :
( ( X30 @ X12 @ X25 )
| ~ ( X30 @ X13 @ X25 )
| ~ ( X30 @ X12 @ X13 ) )
| ( X7 = X11 )
| ( ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X13: $i,X32: $i] :
( ~ ( X5 @ X13 @ X32 )
| ( X5 @ X12 @ X32 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 ) ) )
| ~ ! [X14: $i,X15: $i] :
( ( X31 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X26: $i,X13: $i,X12: $i] :
( ( X31 @ X12 @ X26 )
| ~ ( X31 @ X12 @ X13 )
| ~ ( X31 @ X13 @ X26 ) )
| ( X31 @ X11 @ X7 )
| ~ ( X4 @ X6 @ X11 )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X7 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X11 @ X27 )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) ) ) )
| ( X30 @ X7 @ X11 ) ) ) )
& ( inv
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] : ( X4 @ X7 @ X6 ) ) )
& ( norm
= ( ^ [X4: $i > $i > $o] :
! [X23: $i,X6: $i] :
( ~ ( X4 @ X6 @ X23 )
| ~ ! [X24: $i] :
( ~ ! [X22: $i] :
~ ( X4 @ X24 @ X22 )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X11: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ( X5 @ X6 @ X24 ) ) ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X4 @ X7 @ X6 )
| ( X4 @ X6 @ X7 ) ) )
= sc )
& ( join
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
~ ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X13: $i,X12: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 ) ) )
& ( X6 != X7 )
& ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X27 )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X26: $i,X12: $i] :
( ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X25: $i,X13: $i,X12: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X7 @ X6 ) ) ) ) )
& ( mono
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o,X10: $i,X9: $i,X5: $i > $i > $o] :
( ~ ! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X5 @ X6 @ X7 ) )
| ~ ( X8 @ X4 @ X9 @ X10 )
| ( X8 @ X5 @ X9 @ X10 ) ) ) )
& ( ind
= ( ^ [X4: $i > $i > $o] :
! [X20: $i > $o,X21: $i] :
( ~ ! [X6: $i] :
( ~ ! [X7: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X12: $i,X13: $i,X11: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ( X20 @ X7 ) )
| ( X20 @ X6 ) )
| ( X20 @ X21 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) ) )
= asymm )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( cr
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X37: $i > $i > $o,X36: $i > $i > $o,X7: $i] :
( ( X6 = X7 )
| ~ ! [X13: $i,X25: $i,X12: $i] :
( ( X36 @ X12 @ X25 )
| ~ ( X36 @ X12 @ X13 )
| ~ ( X36 @ X13 @ X25 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 ) )
| ( X5 @ X6 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X27 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X25: $i,X12: $i,X13: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 ) ) ) )
| ( X36 @ X7 @ X6 )
| ~ ! [X15: $i,X14: $i] :
( ( X37 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X37 @ X6 @ X7 )
| ~ ! [X15: $i,X14: $i] :
( ( X36 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X11: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 ) )
& ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X13: $i,X12: $i,X11: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) )
| ~ ! [X13: $i,X26: $i,X12: $i] :
( ~ ( X37 @ X13 @ X26 )
| ( X37 @ X12 @ X26 )
| ~ ( X37 @ X12 @ X13 ) ) ) ) )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( nfof
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ! [X22: $i] :
~ ( X4 @ X6 @ X22 )
& ( ( X6 = X7 )
| ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) ) ) ) )
& ( po
= ( ^ [X4: $i > $i > $o] :
( ! [X6: $i,X7: $i] :
( ( X6 = X7 )
| ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) )
& ! [X7: $i,X6: $i,X11: $i] :
( ( X4 @ X6 @ X11 )
| ~ ( X4 @ X7 @ X11 )
| ~ ( X4 @ X6 @ X7 ) )
& ! [X6: $i] : ( X4 @ X6 @ X6 ) ) ) )
& ( subrel
= ( ^ [X4: $i > $i > $o,X5: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X5 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( trc
= ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ( X16 = X17 )
| ! [X5: $i > $i > $o] :
( ( X5 @ X16 @ X17 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X11: $i,X13: $i,X12: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 ) ) ) ) ) )
& ( rc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X6 = X7 )
| ( X4 @ X6 @ X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ! [X5: $i > $i > $o] :
( ( X5 @ X16 @ X17 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ( X16 = X17 )
| ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X11: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) )
| ( X5 @ X17 @ X16 ) ) ) )
= trsc )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i] : ( X4 @ X6 @ X6 ) )
= refl )
& ( idem
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o] :
( ( X8 @ X4 )
= ( X8 @ ( X8 @ X4 ) ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i] :
! [X7: $i] :
~ ( X4 @ X6 @ X7 ) )
= innf )
& ( ( ^ [X4: $i > $i > $o] :
( ! [X7: $i,X6: $i,X11: $i] :
( ~ ( X4 @ X7 @ X11 )
| ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 ) )
& ! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) ) ) )
= so )
& ( term
= ( ^ [X4: $i > $i > $o] :
! [X18: $i > $o,X19: $i] :
( ~ ( X18 @ X19 )
| ~ ! [X6: $i] :
( ~ ! [X7: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X18 @ X7 ) )
| ~ ( X18 @ X6 ) ) ) ) )
& ( confl
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i,X34: $i > $i > $o,X11: $i,X33: $i > $i > $o] :
( ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X12: $i,X25: $i,X13: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ( X5 @ X11 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X26: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) ) ) )
| ~ ! [X14: $i,X15: $i] :
( ( X33 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X7 = X11 )
| ~ ! [X12: $i,X13: $i,X25: $i] :
( ( X33 @ X12 @ X25 )
| ~ ( X33 @ X12 @ X13 )
| ~ ( X33 @ X13 @ X25 ) )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X34 @ X12 @ X13 )
| ( X34 @ X12 @ X26 )
| ~ ( X34 @ X13 @ X26 ) )
| ( X33 @ X7 @ X11 )
| ~ ! [X15: $i,X14: $i] :
( ( X34 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X11 )
| ~ ! [X13: $i,X26: $i,X12: $i] :
( ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) )
& ( X6 != X11 ) )
| ( ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X12: $i,X13: $i,X35: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X35 )
| ( X5 @ X12 @ X35 ) ) ) )
| ( X34 @ X11 @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Z8wGJ6wj6z/DTF2THF_3057.p',sev441_1) ).
thf(f45,plain,
! [X0: $i] :
( ( d2unsorted @ ( sK0 @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f2970,plain,
( ! [X1: $i] :
( ( sK7 @ X1 )
!= X1 )
| ~ spl1_35
| ~ spl1_38 ),
inference(equality_proxy_clausification,[status(thm)],[f2969]) ).
thf(f2969,plain,
( ! [X1: $i] :
( ( ( sK7 @ X1 )
= X1 )
= $false )
| ~ spl1_35
| ~ spl1_38 ),
inference(not_proxy_clausification,[status(thm)],[f2968]) ).
thf(f2968,plain,
( ! [X1: $i] :
( ( ( sK7 @ X1 )
!= X1 )
= $true )
| ~ spl1_35
| ~ spl1_38 ),
inference(trivial_inequality_removal,[status(thm)],[f2967]) ).
thf(f2967,plain,
( ! [X1: $i] :
( ( ( ( sK7 @ X1 )
!= X1 )
= $true )
| ( $false = $true ) )
| ~ spl1_35
| ~ spl1_38 ),
inference(boolean_simplification,[status(thm)],[f2966]) ).
thf(f2966,plain,
( ! [X1: $i] :
( ( $true = ( ~ $true ) )
| ( ( ( sK7 @ X1 )
!= X1 )
= $true ) )
| ~ spl1_35
| ~ spl1_38 ),
inference(boolean_simplification,[status(thm)],[f2965]) ).
thf(f2965,plain,
( ! [X1: $i] :
( ( ( ( sK7 @ X1 )
!= X1 )
= $true )
| ( ( ( d2unsorted @ d_unsorted_0 )
!= ( d2unsorted @ d_unsorted_0 ) )
= $true ) )
| ~ spl1_35
| ~ spl1_38 ),
inference(beta_eta_normalization,[status(thm)],[f2897]) ).
thf(f2897,plain,
( ! [X1: $i] :
( ( ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ ( d2unsorted @ d_unsorted_0 )
@ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ X1
@ ( sK7 @ X1 ) )
= $true ) )
| ~ spl1_35
| ~ spl1_38 ),
inference(primitive_instantiation,[status(thm)],[f2884]) ).
thf(f2884,plain,
( ! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) )
| ~ spl1_35
| ~ spl1_38 ),
inference(trivial_inequality_removal,[status(thm)],[f2882]) ).
thf(f2882,plain,
( ! [X2: $i > $i > $o,X1: $i] :
( ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $false = $true )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) )
| ~ spl1_35
| ~ spl1_38 ),
inference(backward_demodulation,[status(thm)],[f1256,f2875]) ).
thf(f2875,plain,
( ! [X0: $i] :
( $false
= ( sK6 @ X0 ) )
| ~ spl1_35 ),
inference(superposition,[status(thm)],[f1240,f1310]) ).
thf(f1240,plain,
( ( ( sK6 @ sK13 )
= $false )
| ~ spl1_35 ),
inference(avatar_component_clause,[status(thm)],[f1238]) ).
thf(f1238,definition,
( spl1_35
<=> ( ( sK6 @ sK13 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_35])],[avatar_definition]) ).
thf(f1256,plain,
( ! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) )
| ~ spl1_38 ),
inference(avatar_component_clause,[status(thm)],[f1255]) ).
thf(f1255,definition,
( spl1_38
<=> ! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_38])],[avatar_definition]) ).
thf(f2869,plain,
( ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f2868]) ).
thf(f2868,plain,
( $false
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(subsumption_resolution,[status(thm)],[f2819,f1310]) ).
thf(f2819,plain,
( ! [X3: $i] :
( ( sK26 @ X3 )
!= X3 )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(equality_proxy_clausification,[status(thm)],[f2818]) ).
thf(f2818,plain,
( ! [X3: $i] :
( ( ( sK26 @ X3 )
= X3 )
= $false )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(not_proxy_clausification,[status(thm)],[f2817]) ).
thf(f2817,plain,
( ! [X3: $i] :
( ( ( sK26 @ X3 )
!= X3 )
= $true )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f2816]) ).
thf(f2816,plain,
( ! [X3: $i] :
( ( $false = $true )
| ( ( ( sK26 @ X3 )
!= X3 )
= $true ) )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(boolean_simplification,[status(thm)],[f2815]) ).
thf(f2815,plain,
( ! [X3: $i] :
( ( ( ( sK26 @ X3 )
!= X3 )
= $true )
| ( $true = ( ~ $true ) ) )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(boolean_simplification,[status(thm)],[f2814]) ).
thf(f2814,plain,
( ! [X3: $i] :
( ( ( ( sK26 @ X3 )
!= X3 )
= $true )
| ( ( ( d2unsorted @ d_unsorted_0 )
!= ( d2unsorted @ d_unsorted_0 ) )
= $true ) )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(beta_eta_normalization,[status(thm)],[f2760]) ).
thf(f2760,plain,
( ! [X3: $i] :
( ( ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ X3
@ ( sK26 @ X3 ) )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ ( d2unsorted @ d_unsorted_0 )
@ ( d2unsorted @ d_unsorted_0 ) )
= $true ) )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(primitive_instantiation,[status(thm)],[f2574]) ).
thf(f2574,plain,
( ! [X3: $i,X4: $i > $i > $o] :
( ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true ) )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(trivial_inequality_removal,[status(thm)],[f2573]) ).
thf(f2573,plain,
( ! [X3: $i,X4: $i > $i > $o] :
( ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( $false = $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true ) )
| ~ spl1_2
| ~ spl1_21
| ~ spl1_26 ),
inference(backward_demodulation,[status(thm)],[f826,f2572]) ).
thf(f2572,plain,
( ! [X0: $i] :
( ( sK14 @ X0 )
= $false )
| ~ spl1_2
| ~ spl1_21 ),
inference(trivial_inequality_removal,[status(thm)],[f2569]) ).
thf(f2569,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK14 @ X0 )
= $false ) )
| ~ spl1_2
| ~ spl1_21 ),
inference(superposition,[status(thm)],[f759,f1311]) ).
thf(f1311,plain,
( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( X1 @ X0 )
= $false ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f666,f50]) ).
thf(f666,plain,
( ! [X2: $i > $o,X4: $i] :
( ( $false
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f665]) ).
thf(f665,definition,
( spl1_2
<=> ! [X4: $i,X2: $i > $o] :
( ( ( X2 @ X4 )
= $true )
| ( $false
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f759,plain,
( ( ( sK14 @ sK71 )
= $false )
| ~ spl1_21 ),
inference(avatar_component_clause,[status(thm)],[f757]) ).
thf(f757,definition,
( spl1_21
<=> ( ( sK14 @ sK71 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_21])],[avatar_definition]) ).
thf(f826,plain,
( ! [X3: $i,X4: $i > $i > $o] :
( ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true ) )
| ~ spl1_26 ),
inference(avatar_component_clause,[status(thm)],[f825]) ).
thf(f825,definition,
( spl1_26
<=> ! [X4: $i > $i > $o,X3: $i] :
( ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_26])],[avatar_definition]) ).
thf(f2563,plain,
( ~ spl1_23
| ~ spl1_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f2562]) ).
thf(f2562,plain,
( $false
| ~ spl1_23
| ~ spl1_36 ),
inference(subsumption_resolution,[status(thm)],[f2553,f1310]) ).
thf(f2553,plain,
( ! [X1: $i] :
( ( sK15 @ X1 )
!= X1 )
| ~ spl1_23
| ~ spl1_36 ),
inference(equality_proxy_clausification,[status(thm)],[f2552]) ).
thf(f2552,plain,
( ! [X1: $i] :
( $false
= ( ( sK15 @ X1 )
= X1 ) )
| ~ spl1_23
| ~ spl1_36 ),
inference(not_proxy_clausification,[status(thm)],[f2551]) ).
thf(f2551,plain,
( ! [X1: $i] :
( ( ( sK15 @ X1 )
!= X1 )
= $true )
| ~ spl1_23
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2550]) ).
thf(f2550,plain,
( ! [X1: $i] :
( ( $false = $true )
| ( ( ( sK15 @ X1 )
!= X1 )
= $true ) )
| ~ spl1_23
| ~ spl1_36 ),
inference(boolean_simplification,[status(thm)],[f2549]) ).
thf(f2549,plain,
( ! [X1: $i] :
( ( ( ( sK15 @ X1 )
!= X1 )
= $true )
| ( $true = ( ~ $true ) ) )
| ~ spl1_23
| ~ spl1_36 ),
inference(boolean_simplification,[status(thm)],[f2548]) ).
thf(f2548,plain,
( ! [X1: $i] :
( ( ( ( d2unsorted @ d_unsorted_0 )
!= ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( ( sK15 @ X1 )
!= X1 )
= $true ) )
| ~ spl1_23
| ~ spl1_36 ),
inference(beta_eta_normalization,[status(thm)],[f2482]) ).
thf(f2482,plain,
( ! [X1: $i] :
( ( ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ X1
@ ( sK15 @ X1 ) )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 != Y0 )
@ ( d2unsorted @ d_unsorted_0 )
@ ( d2unsorted @ d_unsorted_0 ) )
= $true ) )
| ~ spl1_23
| ~ spl1_36 ),
inference(primitive_instantiation,[status(thm)],[f2385]) ).
thf(f2385,plain,
( ! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) )
| ~ spl1_23
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2384]) ).
thf(f2384,plain,
( ! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( $false = $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) )
| ~ spl1_23
| ~ spl1_36 ),
inference(forward_demodulation,[status(thm)],[f771,f1320]) ).
thf(f1320,plain,
( ! [X0: $i] :
( $false
= ( sK5 @ X0 ) )
| ~ spl1_36 ),
inference(superposition,[status(thm)],[f1244,f1310]) ).
thf(f1244,plain,
( ( ( sK5 @ sK4 )
= $false )
| ~ spl1_36 ),
inference(avatar_component_clause,[status(thm)],[f1242]) ).
thf(f1242,definition,
( spl1_36
<=> ( ( sK5 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_36])],[avatar_definition]) ).
thf(f771,plain,
( ! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) )
| ~ spl1_23 ),
inference(avatar_component_clause,[status(thm)],[f770]) ).
thf(f770,definition,
( spl1_23
<=> ! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_23])],[avatar_definition]) ).
thf(f2381,plain,
( ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22
| ~ spl1_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f2380]) ).
thf(f2380,plain,
( $false
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2379]) ).
thf(f2379,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22
| ~ spl1_36 ),
inference(forward_demodulation,[status(thm)],[f2378,f1320]) ).
thf(f2378,plain,
( ! [X0: $i] :
( ( sK5 @ X0 )
= $true )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2377]) ).
thf(f2377,plain,
( ! [X0: $i] :
( ( ( sK5 @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22
| ~ spl1_36 ),
inference(forward_demodulation,[status(thm)],[f2359,f1320]) ).
thf(f2359,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK5 @ X0 )
= $true ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2320]) ).
thf(f2320,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( $false = $true )
| ( ( sK5 @ X0 )
= $true ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22
| ~ spl1_36 ),
inference(superposition,[status(thm)],[f1244,f2285]) ).
thf(f2285,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( X1 @ X3 ) )
| ( ( X1 @ X0 )
= $true )
| ( ( X1 @ X2 )
= $true ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f2284]) ).
thf(f2284,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( X1 @ X3 ) )
| ( ( X1 @ X0 )
= $true )
| ( $false = $true )
| ( ( X1 @ X2 )
= $true ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(duplicate_literal_removal,[status(thm)],[f2265]) ).
thf(f2265,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X0 )
= $true )
| ( ( X1 @ X2 )
= $true )
| ( ( X1 @ X0 )
= $true )
| ( $true
= ( X1 @ X3 ) )
| ( $false = $true ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(superposition,[status(thm)],[f688,f2255]) ).
thf(f2255,plain,
( ! [X2: $i > $o,X8: $i,X9: $i,X4: $i,X5: $i] :
( ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl1_2
| ~ spl1_9
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f2254]) ).
thf(f2254,plain,
( ! [X2: $i > $o,X8: $i,X9: $i,X4: $i,X5: $i] :
( ( $false = $true )
| ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl1_2
| ~ spl1_9
| ~ spl1_22 ),
inference(forward_demodulation,[status(thm)],[f703,f1524]) ).
thf(f1524,plain,
( ! [X0: $i,X1: $i] :
( ( sK3 @ X0 @ X1 )
= $true )
| ~ spl1_2
| ~ spl1_22 ),
inference(superposition,[status(thm)],[f1385,f1310]) ).
thf(f1385,plain,
( ! [X0: $i] :
( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ X0 )
= $true )
| ~ spl1_2
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f1382]) ).
thf(f1382,plain,
( ! [X0: $i] :
( ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl1_2
| ~ spl1_22 ),
inference(superposition,[status(thm)],[f763,f666]) ).
thf(f763,plain,
( ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ~ spl1_22 ),
inference(avatar_component_clause,[status(thm)],[f761]) ).
thf(f761,definition,
( spl1_22
<=> ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition]) ).
thf(f703,plain,
( ! [X2: $i > $o,X8: $i,X9: $i,X4: $i,X5: $i] :
( ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
= $true )
| ( ( sK3 @ X9 @ X8 )
= $false )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f702]) ).
thf(f702,definition,
( spl1_9
<=> ! [X5: $i,X4: $i,X8: $i,X9: $i,X2: $i > $o] :
( ( ( sK3 @ X9 @ X8 )
= $false )
| ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition]) ).
thf(f688,plain,
( ! [X2: $i > $o,X4: $i,X5: $i] :
( ( $false
= ( sK82 @ X5 @ X2 @ ( d2unsorted @ d_unsorted_0 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f687]) ).
thf(f687,definition,
( spl1_6
<=> ! [X2: $i > $o,X5: $i,X4: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( d2unsorted @ d_unsorted_0 ) @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f2349,plain,
( ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f2348]) ).
thf(f2348,plain,
( $false
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f2347]) ).
thf(f2347,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(duplicate_literal_removal,[status(thm)],[f2346]) ).
thf(f2346,plain,
( ( $false = $true )
| ( $false = $true )
| ( $false = $true )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(beta_eta_normalization,[status(thm)],[f2299]) ).
thf(f2299,plain,
( ! [X2: $i,X3: $i,X0: $i] :
( ( ( ^ [Y0: $i] : $false
@ X3 )
= $true )
| ( ( ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( ^ [Y0: $i] : $false
@ X0 )
= $true ) )
| ~ spl1_2
| ~ spl1_6
| ~ spl1_9
| ~ spl1_22 ),
inference(primitive_instantiation,[status(thm)],[f2285]) ).
thf(f2253,plain,
( ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22
| ~ spl1_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f2252]) ).
thf(f2252,plain,
( $false
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2251]) ).
thf(f2251,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22
| ~ spl1_36 ),
inference(forward_demodulation,[status(thm)],[f2250,f1320]) ).
thf(f2250,plain,
( ! [X2: $i] :
( ( sK5 @ X2 )
= $true )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2249]) ).
thf(f2249,plain,
( ! [X2: $i] :
( ( $false = $true )
| ( ( sK5 @ X2 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22
| ~ spl1_36 ),
inference(forward_demodulation,[status(thm)],[f2222,f1320]) ).
thf(f2222,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK5 @ X2 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f2193]) ).
thf(f2193,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK5 @ X2 )
= $true )
| ( $false = $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22
| ~ spl1_36 ),
inference(superposition,[status(thm)],[f1320,f2166]) ).
thf(f2166,plain,
( ! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X2 )
= $true )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f2165]) ).
thf(f2165,plain,
( ! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false = $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X2 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(duplicate_literal_removal,[status(thm)],[f2142]) ).
thf(f2142,plain,
( ! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false = $true )
| ( ( X0 @ X2 )
= $true )
| ( ( X0 @ X1 )
= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(superposition,[status(thm)],[f711,f1668]) ).
thf(f1668,plain,
( ! [X3: $i > $o,X10: $i,X1: $i,X6: $i,X7: $i] :
( ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f1667]) ).
thf(f1667,plain,
( ! [X3: $i > $o,X10: $i,X1: $i,X6: $i,X7: $i] :
( ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false = $true )
| ( ( X3 @ X6 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_22 ),
inference(forward_demodulation,[status(thm)],[f706,f1524]) ).
thf(f706,plain,
( ! [X3: $i > $o,X10: $i,X1: $i,X6: $i,X7: $i] :
( ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true )
| ( ( sK3 @ X10 @ X7 )
= $false )
| ( ( X3 @ X1 )
= $true )
| ( ( X3 @ X6 )
= $true ) )
| ~ spl1_10 ),
inference(avatar_component_clause,[status(thm)],[f705]) ).
thf(f705,definition,
( spl1_10
<=> ! [X10: $i,X7: $i,X6: $i,X3: $i > $o,X1: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( sK3 @ X10 @ X7 )
= $false )
| ( ( X3 @ X1 )
= $true )
| ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition]) ).
thf(f711,plain,
( ! [X3: $i > $o,X1: $i,X6: $i] :
( ( ( sK84 @ X3 @ X6 @ ( d2unsorted @ d_unsorted_0 ) @ X6 )
= $false )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f710]) ).
thf(f710,definition,
( spl1_11
<=> ! [X6: $i,X1: $i,X3: $i > $o] :
( ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( sK84 @ X3 @ X6 @ ( d2unsorted @ d_unsorted_0 ) @ X6 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f2212,plain,
( ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f2211]) ).
thf(f2211,plain,
( $false
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f2210]) ).
thf(f2210,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(duplicate_literal_removal,[status(thm)],[f2209]) ).
thf(f2209,plain,
( ( $false = $true )
| ( $false = $true )
| ( $false = $true )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(beta_eta_normalization,[status(thm)],[f2171]) ).
thf(f2171,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( ^ [Y0: $i] : $false
@ X3 )
= $true )
| ( ( ^ [Y0: $i] : $false
@ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_10
| ~ spl1_11
| ~ spl1_22 ),
inference(primitive_instantiation,[status(thm)],[f2166]) ).
thf(f1666,plain,
( ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22
| ~ spl1_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f1665]) ).
thf(f1665,plain,
( $false
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1664]) ).
thf(f1664,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22
| ~ spl1_36 ),
inference(forward_demodulation,[status(thm)],[f1663,f1320]) ).
thf(f1663,plain,
( ! [X0: $i] :
( ( sK5 @ X0 )
= $true )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1662]) ).
thf(f1662,plain,
( ! [X0: $i] :
( ( ( sK5 @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22
| ~ spl1_36 ),
inference(forward_demodulation,[status(thm)],[f1635,f1320]) ).
thf(f1635,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK5 @ X0 )
= $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22
| ~ spl1_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1609]) ).
thf(f1609,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK5 @ X0 )
= $true )
| ( $false = $true )
| ( $true
= ( sK5 @ X1 ) ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22
| ~ spl1_36 ),
inference(superposition,[status(thm)],[f1574,f1244]) ).
thf(f1574,plain,
( ! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X1 )
= $true )
| ( ( X0 @ X2 )
= $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f1573]) ).
thf(f1573,plain,
( ! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( X0 @ X3 )
= $true )
| ( $false = $true )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(duplicate_literal_removal,[status(thm)],[f1563]) ).
thf(f1563,plain,
( ! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X2 )
= $true )
| ( $false = $true )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(superposition,[status(thm)],[f694,f1537]) ).
thf(f1537,plain,
( ! [X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i] :
( ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f1533]) ).
thf(f1533,plain,
( ! [X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i] :
( ( ( X3 @ X1 )
= $true )
| ( $false = $true )
| ( ( X3 @ X6 )
= $true )
| ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
= $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_22 ),
inference(backward_demodulation,[status(thm)],[f685,f1524]) ).
thf(f685,plain,
( ! [X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i] :
( ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
= $true )
| ( $false
= ( sK3 @ X8 @ X7 ) )
| ( ( X3 @ X1 )
= $true )
| ( ( X3 @ X6 )
= $true ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[status(thm)],[f684]) ).
thf(f684,definition,
( spl1_5
<=> ! [X7: $i,X8: $i,X6: $i,X3: $i > $o,X1: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( sK3 @ X8 @ X7 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition]) ).
thf(f694,plain,
( ! [X3: $i > $o,X1: $i,X6: $i] :
( ( $false
= ( sK85 @ X3 @ X6 @ ( d2unsorted @ d_unsorted_0 ) @ X6 ) )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f693]) ).
thf(f693,definition,
( spl1_7
<=> ! [X6: $i,X1: $i,X3: $i > $o] :
( ( $false
= ( sK85 @ X3 @ X6 @ ( d2unsorted @ d_unsorted_0 ) @ X6 ) )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f1639,plain,
( ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f1638]) ).
thf(f1638,plain,
( $false
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(trivial_inequality_removal,[status(thm)],[f1637]) ).
thf(f1637,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(duplicate_literal_removal,[status(thm)],[f1636]) ).
thf(f1636,plain,
( ( $false = $true )
| ( $false = $true )
| ( $false = $true )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(beta_eta_normalization,[status(thm)],[f1607]) ).
thf(f1607,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] : $false
@ X3 )
= $true )
| ( ( ^ [Y0: $i] : $false
@ X2 )
= $true )
| ( ( ^ [Y0: $i] : $false
@ X1 )
= $true ) )
| ~ spl1_2
| ~ spl1_5
| ~ spl1_7
| ~ spl1_22 ),
inference(primitive_instantiation,[status(thm)],[f1574]) ).
thf(f1270,plain,
( spl1_36
| spl1_22
| spl1_38 ),
inference(avatar_split_clause,[status(thm)],[f1269,f1255,f761,f1242]) ).
thf(f1269,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f1268,f50]) ).
thf(f1268,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK11 @ X2 ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f1267,f50]) ).
thf(f1267,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f1266,f50]) ).
thf(f1266,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK8 @ X2 ) ) )
| ( ( sK6 @ X1 )
= $true )
| ( ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f101,f50]) ).
thf(f101,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
= $true )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $false
= ( ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( sK6 @ X1 )
= $true )
| ( ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( ~ ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) ) )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $false
= ( ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( ~ ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
| ( X2 @ ( sK10 @ X2 ) @ ( sK11 @ X2 ) ) )
= $false )
| ( $false
= ( ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK6 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $false
= ( ~ ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
| ( X2 @ ( sK10 @ X2 ) @ ( sK11 @ X2 ) )
| ~ ( X2 @ ( sK10 @ X2 ) @ ( sK12 @ X2 ) ) ) )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( $false
= ( ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( $false
= ( ( X2 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
| ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( $false
= ( ~ ( X2 @ ( sK12 @ X2 ) @ ( sK11 @ X2 ) )
| ( X2 @ ( sK10 @ X2 ) @ ( sK11 @ X2 ) )
| ~ ( X2 @ ( sK10 @ X2 ) @ ( sK12 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 @ ( sK11 @ X2 ) )
| ( X2 @ ( sK10 @ X2 ) @ ( sK11 @ X2 ) )
| ~ ( X2 @ ( sK10 @ X2 ) @ Y0 ) )
@ ( sK12 @ X2 ) ) )
| ( $false
= ( ( X2 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
| ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 @ ( sK11 @ X2 ) )
| ( X2 @ ( sK10 @ X2 ) @ ( sK11 @ X2 ) )
| ~ ( X2 @ ( sK10 @ X2 ) @ Y0 ) ) ) )
| ( $false
= ( ( X2 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
| ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK5 @ sK4 )
= $false )
| ( ( sK6 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ ( sK10 @ X2 ) @ Y0 )
| ~ ( X2 @ ( sK10 @ X2 ) @ Y1 ) ) )
@ ( sK11 @ X2 ) ) )
| ( $false
= ( ( X2 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
| ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ ( sK10 @ X2 ) @ Y0 )
| ~ ( X2 @ ( sK10 @ X2 ) @ Y1 ) ) ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( $false
= ( ( X2 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
| ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $false
= ( ( X2 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
| ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) )
@ ( sK10 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( $false
= ( ( X2 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) )
| ~ ( sK3 @ ( sK9 @ X2 ) @ ( sK8 @ X2 ) ) ) )
| ( ( sK6 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK8 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK8 @ X2 ) ) )
@ ( sK9 @ X2 ) ) )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK5 @ sK4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK8 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK8 @ X2 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK6 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK8 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK8 @ X2 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK5 @ sK4 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ ( sK8 @ X2 ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK6 @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( ( X2 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ( X2 @ Y0 @ Y1 )
| ~ ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
| ( X2 @ X1 @ ( sK7 @ X1 ) ) )
= $true )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X1 @ ( sK7 @ X1 ) ) )
@ X2 )
= $true )
| ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: $i] :
( ( ( sK6 @ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X1 @ ( sK7 @ X1 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X1 @ ( sK7 @ X1 ) ) ) )
=> ( sK6 @ ( sK7 @ X1 ) ) )
= $false )
| ( ( sK5 @ sK4 )
= $false )
| ( ( sK6 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: $i] :
( ( ( sK5 @ sK4 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) )
@ ( sK7 @ X1 ) ) )
| ( ( sK6 @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ( ( sK5 @ sK4 )
= $false )
| ( ( sK6 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
=> ( sK6 @ X1 ) )
= $true )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
=> ( sK6 @ Y0 ) )
@ X1 )
= $true )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( sK5 @ sK4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
=> ( sK6 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( sK5 @ sK4 )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK6 @ Y1 ) ) )
=> ( sK6 @ Y0 ) ) )
=> ( !! @ $i @ sK6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) )
@ sK6 )
= $false )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( ( sK5 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [Y0: $i > $o] :
( ( Y0 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK5 )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( sK3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ sK4 )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( sK3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( sK3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK3 )
!= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i @ Y1 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y4 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
@ Y0
@ Y2
@ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f47,f40,f27]) ).
thf(f27,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f40,plain,
( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f47,plain,
( ind
!= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( tc @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ind
!= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( tc @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ind
!= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( tc @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( tc @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) )
=> ! [X4: $i] : ( X1 @ X4 ) ) )
!= ind ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ^ [X4: $i > $i > $o] :
! [X20: $i > $o] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( tc @ X4 @ X6 @ X7 )
=> ( X20 @ X7 ) )
=> ( X20 @ X6 ) )
=> ! [X6: $i] : ( X20 @ X6 ) ) )
!= ind ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ^ [X4: $i > $i > $o] :
! [X20: $i > $o] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( tc @ X4 @ X6 @ X7 )
=> ( X20 @ X7 ) )
=> ( X20 @ X6 ) )
=> ! [X6: $i] : ( X20 @ X6 ) ) )
= ind ),
file('/export/starexec/sandbox2/tmp/tmp.Z8wGJ6wj6z/DTF2THF_3057.p',satisfying_the_induction_principle) ).
thf(f1245,plain,
( spl1_35
| spl1_36 ),
inference(avatar_split_clause,[status(thm)],[f105,f1242,f1238]) ).
thf(f105,plain,
( ( ( sK6 @ sK13 )
= $false )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $false
= ( !! @ $i @ sK6 ) )
| ( ( sK5 @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f969,plain,
( spl1_23
| spl1_26
| spl1_22 ),
inference(avatar_split_clause,[status(thm)],[f968,f761,f825,f770]) ).
thf(f968,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f967]) ).
thf(f967,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f966,f50]) ).
thf(f966,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK23 @ X2 ) )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f965,f50]) ).
thf(f965,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK51 @ X4 ) )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK23 @ X2 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f964,f50]) ).
thf(f964,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK51 @ X4 ) )
= $true )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( sK14 @ X3 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f963,f50]) ).
thf(f963,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( sK14 @ X3 )
= $true )
| ( ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK51 @ X4 ) )
= $true )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f962,f50]) ).
thf(f962,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( sK14 @ X3 )
= $true )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK51 @ X4 ) )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f961,f50]) ).
thf(f961,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK57 @ X4 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK51 @ X4 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f960,f50]) ).
thf(f960,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X4 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK57 @ X4 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f342,f50]) ).
thf(f342,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X4 @ ( sK58 @ X4 ) @ ( sK57 @ X4 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f341]) ).
thf(f341,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ~ ( X4 @ ( sK58 @ X4 ) @ ( sK57 @ X4 ) ) )
= $false )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f339]) ).
thf(f339,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ~ ( X4 @ ( sK58 @ X4 ) @ ( sK57 @ X4 ) )
| ( X4 @ ( sK56 @ X4 ) @ ( sK57 @ X4 ) ) )
= $false )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f337]) ).
thf(f337,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( sK14 @ X3 )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $false
= ( ~ ( X4 @ ( sK58 @ X4 ) @ ( sK57 @ X4 ) )
| ( X4 @ ( sK56 @ X4 ) @ ( sK57 @ X4 ) )
| ~ ( X4 @ ( sK56 @ X4 ) @ ( sK58 @ X4 ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f336]) ).
thf(f336,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X4 @ Y0 @ ( sK57 @ X4 ) )
| ( X4 @ ( sK56 @ X4 ) @ ( sK57 @ X4 ) )
| ~ ( X4 @ ( sK56 @ X4 ) @ Y0 ) )
@ ( sK58 @ X4 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f335]) ).
thf(f335,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X4 @ Y0 @ ( sK57 @ X4 ) )
| ( X4 @ ( sK56 @ X4 ) @ ( sK57 @ X4 ) )
| ~ ( X4 @ ( sK56 @ X4 ) @ Y0 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f334]) ).
thf(f334,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X4 @ Y1 @ Y0 )
| ( X4 @ ( sK56 @ X4 ) @ Y0 )
| ~ ( X4 @ ( sK56 @ X4 ) @ Y1 ) ) )
@ ( sK57 @ X4 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f333]) ).
thf(f333,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X4 @ Y1 @ Y0 )
| ( X4 @ ( sK56 @ X4 ) @ Y0 )
| ~ ( X4 @ ( sK56 @ X4 ) @ Y1 ) ) ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f332]) ).
thf(f332,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( ~ ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X4 @ Y1 @ Y0 )
| ( X4 @ ( sK56 @ X4 ) @ Y0 )
| ~ ( X4 @ ( sK56 @ X4 ) @ Y1 ) ) ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f331]) ).
thf(f331,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( ~ ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) )
@ ( sK56 @ X4 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f330]) ).
thf(f330,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( ~ ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
= $false )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( ( sK14 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f315]) ).
thf(f315,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( ( ~ ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f314]) ).
thf(f314,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( ( X4 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) )
| ~ ( sK3 @ ( sK52 @ X4 ) @ ( sK51 @ X4 ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f313]) ).
thf(f313,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( X4 @ Y0 @ ( sK51 @ X4 ) )
| ~ ( sK3 @ Y0 @ ( sK51 @ X4 ) ) )
@ ( sK52 @ X4 ) )
= $false )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f312]) ).
thf(f312,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X4 @ Y0 @ ( sK51 @ X4 ) )
| ~ ( sK3 @ Y0 @ ( sK51 @ X4 ) ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f311]) ).
thf(f311,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ ( sK51 @ X4 ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f310]) ).
thf(f310,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f309]) ).
thf(f309,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f308]) ).
thf(f308,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f307]) ).
thf(f307,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( $false
= ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f305]) ).
thf(f305,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( X4 @ X3 @ ( sK26 @ X3 ) )
= $true )
| ( ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f304]) ).
thf(f304,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
| ( X4 @ X3 @ ( sK26 @ X3 ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f302]) ).
thf(f302,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $false
= ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ ( sK50 @ X2 ) @ ( sK25 @ X2 ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X4 @ Y2 @ Y1 )
| ( X4 @ Y0 @ Y1 )
| ~ ( X4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X4 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
| ( X4 @ X3 @ ( sK26 @ X3 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f301]) ).
thf(f301,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i,X4: $i > $i > $o] :
( ( $false
= ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ ( sK50 @ X2 ) @ ( sK25 @ X2 ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) )
@ X4 )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( ( sK14 @ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f300]) ).
thf(f300,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
| ( $false
= ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ ( sK50 @ X2 ) @ ( sK25 @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f299]) ).
thf(f299,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
= $true )
| ( ( sK14 @ X3 )
= $true )
| ( $false
= ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ ( sK50 @ X2 ) @ ( sK25 @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f297]) ).
thf(f297,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
=> ( sK14 @ ( sK26 @ X3 ) ) )
= $false )
| ( $false
= ( ~ ( X2 @ ( sK50 @ X2 ) @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ ( sK50 @ X2 ) @ ( sK25 @ X2 ) ) ) )
| ( ( ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f296]) ).
thf(f296,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ X3 )
= $true )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
=> ( sK14 @ ( sK26 @ X3 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ Y0 @ ( sK25 @ X2 ) ) )
@ ( sK50 @ X2 ) )
= $false )
| ( ( ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( sK14 @ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ Y0 @ ( sK25 @ X2 ) ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
=> ( sK14 @ ( sK26 @ X3 ) ) )
= $false )
| ( ( ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
=> ( sK14 @ ( sK26 @ X3 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 @ ( sK27 @ X2 ) )
| ~ ( X2 @ ( sK27 @ X2 ) @ ( sK25 @ X2 ) )
| ( X2 @ Y0 @ ( sK25 @ X2 ) ) ) ) )
| ( ( sK14 @ X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
=> ( sK14 @ ( sK26 @ X3 ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK25 @ X2 ) )
| ( X2 @ Y1 @ ( sK25 @ X2 ) ) ) )
@ ( sK27 @ X2 ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( ( sK14 @ X3 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK25 @ X2 ) )
| ( X2 @ Y1 @ ( sK25 @ X2 ) ) ) ) )
= $false )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ X3 @ ( sK26 @ X3 ) ) ) )
=> ( sK14 @ ( sK26 @ X3 ) ) )
= $false )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f176]) ).
thf(f176,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) )
@ ( sK26 @ X3 ) ) )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ X3 )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK25 @ X2 ) )
| ( X2 @ Y1 @ ( sK25 @ X2 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( ( sK14 @ X3 )
= $true )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK25 @ X2 ) )
| ( X2 @ Y1 @ ( sK25 @ X2 ) ) ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f174]) ).
thf(f174,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( sK14 @ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) )
@ ( sK25 @ X2 ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( ( sK14 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( sK14 @ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( sK14 @ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( ( ( X2 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) )
| ~ ( sK3 @ ( sK24 @ X2 ) @ ( sK23 @ X2 ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f170]) ).
thf(f170,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( sK14 @ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK23 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK23 @ X2 ) ) )
@ ( sK24 @ X2 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK23 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK23 @ X2 ) ) ) )
= $false )
| ( ( sK14 @ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( sK14 @ X3 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK23 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK23 @ X2 ) ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ ( sK23 @ X2 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( sK14 @ X3 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( sK14 @ X3 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f165]) ).
thf(f165,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( sK14 @ X3 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f164]) ).
thf(f164,plain,
! [X2: $i > $i > $o,X3: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f162]) ).
thf(f162,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f161]) ).
thf(f161,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f160]) ).
thf(f160,plain,
! [X1: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f158]) ).
thf(f158,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( $false
= ( ( sK5 @ ( sK15 @ X1 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
! [X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) )
@ ( sK15 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X1: $i] :
( ( ( ( sK5 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( sK14 @ Y1 ) ) )
=> ( sK14 @ Y0 ) ) )
=> ( !! @ $i @ sK14 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) )
@ sK14 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK5 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f777,plain,
( spl1_23
| spl1_21
| spl1_22 ),
inference(avatar_split_clause,[status(thm)],[f776,f761,f757,f770]) ).
thf(f776,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( $true
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( sK14 @ sK71 )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f775,f50]) ).
thf(f775,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
= $true )
| ( ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK77 @ X2 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f774,f50]) ).
thf(f774,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK72 @ X2 ) )
= $true )
| ( ( X2 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK77 @ X2 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f773,f50]) ).
thf(f773,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( X2 @ ( sK78 @ X2 ) @ ( sK77 @ X2 ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK72 @ X2 ) )
= $true )
| ( ( sK14 @ sK71 )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f447,f50]) ).
thf(f447,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true )
| ( ( X2 @ ( sK78 @ X2 ) @ ( sK77 @ X2 ) )
= $true )
| ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f446]) ).
thf(f446,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( ~ ( X2 @ ( sK78 @ X2 ) @ ( sK77 @ X2 ) ) )
= $false )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true )
| ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f444]) ).
thf(f444,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( ~ ( X2 @ ( sK78 @ X2 ) @ ( sK77 @ X2 ) )
| ~ ( X2 @ ( sK77 @ X2 ) @ ( sK73 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true )
| ( ( sK14 @ sK71 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f442]) ).
thf(f442,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK14 @ sK71 )
= $false )
| ( $false
= ( ~ ( X2 @ ( sK78 @ X2 ) @ ( sK77 @ X2 ) )
| ~ ( X2 @ ( sK77 @ X2 ) @ ( sK73 @ X2 ) )
| ( X2 @ ( sK78 @ X2 ) @ ( sK73 @ X2 ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f441]) ).
thf(f441,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( X2 @ Y0 @ ( sK77 @ X2 ) )
| ~ ( X2 @ ( sK77 @ X2 ) @ ( sK73 @ X2 ) )
| ( X2 @ Y0 @ ( sK73 @ X2 ) ) )
@ ( sK78 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f440]) ).
thf(f440,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X2 @ Y0 @ ( sK77 @ X2 ) )
| ~ ( X2 @ ( sK77 @ X2 ) @ ( sK73 @ X2 ) )
| ( X2 @ Y0 @ ( sK73 @ X2 ) ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true )
| ( ( sK14 @ sK71 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f439]) ).
thf(f439,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK14 @ sK71 )
= $false )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK73 @ X2 ) )
| ( X2 @ Y1 @ ( sK73 @ X2 ) ) ) )
@ ( sK77 @ X2 ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f438]) ).
thf(f438,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK73 @ X2 ) )
| ( X2 @ Y1 @ ( sK73 @ X2 ) ) ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f426]) ).
thf(f426,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $false
= ( ~ ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ sK71 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK73 @ X2 ) )
| ( X2 @ Y1 @ ( sK73 @ X2 ) ) ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f425]) ).
thf(f425,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ sK71 )
= $false )
| ( ( ( X2 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) )
| ~ ( sK3 @ ( sK74 @ X2 ) @ ( sK72 @ X2 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK73 @ X2 ) )
| ( X2 @ Y1 @ ( sK73 @ X2 ) ) ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f424]) ).
thf(f424,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK72 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK72 @ X2 ) ) )
@ ( sK74 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK73 @ X2 ) )
| ( X2 @ Y1 @ ( sK73 @ X2 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f423]) ).
thf(f423,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK72 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK72 @ X2 ) ) ) )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X2 @ Y1 @ Y0 )
| ~ ( X2 @ Y0 @ ( sK73 @ X2 ) )
| ( X2 @ Y1 @ ( sK73 @ X2 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f422]) ).
thf(f422,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( $true
= ( sK5 @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) )
@ ( sK73 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK72 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK72 @ X2 ) ) ) )
= $false )
| ( ( sK14 @ sK71 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f421]) ).
thf(f421,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) ) )
| ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK72 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK72 @ X2 ) ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f420]) ).
thf(f420,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 @ ( sK72 @ X2 ) )
| ~ ( sK3 @ Y0 @ ( sK72 @ X2 ) ) ) )
= $false )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ sK71 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f419]) ).
thf(f419,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ sK71 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ ( sK72 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f418]) ).
thf(f418,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( X2 @ X1 @ ( sK15 @ X1 ) ) )
| ( ( sK14 @ sK71 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f417]) ).
thf(f417,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ sK71 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f416]) ).
thf(f416,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) ) )
= $true )
| ( ( sK14 @ sK71 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f415]) ).
thf(f415,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X2 @ Y2 @ Y1 )
| ~ ( X2 @ Y1 @ Y0 )
| ( X2 @ Y2 @ Y0 ) ) ) ) )
| ( X2 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f414]) ).
thf(f414,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( ( sK14 @ sK71 )
= $false )
| ( ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f413]) ).
thf(f413,plain,
! [X1: $i] :
( ( ( sK14 @ sK71 )
= $false )
| ( $true
= ( sK5 @ X1 ) )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( !! @ $i @ sK14 )
= $false )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ X1 @ ( sK15 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f158]) ).
thf(f712,plain,
( spl1_9
| spl1_11 ),
inference(avatar_split_clause,[status(thm)],[f708,f710,f702]) ).
thf(f708,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $false
= ( sK3 @ X8 @ X7 ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( sK82 @ X5 @ X2 @ X8 @ X7 )
= $true )
| ( ( sK84 @ X3 @ X6 @ ( d2unsorted @ d_unsorted_0 ) @ X6 )
= $false )
| ( ( X3 @ X1 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f585,f50]) ).
thf(f585,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( $false
= ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( sK82 @ X5 @ X2 @ X8 @ X7 )
= $true )
| ( $false
= ( sK3 @ X8 @ X7 ) )
| ( ( X3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f584]) ).
thf(f584,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( ~ ( sK3 @ X8 @ X7 ) )
= $true )
| ( ( sK82 @ X5 @ X2 @ X8 @ X7 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f583]) ).
thf(f583,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ( sK82 @ X5 @ X2 @ X8 @ X7 )
| ~ ( sK3 @ X8 @ X7 ) )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f582]) ).
thf(f582,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $false
= ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK82 @ X5 @ X2 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) )
@ X8 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f565]) ).
thf(f565,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK82 @ X5 @ X2 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f564]) ).
thf(f564,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK84 @ X3 @ X6 @ Y2 @ Y1 )
| ~ ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ( sK84 @ X3 @ X6 @ Y2 @ Y0 ) ) ) ) )
| ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) ) )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK82 @ X5 @ X2 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f563]) ).
thf(f563,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK84 @ X3 @ X6 @ Y2 @ Y1 )
| ~ ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ( sK84 @ X3 @ X6 @ Y2 @ Y0 ) ) ) ) )
| ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ X7 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f562]) ).
thf(f562,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK84 @ X3 @ X6 @ Y2 @ Y1 )
| ~ ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ( sK84 @ X3 @ X6 @ Y2 @ Y0 ) ) ) ) )
| ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f560]) ).
thf(f560,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK84 @ X3 @ X6 @ Y2 @ Y1 )
| ~ ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ( sK84 @ X3 @ X6 @ Y2 @ Y0 ) ) ) ) )
| ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f559]) ).
thf(f559,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( X2 @ X5 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK84 @ X3 @ X6 @ Y2 @ Y1 )
| ~ ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ( sK84 @ X3 @ X6 @ Y2 @ Y0 ) ) ) ) )
| ( sK84 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f558]) ).
thf(f558,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) )
@ ( sK84 @ X3 @ X6 ) )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f557]) ).
thf(f557,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f503]) ).
thf(f503,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f502]) ).
thf(f502,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK82 @ X5 @ X2 @ Y2 @ Y1 )
| ( sK82 @ X5 @ X2 @ Y0 @ Y1 )
| ~ ( sK82 @ X5 @ X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( X3 @ X1 )
= $true )
| ( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( X2 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f501]) ).
thf(f501,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( ( X3 @ X6 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK82 @ X5 @ X2 @ Y2 @ Y1 )
| ( sK82 @ X5 @ X2 @ Y0 @ Y1 )
| ~ ( sK82 @ X5 @ X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f500]) ).
thf(f500,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X6 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK82 @ X5 @ X2 @ Y2 @ Y1 )
| ( sK82 @ X5 @ X2 @ Y0 @ Y1 )
| ~ ( sK82 @ X5 @ X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK82 @ X5 @ X2 @ Y2 @ Y1 )
| ( sK82 @ X5 @ X2 @ Y0 @ Y1 )
| ~ ( sK82 @ X5 @ X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( X2 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f497]) ).
thf(f497,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK82 @ X5 @ X2 @ Y2 @ Y1 )
| ( sK82 @ X5 @ X2 @ Y0 @ Y1 )
| ~ ( sK82 @ X5 @ X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
| ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f496]) ).
thf(f496,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ ( sK79 @ X2 ) @ X5 ) )
@ ( sK82 @ X5 @ X2 ) )
= $false )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f495]) ).
thf(f495,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ ( sK79 @ X2 ) @ X5 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f494]) ).
thf(f494,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( ( X2 @ X4 )
= $true )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ ( sK79 @ X2 ) @ X5 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f467]) ).
thf(f467,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ ( sK79 @ X2 ) @ X5 ) ) )
=> ( X2 @ X5 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( ( X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f466]) ).
thf(f466,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( ( X3 @ ( sK80 @ X3 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $false )
| ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ ( sK79 @ X2 ) @ X5 ) ) )
=> ( X2 @ X5 ) )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f465]) ).
thf(f465,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( ( X3 @ ( sK80 @ X3 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK79 @ X2 ) @ Y0 ) ) )
=> ( X2 @ Y0 ) )
@ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f464]) ).
thf(f464,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK79 @ X2 ) @ Y0 ) ) )
=> ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( ( X3 @ ( sK80 @ X3 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f463]) ).
thf(f463,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK79 @ X2 ) @ Y0 ) ) )
=> ( X2 @ Y0 ) ) )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ ( sK80 @ X3 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f462]) ).
thf(f462,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK79 @ X2 ) @ Y0 ) ) )
=> ( X2 @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f460]) ).
thf(f460,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK79 @ X2 ) @ Y0 ) ) )
=> ( X2 @ Y0 ) ) )
=> ( X2 @ ( sK79 @ X2 ) ) )
= $false )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( ( X2 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f459]) ).
thf(f459,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) )
@ ( sK79 @ X2 ) )
= $false )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f458]) ).
thf(f458,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) ) )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( ( X2 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f457]) ).
thf(f457,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) ) )
| ( ( X3 @ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f456]) ).
thf(f456,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( !! @ $i @ X2 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f455]) ).
thf(f455,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i] :
( ( $true
= ( ( X3 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ( ( !! @ $i @ X2 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) )
=> ( !! @ $i @ X2 ) )
= $true )
| ( $true
= ( ( X3 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f453]) ).
thf(f453,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) )
=> ( !! @ $i @ X2 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f452]) ).
thf(f452,plain,
! [X2: $i > $o,X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) )
=> ( !! @ $i @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f451]) ).
thf(f451,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) )
@ X2 )
= $true )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f450]) ).
thf(f450,plain,
! [X1: $i] :
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) )
= $true )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f449]) ).
thf(f449,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( sK3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( sK3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( sK3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ $i @ Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f707,plain,
( spl1_9
| spl1_10 ),
inference(avatar_split_clause,[status(thm)],[f598,f705,f702]) ).
thf(f598,plain,
! [X2: $i > $o,X3: $i > $o,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( sK3 @ X9 @ X8 )
= $false )
| ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
= $true )
| ( ( sK3 @ X10 @ X7 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f597]) ).
thf(f597,plain,
! [X2: $i > $o,X3: $i > $o,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( sK3 @ X10 @ X7 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true )
| ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( ~ ( sK3 @ X9 @ X8 ) )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f596]) ).
thf(f596,plain,
! [X2: $i > $o,X3: $i > $o,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
| ~ ( sK3 @ X9 @ X8 ) )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( sK3 @ X10 @ X7 )
= $false )
| ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f595]) ).
thf(f595,plain,
! [X2: $i > $o,X3: $i > $o,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ~ ( sK3 @ X10 @ X7 ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
= $true )
| ( ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
| ~ ( sK3 @ X9 @ X8 ) )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f594]) ).
thf(f594,plain,
! [X2: $i > $o,X3: $i > $o,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( ( sK84 @ X3 @ X6 @ X10 @ X7 )
| ~ ( sK3 @ X10 @ X7 ) )
= $true )
| ( ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
| ~ ( sK3 @ X9 @ X8 ) )
= $true )
| ( ( X2 @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f593]) ).
thf(f593,plain,
! [X2: $i > $o,X3: $i > $o,X10: $i,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK84 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) )
@ X10 )
= $true )
| ( ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
| ~ ( sK3 @ X9 @ X8 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f592]) ).
thf(f592,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK84 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) )
= $true )
| ( ( ( sK82 @ X5 @ X2 @ X9 @ X8 )
| ~ ( sK3 @ X9 @ X8 ) )
= $true )
| ( ( X3 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f591]) ).
thf(f591,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X9: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK82 @ X5 @ X2 @ Y0 @ X8 )
| ~ ( sK3 @ Y0 @ X8 ) )
@ X9 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK84 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f590]) ).
thf(f590,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK82 @ X5 @ X2 @ Y0 @ X8 )
| ~ ( sK3 @ Y0 @ X8 ) ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK84 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f589]) ).
thf(f589,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK84 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ X8 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f588]) ).
thf(f588,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK84 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) )
= $true )
| ( ( X3 @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f587]) ).
thf(f587,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ X7 )
= $true )
| ( ( X3 @ X6 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f586]) ).
thf(f586,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f561]) ).
thf(f561,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK84 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK82 @ X5 @ X2 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f560]) ).
thf(f695,plain,
( spl1_7
| spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f691,f687,f693]) ).
thf(f691,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK85 @ X3 @ X6 @ ( d2unsorted @ d_unsorted_0 ) @ X6 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( d2unsorted @ d_unsorted_0 ) @ X5 ) )
| ( ( X3 @ X1 )
= $true )
| ( ( X3 @ X6 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f690,f50]) ).
thf(f690,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( d2unsorted @ d_unsorted_0 ) @ X5 ) )
| ( ( sK85 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 )
= $false )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f607,f50]) ).
thf(f607,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( sK85 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 )
= $false )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f606]) ).
thf(f606,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK85 @ X3 @ X6 @ Y2 @ Y1 )
| ~ ( sK85 @ X3 @ X6 @ Y1 @ Y0 )
| ( sK85 @ X3 @ X6 @ Y2 @ Y0 ) ) ) ) )
| ( sK85 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 ) )
= $false )
| ( ( X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f604]) ).
thf(f604,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK85 @ X3 @ X6 @ Y2 @ Y1 )
| ~ ( sK85 @ X3 @ X6 @ Y1 @ Y0 )
| ( sK85 @ X3 @ X6 @ Y2 @ Y0 ) ) ) ) )
| ( sK85 @ X3 @ X6 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK85 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X3 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f603]) ).
thf(f603,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) )
@ ( sK85 @ X3 @ X6 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f602]) ).
thf(f602,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f601]) ).
thf(f601,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f600]) ).
thf(f600,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( X3 @ X6 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ( Y0 @ ( sK80 @ X3 ) @ X6 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( sK3 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f599]) ).
thf(f599,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X6 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f498]) ).
thf(f498,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK80 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f497]) ).
thf(f689,plain,
( spl1_5
| spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f682,f687,f684]) ).
thf(f682,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( $false
= ( sK3 @ X8 @ X7 ) )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( d2unsorted @ d_unsorted_0 ) @ X5 ) )
| ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f626,f50]) ).
thf(f626,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( $false
= ( sK3 @ X8 @ X7 ) )
| ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f625]) ).
thf(f625,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( ~ ( sK3 @ X8 @ X7 ) )
= $true )
| ( ( X2 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f624]) ).
thf(f624,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( ( sK85 @ X3 @ X6 @ X8 @ X7 )
| ~ ( sK3 @ X8 @ X7 ) )
= $true )
| ( ( X3 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f623]) ).
thf(f623,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK85 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) )
@ X8 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X5 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f622]) ).
thf(f622,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( X3 @ X6 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK85 @ X3 @ X6 @ Y0 @ X7 )
| ~ ( sK3 @ Y0 @ X7 ) ) ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f621]) ).
thf(f621,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK85 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) )
@ X7 ) )
| ( ( X3 @ X6 )
= $true )
| ( ( X2 @ X5 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X3 @ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f620]) ).
thf(f620,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X2 @ X5 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK85 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( X3 @ X6 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f605]) ).
thf(f605,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ X6 )
= $true )
| ( $false
= ( sK82 @ X5 @ X2 @ ( sK79 @ X2 ) @ X5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK85 @ X3 @ X6 @ Y1 @ Y0 )
| ~ ( sK3 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( X2 @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f604]) ).
thf(f681,plain,
( spl1_2
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f680,f665,f665]) ).
thf(f680,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true )
| ( ( X3 @ ( d2unsorted @ d_unsorted_0 ) )
= $false )
| ( $false
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f679,f50]) ).
thf(f679,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( X3 @ ( sK86 @ X3 ) )
= $false )
| ( $false
= ( X2 @ ( d2unsorted @ d_unsorted_0 ) ) )
| ( ( X3 @ X1 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f630,f50]) ).
thf(f630,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK79 @ X2 ) ) )
| ( ( X3 @ X1 )
= $true )
| ( ( X3 @ ( sK86 @ X3 ) )
= $false )
| ( ( X2 @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f628]) ).
thf(f628,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $false
= ( ( X3 @ ( sK86 @ X3 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ( Y1 @ ( sK86 @ X3 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( sK3 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( X2 @ ( sK79 @ X2 ) ) )
| ( ( X3 @ X1 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f627]) ).
thf(f627,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK79 @ X2 ) ) )
| ( ( X2 @ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
@ ( sK86 @ X3 ) )
= $false )
| ( ( X3 @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f461]) ).
thf(f461,plain,
! [X2: $i > $o,X3: $i > $o,X1: $i,X4: $i] :
( ( ( X3 @ X1 )
= $true )
| ( $false
= ( X2 @ ( sK79 @ X2 ) ) )
| ( ( X2 @ X4 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X3 @ Y1 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( sK3 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.10/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n014.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 09:30:51 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.28/0.46 % Domain : Software Verification
% 0.28/0.46 % Problem : Benchmark: SEV441^1, Active target: satisfying_the_induction_principle
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Kon26]
% 0.28/0.46 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : ? v9.3.0
% 0.28/0.46 % Syntax : Number of formulae : 35 ( 1 unt; 33 typ; 0 def)
% 0.28/0.46 % Number of atoms : 82 ( 51 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 33 ( 41 avg)
% 0.28/0.46 % Number of connectives : 985 ( 227 ~; 218 |; 43 &; 493 @)
% 0.28/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 32 ( 17 avg)
% 0.28/0.46 % Number of types : 4 ( 2 usr)
% 0.28/0.46 % Number of type conns : 263 ( 263 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 32 ( 31 usr; 1 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 315 ( 48 ^; 266 !; 1 ?; 315 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(unsorted_type,type,
% 0.28/0.46 unsorted: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(subrel_decl,type,
% 0.28/0.46 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(inv_decl,type,
% 0.28/0.46 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(idem_decl,type,
% 0.28/0.46 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(infl_decl,type,
% 0.28/0.46 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mono_decl,type,
% 0.28/0.46 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(refl_decl,type,
% 0.28/0.46 refl: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(irrefl_decl,type,
% 0.28/0.46 irrefl: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(rc_decl,type,
% 0.28/0.46 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(symm_decl,type,
% 0.28/0.46 symm: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(antisymm_decl,type,
% 0.28/0.46 antisymm: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(asymm_decl,type,
% 0.28/0.46 asymm: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sc_decl,type,
% 0.28/0.46 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(trans_decl,type,
% 0.28/0.46 trans: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(tc_decl,type,
% 0.28/0.46 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(trc_decl,type,
% 0.28/0.46 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(trsc_decl,type,
% 0.28/0.46 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(po_decl,type,
% 0.28/0.46 po: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(so_decl,type,
% 0.28/0.46 so: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(total_decl,type,
% 0.28/0.46 total: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(term_decl,type,
% 0.28/0.46 term: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(ind_decl,type,
% 0.28/0.46 ind: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(innf_decl,type,
% 0.28/0.46 innf: ( $i > $i > $o ) > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(nfof_decl,type,
% 0.28/0.46 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(norm_decl,type,
% 0.28/0.46 norm: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(join_decl,type,
% 0.28/0.46 join: ( $i > $i > $o ) > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(lconfl_decl,type,
% 0.28/0.46 lconfl: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(sconfl_decl,type,
% 0.28/0.46 sconfl: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(confl_decl,type,
% 0.28/0.46 confl: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cr_decl,type,
% 0.28/0.46 cr: ( $i > $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 %----Types of the domains
% 0.28/0.46 thf(d_unsorted_type,type,
% 0.28/0.46 d_unsorted: $tType ).
% 0.28/0.46
% 0.28/0.46 %----Types of the promotion functions
% 0.28/0.46 thf(d2unsorted_decl,type,
% 0.28/0.46 d2unsorted: d_unsorted > $i ).
% 0.28/0.46
% 0.28/0.46 %----Types of the domain elements
% 0.28/0.46 thf(d_unsorted_0_decl,type,
% 0.28/0.46 d_unsorted_0: d_unsorted ).
% 0.28/0.46
% 0.28/0.46 thf(sev441_1,axiom,
% 0.28/0.46 ( ! [U: $i] :
% 0.28/0.46 ? [DU: d_unsorted] :
% 0.28/0.46 ( U
% 0.28/0.46 = ( d2unsorted @ DU ) )
% 0.28/0.46 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.28/0.46 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.28/0.46 ( ( ( d2unsorted @ DU1 )
% 0.28/0.46 = ( d2unsorted @ DU2 ) )
% 0.28/0.46 => ( DU1 = DU2 ) )
% 0.28/0.46 & ( subrel
% 0.28/0.46 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 0.28/0.46 ! [X: $i,Y: $i] :
% 0.28/0.46 ( ~ ( R @ X @ Y )
% 0.28/0.46 | ( S @ X @ Y ) ) ) )
% 0.28/0.46 & ( inv
% 0.28/0.46 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 0.28/0.46 & ( idem
% 0.28/0.46 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.28/0.46 ! [R: $i > $i > $o] :
% 0.28/0.46 ( ( F @ R )
% 0.28/0.46 = ( F @ ( F @ R ) ) ) ) )
% 0.28/0.46 & ( infl
% 0.28/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.28/0.47 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ( F @ R @ X @ Y ) ) ) )
% 0.28/0.47 & ( mono
% 0.28/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.28/0.47 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 0.28/0.47 ( ~ ! [X: $i,Y: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ( S @ X @ Y ) )
% 0.28/0.47 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 0.28/0.47 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 0.28/0.47 & ( refl
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i] : ( R @ X @ X ) ) )
% 0.28/0.47 & ( irrefl
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i] :
% 0.28/0.47 ~ ( R @ X @ X ) ) )
% 0.28/0.47 & ( rc
% 0.28/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.28/0.47 ( ( X = Y )
% 0.28/0.47 | ( R @ X @ Y ) ) ) )
% 0.28/0.47 & ( symm
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ( R @ Y @ X ) ) ) )
% 0.28/0.47 & ( antisymm
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ~ ( R @ Y @ X )
% 0.28/0.47 | ( X = Y ) ) ) )
% 0.28/0.47 & ( asymm
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ~ ( R @ Y @ X ) ) ) )
% 0.28/0.47 & ( sc
% 0.28/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.28/0.47 ( ( R @ Y @ X )
% 0.28/0.47 | ( R @ X @ Y ) ) ) )
% 0.28/0.47 & ( trans
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i,Z: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ~ ( R @ Y @ Z )
% 0.28/0.47 | ( R @ X @ Z ) ) ) )
% 0.28/0.47 & ( tc
% 0.28/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.28/0.47 ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Y ) ) ) )
% 0.28/0.47 & ( trc
% 0.28/0.47 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.28/0.47 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.28/0.47 | ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.28/0.47 & ( trsc
% 0.28/0.47 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.28/0.47 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.28/0.47 | ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 0.28/0.47 | ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.28/0.47 & ( po
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ( ! [X: $i] : ( R @ X @ X )
% 0.28/0.47 & ! [X: $i,Y: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ~ ( R @ Y @ X )
% 0.28/0.47 | ( X = Y ) )
% 0.28/0.47 & ! [X: $i,Y: $i,Z: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ~ ( R @ Y @ Z )
% 0.28/0.47 | ( R @ X @ Z ) ) ) ) )
% 0.28/0.47 & ( so
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ( ! [X: $i,Y: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ~ ( R @ Y @ X ) )
% 0.28/0.47 & ! [X: $i,Y: $i,Z: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Y )
% 0.28/0.47 | ~ ( R @ Y @ Z )
% 0.28/0.47 | ( R @ X @ Z ) ) ) ) )
% 0.28/0.47 & ( total
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i] :
% 0.28/0.47 ( ( X = Y )
% 0.28/0.47 | ( R @ X @ Y )
% 0.28/0.47 | ( R @ Y @ X ) ) ) )
% 0.28/0.47 & ( term
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [A: $i > $o,Bound_variable_862: $i] :
% 0.28/0.47 ( ~ ( A @ Bound_variable_862 )
% 0.28/0.47 | ~ ! [X: $i] :
% 0.28/0.47 ( ~ ( A @ X )
% 0.28/0.47 | ~ ! [Y: $i] :
% 0.28/0.47 ( ~ ( A @ Y )
% 0.28/0.47 | ~ ( R @ X @ Y ) ) ) ) ) )
% 0.28/0.47 & ( ind
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [P: $i > $o,Bound_variable_917: $i] :
% 0.28/0.47 ( ~ ! [X: $i] :
% 0.28/0.47 ( ~ ! [Y: $i] :
% 0.28/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Y ) )
% 0.28/0.47 | ( P @ Y ) )
% 0.28/0.47 | ( P @ X ) )
% 0.28/0.47 | ( P @ Bound_variable_917 ) ) ) )
% 0.28/0.47 & ( innf
% 0.28/0.47 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.28/0.47 ! [Y: $i] :
% 0.28/0.47 ~ ( R @ X @ Y ) ) )
% 0.28/0.47 & ( nfof
% 0.28/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.28/0.47 ( ( ( X = Y )
% 0.28/0.47 | ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ X ) ) )
% 0.28/0.47 & ! [Bound_variable_985: $i] :
% 0.28/0.47 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 0.28/0.47 & ( norm
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Bound_variable_1075: $i] :
% 0.28/0.47 ( ~ ( R @ X @ Bound_variable_1075 )
% 0.28/0.47 | ~ ! [Bound_variable_1049: $i] :
% 0.28/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Bound_variable_1049 ) )
% 0.28/0.47 | ~ ! [Bound_variable_985: $i] :
% 0.28/0.47 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 0.28/0.47 & ( join
% 0.28/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.28/0.47 ~ ( ( X != Y )
% 0.28/0.47 & ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ X ) )
% 0.28/0.47 & ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Y ) )
% 0.28/0.47 & ! [Bound_variable_1218: $i] :
% 0.28/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.28/0.47 | ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 0.28/0.47 & ( lconfl
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 0.28/0.47 ( ~ ( R @ X @ Z )
% 0.28/0.47 | ~ ( R @ X @ Y )
% 0.28/0.47 | ( Y = Z )
% 0.28/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.28/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.28/0.47 | ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1293 @ Y @ Z )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 0.28/0.47 & ( sconfl
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 0.28/0.47 ( ~ ( R @ X @ Z )
% 0.28/0.47 | ( ( X != Y )
% 0.28/0.47 & ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Y ) ) )
% 0.28/0.47 | ( Y = Z )
% 0.28/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.28/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.28/0.47 | ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1371 @ Y @ Z )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 0.28/0.47 & ( confl
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 0.28/0.47 ( ( ( X != Z )
% 0.28/0.47 & ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Z ) ) )
% 0.28/0.47 | ( ( X != Y )
% 0.28/0.47 & ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Y ) ) )
% 0.28/0.47 | ( Y = Z )
% 0.28/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.28/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.28/0.47 | ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1444 @ Y @ Z )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 0.28/0.47 & ( cr
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 0.28/0.47 ( ( ( X != Y )
% 0.28/0.47 & ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ X ) )
% 0.28/0.47 & ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Y ) ) )
% 0.28/0.47 | ( X = Y )
% 0.28/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.28/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.28/0.47 | ~ ! [S: $i > $i > $o] :
% 0.28/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( S @ X @ Bound_variable_1218 ) ) )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.28/0.47 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1522 @ Y @ X )
% 0.28/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.28/0.47 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 0.28/0.47 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.28/0.47 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.28/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.28/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.28/0.47 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.28/0.47 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(satisfying_the_induction_principle,conjecture,
% 0.28/0.47 ( ind
% 0.28/0.47 = ( ^ [R: $i > $i > $o] :
% 0.28/0.47 ! [P: $i > $o] :
% 0.28/0.47 ( ! [X: $i] :
% 0.28/0.47 ( ! [Y: $i] :
% 0.28/0.47 ( ( tc @ R @ X @ Y )
% 0.28/0.47 => ( P @ Y ) )
% 0.28/0.47 => ( P @ X ) )
% 0.28/0.47 => ! [X: $i] : ( P @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.93/1.37 ---- Embedded in THF ---
% 1.93/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.93/1.37 %%% Generated on Tue May 05 09:30:52 EDT 2026
% 1.93/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.93/1.37 %%% Logic specification used:
% 1.93/1.37 %%% thf(spec, logic, $$dhol).
% 1.93/1.37
% 1.93/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Z8wGJ6wj6z/DTF2DTF3057.p
% See solution above
% 1.93/1.37 ------------------------
% 1.93/1.39 ---- Cleaned THF ---
% 1.93/1.39 thf(unsorted_type,type,
% 1.93/1.39 unsorted: $tType ).
% 1.93/1.39
% 1.93/1.39 thf(subrel_decl,type,
% 1.93/1.39 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(inv_decl,type,
% 1.93/1.39 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(idem_decl,type,
% 1.93/1.39 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(infl_decl,type,
% 1.93/1.39 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(mono_decl,type,
% 1.93/1.39 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(refl_decl,type,
% 1.93/1.39 refl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(irrefl_decl,type,
% 1.93/1.39 irrefl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(rc_decl,type,
% 1.93/1.39 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(symm_decl,type,
% 1.93/1.39 symm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(antisymm_decl,type,
% 1.93/1.39 antisymm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(asymm_decl,type,
% 1.93/1.39 asymm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(sc_decl,type,
% 1.93/1.39 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(trans_decl,type,
% 1.93/1.39 trans: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(tc_decl,type,
% 1.93/1.39 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(trc_decl,type,
% 1.93/1.39 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(trsc_decl,type,
% 1.93/1.39 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(po_decl,type,
% 1.93/1.39 po: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(so_decl,type,
% 1.93/1.39 so: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(total_decl,type,
% 1.93/1.39 total: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(term_decl,type,
% 1.93/1.39 term: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(ind_decl,type,
% 1.93/1.39 ind: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(innf_decl,type,
% 1.93/1.39 innf: ( $i > $i > $o ) > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(nfof_decl,type,
% 1.93/1.39 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(norm_decl,type,
% 1.93/1.39 norm: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(join_decl,type,
% 1.93/1.39 join: ( $i > $i > $o ) > $i > $i > $o ).
% 1.93/1.39
% 1.93/1.39 thf(lconfl_decl,type,
% 1.93/1.39 lconfl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(sconfl_decl,type,
% 1.93/1.39 sconfl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(confl_decl,type,
% 1.93/1.39 confl: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(cr_decl,type,
% 1.93/1.39 cr: ( $i > $i > $o ) > $o ).
% 1.93/1.39
% 1.93/1.39 thf(d_unsorted_type,type,
% 1.93/1.39 d_unsorted: $tType ).
% 1.93/1.39
% 1.93/1.39 thf(d2unsorted_decl,type,
% 1.93/1.39 d2unsorted: d_unsorted > $i ).
% 1.93/1.39
% 1.93/1.39 thf(d_unsorted_0_decl,type,
% 1.93/1.39 d_unsorted_0: d_unsorted ).
% 1.93/1.39
% 1.93/1.39 thf(sev441_1,axiom,
% 1.93/1.39 ( ! [U: $i] :
% 1.93/1.39 ? [DU: d_unsorted] :
% 1.93/1.39 ( U
% 1.93/1.39 = ( d2unsorted @ DU ) )
% 1.93/1.39 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 1.93/1.39 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 1.93/1.39 ( ( ( d2unsorted @ DU1 )
% 1.93/1.39 = ( d2unsorted @ DU2 ) )
% 1.93/1.39 => ( DU1 = DU2 ) )
% 1.93/1.39 & ( subrel
% 1.93/1.39 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ( S @ X @ Y ) ) ) )
% 1.93/1.39 & ( inv
% 1.93/1.39 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 1.93/1.39 & ( idem
% 1.93/1.39 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 1.93/1.39 ! [R: $i > $i > $o] :
% 1.93/1.39 ( ( F @ R )
% 1.93/1.39 = ( F @ ( F @ R ) ) ) ) )
% 1.93/1.39 & ( infl
% 1.93/1.39 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 1.93/1.39 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ( F @ R @ X @ Y ) ) ) )
% 1.93/1.39 & ( mono
% 1.93/1.39 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 1.93/1.39 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 1.93/1.39 ( ~ ! [X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ( S @ X @ Y ) )
% 1.93/1.39 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 1.93/1.39 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 1.93/1.39 & ( refl
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i] : ( R @ X @ X ) ) )
% 1.93/1.39 & ( irrefl
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i] :
% 1.93/1.39 ~ ( R @ X @ X ) ) )
% 1.93/1.39 & ( rc
% 1.93/1.39 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.39 ( ( X = Y )
% 1.93/1.39 | ( R @ X @ Y ) ) ) )
% 1.93/1.39 & ( symm
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ( R @ Y @ X ) ) ) )
% 1.93/1.39 & ( antisymm
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ~ ( R @ Y @ X )
% 1.93/1.39 | ( X = Y ) ) ) )
% 1.93/1.39 & ( asymm
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ~ ( R @ Y @ X ) ) ) )
% 1.93/1.39 & ( sc
% 1.93/1.39 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.39 ( ( R @ Y @ X )
% 1.93/1.39 | ( R @ X @ Y ) ) ) )
% 1.93/1.39 & ( trans
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i,Z: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ~ ( R @ Y @ Z )
% 1.93/1.39 | ( R @ X @ Z ) ) ) )
% 1.93/1.39 & ( tc
% 1.93/1.39 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.39 ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Y ) ) ) )
% 1.93/1.39 & ( trc
% 1.93/1.39 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 1.93/1.39 ( ( Flatten_var_0 = Flatten_var_1 )
% 1.93/1.39 | ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 1.93/1.39 & ( trsc
% 1.93/1.39 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 1.93/1.39 ( ( Flatten_var_0 = Flatten_var_1 )
% 1.93/1.39 | ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 1.93/1.39 | ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 1.93/1.39 & ( po
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ( ! [X: $i] : ( R @ X @ X )
% 1.93/1.39 & ! [X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ~ ( R @ Y @ X )
% 1.93/1.39 | ( X = Y ) )
% 1.93/1.39 & ! [X: $i,Y: $i,Z: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ~ ( R @ Y @ Z )
% 1.93/1.39 | ( R @ X @ Z ) ) ) ) )
% 1.93/1.39 & ( so
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ( ! [X: $i,Y: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ~ ( R @ Y @ X ) )
% 1.93/1.39 & ! [X: $i,Y: $i,Z: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Y )
% 1.93/1.39 | ~ ( R @ Y @ Z )
% 1.93/1.39 | ( R @ X @ Z ) ) ) ) )
% 1.93/1.39 & ( total
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i] :
% 1.93/1.39 ( ( X = Y )
% 1.93/1.39 | ( R @ X @ Y )
% 1.93/1.39 | ( R @ Y @ X ) ) ) )
% 1.93/1.39 & ( term
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [A: $i > $o,Bound_variable_862: $i] :
% 1.93/1.39 ( ~ ( A @ Bound_variable_862 )
% 1.93/1.39 | ~ ! [X: $i] :
% 1.93/1.39 ( ~ ( A @ X )
% 1.93/1.39 | ~ ! [Y: $i] :
% 1.93/1.39 ( ~ ( A @ Y )
% 1.93/1.39 | ~ ( R @ X @ Y ) ) ) ) ) )
% 1.93/1.39 & ( ind
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [P: $i > $o,Bound_variable_917: $i] :
% 1.93/1.39 ( ~ ! [X: $i] :
% 1.93/1.39 ( ~ ! [Y: $i] :
% 1.93/1.39 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Y ) )
% 1.93/1.39 | ( P @ Y ) )
% 1.93/1.39 | ( P @ X ) )
% 1.93/1.39 | ( P @ Bound_variable_917 ) ) ) )
% 1.93/1.39 & ( innf
% 1.93/1.39 = ( ^ [R: $i > $i > $o,X: $i] :
% 1.93/1.39 ! [Y: $i] :
% 1.93/1.39 ~ ( R @ X @ Y ) ) )
% 1.93/1.39 & ( nfof
% 1.93/1.39 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.39 ( ( ( X = Y )
% 1.93/1.39 | ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ X ) ) )
% 1.93/1.39 & ! [Bound_variable_985: $i] :
% 1.93/1.39 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 1.93/1.39 & ( norm
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Bound_variable_1075: $i] :
% 1.93/1.39 ( ~ ( R @ X @ Bound_variable_1075 )
% 1.93/1.39 | ~ ! [Bound_variable_1049: $i] :
% 1.93/1.39 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Bound_variable_1049 ) )
% 1.93/1.39 | ~ ! [Bound_variable_985: $i] :
% 1.93/1.39 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 1.93/1.39 & ( join
% 1.93/1.39 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 1.93/1.39 ~ ( ( X != Y )
% 1.93/1.39 & ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ X ) )
% 1.93/1.39 & ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Y ) )
% 1.93/1.39 & ! [Bound_variable_1218: $i] :
% 1.93/1.39 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.39 | ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 1.93/1.39 & ( lconfl
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 1.93/1.39 ( ~ ( R @ X @ Z )
% 1.93/1.39 | ~ ( R @ X @ Y )
% 1.93/1.39 | ( Y = Z )
% 1.93/1.39 | ~ ! [Bound_variable_1218: $i] :
% 1.93/1.39 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.39 | ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Z @ Bound_variable_1218 ) ) )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1293 @ Y @ Z )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 1.93/1.39 & ( sconfl
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 1.93/1.39 ( ~ ( R @ X @ Z )
% 1.93/1.39 | ( ( X != Y )
% 1.93/1.39 & ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Y ) ) )
% 1.93/1.39 | ( Y = Z )
% 1.93/1.39 | ~ ! [Bound_variable_1218: $i] :
% 1.93/1.39 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.39 | ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Z @ Bound_variable_1218 ) ) )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1371 @ Y @ Z )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 1.93/1.39 & ( confl
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 1.93/1.39 ( ( ( X != Z )
% 1.93/1.39 & ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Z ) ) )
% 1.93/1.39 | ( ( X != Y )
% 1.93/1.39 & ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Y ) ) )
% 1.93/1.39 | ( Y = Z )
% 1.93/1.39 | ~ ! [Bound_variable_1218: $i] :
% 1.93/1.39 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.39 | ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Z @ Bound_variable_1218 ) ) )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1444 @ Y @ Z )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 1.93/1.39 & ( cr
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 1.93/1.39 ( ( ( X != Y )
% 1.93/1.39 & ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ X ) )
% 1.93/1.39 & ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Z )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Z ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Y ) ) )
% 1.93/1.39 | ( X = Y )
% 1.93/1.39 | ~ ! [Bound_variable_1218: $i] :
% 1.93/1.39 ( ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ Y @ Bound_variable_1218 ) )
% 1.93/1.39 | ~ ! [S: $i > $i > $o] :
% 1.93/1.39 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( S @ X @ Bound_variable_1218 ) ) )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 1.93/1.39 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1522 @ Y @ X )
% 1.93/1.39 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 1.93/1.39 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 1.93/1.39 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 1.93/1.39 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 1.93/1.39 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 1.93/1.39 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 1.93/1.39 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 1.93/1.39 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 1.93/1.39
% 1.93/1.39 thf(satisfying_the_induction_principle,conjecture,
% 1.93/1.39 ( ind
% 1.93/1.39 = ( ^ [R: $i > $i > $o] :
% 1.93/1.39 ! [P: $i > $o] :
% 1.93/1.39 ( ! [X: $i] :
% 1.93/1.39 ( ! [Y: $i] :
% 1.93/1.39 ( ( tc @ R @ X @ Y )
% 1.93/1.39 => ( P @ Y ) )
% 1.93/1.39 => ( P @ X ) )
% 1.93/1.39 => ! [X: $i] : ( P @ X ) ) ) ) ).
% 1.93/1.39 ------------------------
% 2.14/1.41 % (3159)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/2Mi)
% 2.14/1.41 % (3159)Instruction limit reached!
% 2.14/1.41 % (3159)------------------------------
% 2.14/1.41 % (3159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.41 % (3159)Termination reason: Unknown
% 2.14/1.41 % (3159)Termination phase: shuffling
% 2.14/1.41
% 2.14/1.41 % (3159)Memory used [KB]: 1151
% 2.14/1.41 % (3157)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/4Mi)
% 2.14/1.41 % (3159)Time elapsed: 0.002 s
% 2.14/1.41 % (3159)Instructions burned: 2 (million)
% 2.14/1.41 % (3159)------------------------------
% 2.14/1.41 % (3159)------------------------------
% 2.14/1.41 % (3158)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/27Mi)
% 2.14/1.41 % (3157)Instruction limit reached!
% 2.14/1.41 % (3157)------------------------------
% 2.14/1.41 % (3157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.41 % (3157)Termination reason: Unknown
% 2.14/1.41 % (3157)Termination phase: shuffling
% 2.14/1.41
% 2.14/1.41 % (3157)Memory used [KB]: 1279
% 2.14/1.41 % (3157)Time elapsed: 0.003 s
% 2.14/1.41 % (3157)Instructions burned: 6 (million)
% 2.14/1.41 % (3157)------------------------------
% 2.14/1.41 % (3157)------------------------------
% 2.14/1.42 % (3156)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/183Mi)
% 2.14/1.42 % (3160)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/2Mi)
% 2.14/1.42 % (3161)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/275Mi)
% 2.14/1.42 % (3158)Instruction limit reached!
% 2.14/1.42 % (3158)------------------------------
% 2.14/1.42 % (3158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.42 % (3162)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/18Mi)
% 2.14/1.42 % (3158)Termination reason: Unknown
% 2.14/1.42 % (3158)Termination phase: Preprocessing 3
% 2.14/1.42
% 2.14/1.42 % (3158)Memory used [KB]: 1535
% 2.14/1.42 % (3158)Time elapsed: 0.009 s
% 2.14/1.42 % (3158)Instructions burned: 28 (million)
% 2.14/1.42 % (3158)------------------------------
% 2.14/1.42 % (3158)------------------------------
% 2.14/1.42 % (3160)Instruction limit reached!
% 2.14/1.42 % (3160)------------------------------
% 2.14/1.42 % (3160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.42 % (3160)Termination reason: Unknown
% 2.14/1.42 % (3160)Termination phase: shuffling
% 2.14/1.42
% 2.14/1.42 % (3160)Memory used [KB]: 1023
% 2.14/1.42 % (3160)Time elapsed: 0.003 s
% 2.14/1.42 % (3160)Instructions burned: 2 (million)
% 2.14/1.42 % (3160)------------------------------
% 2.14/1.42 % (3160)------------------------------
% 2.14/1.42 % (3163)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/3Mi)
% 2.14/1.42 % (3164)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/37Mi)
% 2.14/1.42 % (3163)Instruction limit reached!
% 2.14/1.42 % (3163)------------------------------
% 2.14/1.42 % (3163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.42 % (3163)Termination reason: Unknown
% 2.14/1.42 % (3163)Termination phase: shuffling
% 2.14/1.42
% 2.14/1.42 % (3163)Memory used [KB]: 1151
% 2.14/1.42 % (3163)Time elapsed: 0.002 s
% 2.14/1.42 % (3163)Instructions burned: 4 (million)
% 2.14/1.42 % (3163)------------------------------
% 2.14/1.42 % (3163)------------------------------
% 2.14/1.43 % (3162)Instruction limit reached!
% 2.14/1.43 % (3162)------------------------------
% 2.14/1.43 % (3162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.43 % (3162)Termination reason: Unknown
% 2.14/1.43 % (3162)Termination phase: Property scanning
% 2.14/1.43
% 2.14/1.43 % (3162)Memory used [KB]: 1407
% 2.14/1.43 % (3162)Time elapsed: 0.011 s
% 2.14/1.43 % (3162)Instructions burned: 19 (million)
% 2.14/1.43 % (3162)------------------------------
% 2.14/1.43 % (3162)------------------------------
% 2.14/1.43 % (3165)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/15Mi)
% 2.14/1.43 % (3167)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/1041Mi)
% 2.14/1.43 % (3164)Instruction limit reached!
% 2.14/1.43 % (3164)------------------------------
% 2.14/1.43 % (3164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.43 % (3164)Termination reason: Unknown
% 2.14/1.43 % (3164)Termination phase: Saturation
% 2.14/1.43
% 2.14/1.43 % (3164)Memory used [KB]: 6012
% 2.14/1.43 % (3164)Time elapsed: 0.012 s
% 2.14/1.43 % (3164)Instructions burned: 38 (million)
% 2.14/1.43 % (3164)------------------------------
% 2.14/1.43 % (3164)------------------------------
% 2.14/1.43 % (3165)Instruction limit reached!
% 2.14/1.43 % (3165)------------------------------
% 2.14/1.43 % (3165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.43 % (3165)Termination reason: Unknown
% 2.14/1.43 % (3165)Termination phase: shuffling
% 2.14/1.43
% 2.14/1.43 % (3165)Memory used [KB]: 1407
% 2.14/1.43 % (3165)Time elapsed: 0.006 s
% 2.14/1.43 % (3165)Instructions burned: 15 (million)
% 2.14/1.43 % (3165)------------------------------
% 2.14/1.43 % (3165)------------------------------
% 2.14/1.43 % (3161)Refutation not found, incomplete strategy
% 2.14/1.43 % (3161)------------------------------
% 2.14/1.43 % (3161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.43 % (3161)Termination reason: Refutation not found, incomplete strategy
% 2.14/1.43
% 2.14/1.43
% 2.14/1.43 % (3161)Memory used [KB]: 6012
% 2.14/1.43 % (3161)Time elapsed: 0.018 s
% 2.14/1.43 % (3161)Instructions burned: 31 (million)
% 2.14/1.43 % (3161)------------------------------
% 2.14/1.43 % (3161)------------------------------
% 2.14/1.43 % (3166)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/3Mi)
% 2.14/1.44 % (3166)Instruction limit reached!
% 2.14/1.44 % (3166)------------------------------
% 2.14/1.44 % (3166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.44 % (3166)Termination reason: Unknown
% 2.14/1.44 % (3166)Termination phase: shuffling
% 2.14/1.44
% 2.14/1.44 % (3166)Memory used [KB]: 1151
% 2.14/1.44 % (3166)Time elapsed: 0.004 s
% 2.14/1.44 % (3166)Instructions burned: 4 (million)
% 2.14/1.44 % (3166)------------------------------
% 2.14/1.44 % (3166)------------------------------
% 2.14/1.44 % (3169)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/16Mi)
% 2.14/1.44 % (3170)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/3Mi)
% 2.14/1.44 % (3170)Instruction limit reached!
% 2.14/1.44 % (3170)------------------------------
% 2.14/1.44 % (3170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.44 % (3170)Termination reason: Unknown
% 2.14/1.44 % (3170)Termination phase: shuffling
% 2.14/1.44
% 2.14/1.44 % (3170)Memory used [KB]: 1151
% 2.14/1.44 % (3170)Time elapsed: 0.003 s
% 2.14/1.44 % (3170)Instructions burned: 4 (million)
% 2.14/1.44 % (3170)------------------------------
% 2.14/1.44 % (3170)------------------------------
% 2.14/1.44 % (3168)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/7Mi)
% 2.14/1.45 % (3169)Instruction limit reached!
% 2.14/1.45 % (3169)------------------------------
% 2.14/1.45 % (3169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.45 % (3169)Termination reason: Unknown
% 2.14/1.45 % (3169)Termination phase: Property scanning
% 2.14/1.45
% 2.14/1.45 % (3169)Memory used [KB]: 1535
% 2.14/1.45 % (3169)Time elapsed: 0.007 s
% 2.14/1.45 % (3169)Instructions burned: 19 (million)
% 2.14/1.45 % (3169)------------------------------
% 2.14/1.45 % (3169)------------------------------
% 2.14/1.45 % (3168)Instruction limit reached!
% 2.14/1.45 % (3168)------------------------------
% 2.14/1.45 % (3168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.45 % (3168)Termination reason: Unknown
% 2.14/1.45 % (3168)Termination phase: shuffling
% 2.14/1.45
% 2.14/1.45 % (3168)Memory used [KB]: 1279
% 2.14/1.45 % (3168)Time elapsed: 0.006 s
% 2.14/1.45 % (3168)Instructions burned: 8 (million)
% 2.14/1.45 % (3168)------------------------------
% 2.14/1.45 % (3168)------------------------------
% 2.14/1.45 % (3171)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/3Mi)
% 2.14/1.45 % (3173)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/3Mi)
% 2.14/1.45 % (3171)Instruction limit reached!
% 2.14/1.45 % (3171)------------------------------
% 2.14/1.45 % (3171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.45 % (3171)Termination reason: Unknown
% 2.14/1.45 % (3171)Termination phase: shuffling
% 2.14/1.45
% 2.14/1.45 % (3171)Memory used [KB]: 1151
% 2.14/1.45 % (3171)Time elapsed: 0.004 s
% 2.14/1.45 % (3171)Instructions burned: 4 (million)
% 2.14/1.45 % (3171)------------------------------
% 2.14/1.45 % (3171)------------------------------
% 2.14/1.45 % (3173)Instruction limit reached!
% 2.14/1.45 % (3173)------------------------------
% 2.14/1.45 % (3173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.45 % (3173)Termination reason: Unknown
% 2.14/1.45 % (3173)Termination phase: shuffling
% 2.14/1.45
% 2.14/1.45 % (3173)Memory used [KB]: 1151
% 2.14/1.45 % (3173)Time elapsed: 0.003 s
% 2.14/1.45 % (3173)Instructions burned: 5 (million)
% 2.14/1.45 % (3173)------------------------------
% 2.14/1.45 % (3173)------------------------------
% 2.14/1.45 % (3172)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/7Mi)
% 2.14/1.46 % (3174)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/4Mi)
% 2.14/1.46 % (3174)Instruction limit reached!
% 2.14/1.46 % (3174)------------------------------
% 2.14/1.46 % (3174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.46 % (3174)Termination reason: Unknown
% 2.14/1.46 % (3174)Termination phase: shuffling
% 2.14/1.46
% 2.14/1.46 % (3174)Memory used [KB]: 1151
% 2.14/1.46 % (3174)Time elapsed: 0.003 s
% 2.14/1.46 % (3174)Instructions burned: 5 (million)
% 2.14/1.46 % (3174)------------------------------
% 2.14/1.46 % (3174)------------------------------
% 2.14/1.46 % (3172)Instruction limit reached!
% 2.14/1.46 % (3172)------------------------------
% 2.14/1.46 % (3172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.46 % (3172)Termination reason: Unknown
% 2.14/1.46 % (3172)Termination phase: shuffling
% 2.14/1.46
% 2.14/1.46 % (3172)Memory used [KB]: 1279
% 2.14/1.46 % (3172)Time elapsed: 0.006 s
% 2.14/1.46 % (3172)Instructions burned: 8 (million)
% 2.14/1.46 % (3172)------------------------------
% 2.14/1.46 % (3172)------------------------------
% 2.14/1.46 % (3177)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/6Mi)
% 2.14/1.47 % (3175)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/18Mi)
% 2.14/1.47 % (3177)Instruction limit reached!
% 2.14/1.47 % (3177)------------------------------
% 2.14/1.47 % (3177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.47 % (3177)Termination reason: Unknown
% 2.14/1.47 % (3177)Termination phase: shuffling
% 2.14/1.47
% 2.14/1.47 % (3177)Memory used [KB]: 1279
% 2.14/1.47 % (3177)Time elapsed: 0.004 s
% 2.14/1.47 % (3177)Instructions burned: 8 (million)
% 2.14/1.47 % (3177)------------------------------
% 2.14/1.47 % (3177)------------------------------
% 2.14/1.47 % (3176)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/710Mi)
% 2.14/1.47 % (3178)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/902Mi)
% 2.14/1.47 % (3179)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/21Mi)
% 2.14/1.47 % (3175)Instruction limit reached!
% 2.14/1.47 % (3175)------------------------------
% 2.14/1.47 % (3175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.47 % (3175)Termination reason: Unknown
% 2.14/1.47 % (3175)Termination phase: Property scanning
% 2.14/1.47
% 2.14/1.47 % (3175)Memory used [KB]: 1407
% 2.14/1.47 % (3175)Time elapsed: 0.011 s
% 2.14/1.47 % (3175)Instructions burned: 18 (million)
% 2.14/1.47 % (3175)------------------------------
% 2.14/1.47 % (3175)------------------------------
% 2.14/1.48 % (3180)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/5Mi)
% 2.14/1.48 % (3180)Instruction limit reached!
% 2.14/1.48 % (3180)------------------------------
% 2.14/1.48 % (3180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (3180)Termination reason: Unknown
% 2.14/1.48 % (3180)Termination phase: shuffling
% 2.14/1.48
% 2.14/1.48 % (3180)Memory used [KB]: 1279
% 2.14/1.48 % (3180)Time elapsed: 0.004 s
% 2.14/1.48 % (3180)Instructions burned: 8 (million)
% 2.14/1.48 % (3180)------------------------------
% 2.14/1.48 % (3180)------------------------------
% 2.14/1.48 % (3179)Instruction limit reached!
% 2.14/1.48 % (3179)------------------------------
% 2.14/1.48 % (3179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (3179)Termination reason: Unknown
% 2.14/1.48 % (3179)Termination phase: Property scanning
% 2.14/1.48
% 2.14/1.48 % (3179)Memory used [KB]: 1407
% 2.14/1.48 % (3179)Time elapsed: 0.008 s
% 2.14/1.48 % (3179)Instructions burned: 24 (million)
% 2.14/1.48 % (3179)------------------------------
% 2.14/1.48 % (3179)------------------------------
% 2.14/1.48 % (3178)Refutation not found, incomplete strategy
% 2.14/1.48 % (3178)------------------------------
% 2.14/1.48 % (3178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (3178)Termination reason: Refutation not found, incomplete strategy
% 2.14/1.48
% 2.14/1.48
% 2.14/1.48 % (3178)Memory used [KB]: 6012
% 2.14/1.48 % (3178)Time elapsed: 0.016 s
% 2.14/1.48 % (3178)Instructions burned: 51 (million)
% 2.14/1.48 % (3178)------------------------------
% 2.14/1.48 % (3178)------------------------------
% 2.14/1.49 % (3182)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/377Mi)
% 2.14/1.49 % (3183)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/779Mi)
% 2.14/1.49 % (3181)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/6Mi)
% 2.14/1.49 % (3184)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_3057 for (2999ds/19Mi)
% 2.14/1.49 % (3181)Instruction limit reached!
% 2.14/1.49 % (3181)------------------------------
% 2.14/1.49 % (3181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.49 % (3181)Termination reason: Unknown
% 2.14/1.49 % (3181)Termination phase: shuffling
% 2.14/1.49
% 2.14/1.49 % (3181)Memory used [KB]: 1279
% 2.14/1.49 % (3181)Time elapsed: 0.004 s
% 2.14/1.49 % (3181)Instructions burned: 6 (million)
% 2.14/1.49 % (3181)------------------------------
% 2.14/1.49 % (3181)------------------------------
% 2.14/1.50 % (3184)Instruction limit reached!
% 2.14/1.50 % (3184)------------------------------
% 2.14/1.50 % (3184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.50 % (3184)Termination reason: Unknown
% 2.14/1.50 % (3184)Termination phase: Property scanning
% 2.14/1.50
% 2.14/1.50 % (3184)Memory used [KB]: 1407
% 2.14/1.50 % (3184)Time elapsed: 0.008 s
% 2.14/1.50 % (3184)Instructions burned: 22 (million)
% 2.14/1.50 % (3184)------------------------------
% 2.14/1.50 % (3184)------------------------------
% 2.14/1.50 % (3156)Instruction limit reached!
% 2.14/1.50 % (3156)------------------------------
% 2.14/1.50 % (3156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.50 % (3156)Termination reason: Unknown
% 2.14/1.50 % (3156)Termination phase: Saturation
% 2.14/1.50
% 2.14/1.50 % (3156)Memory used [KB]: 6780
% 2.14/1.50 % (3156)Time elapsed: 0.087 s
% 2.14/1.50 % (3156)Instructions burned: 184 (million)
% 2.14/1.50 % (3156)------------------------------
% 2.14/1.50 % (3156)------------------------------
% 2.14/1.51 % (3185)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/879Mi)
% 2.14/1.51 % (3186)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/17Mi)
% 2.14/1.51 % (3187)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/3Mi)
% 2.14/1.51 % (3187)Instruction limit reached!
% 2.14/1.51 % (3187)------------------------------
% 2.14/1.51 % (3187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.51 % (3187)Termination reason: Unknown
% 2.14/1.51 % (3187)Termination phase: shuffling
% 2.14/1.51
% 2.14/1.51 % (3187)Memory used [KB]: 1151
% 2.14/1.51 % (3187)Time elapsed: 0.002 s
% 2.14/1.51 % (3187)Instructions burned: 4 (million)
% 2.14/1.51 % (3187)------------------------------
% 2.14/1.51 % (3187)------------------------------
% 2.14/1.51 % (3186)Instruction limit reached!
% 2.14/1.51 % (3186)------------------------------
% 2.14/1.51 % (3186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.51 % (3186)Termination reason: Unknown
% 2.14/1.51 % (3186)Termination phase: Property scanning
% 2.14/1.51
% 2.14/1.51 % (3186)Memory used [KB]: 1407
% 2.14/1.51 % (3186)Time elapsed: 0.007 s
% 2.14/1.51 % (3186)Instructions burned: 19 (million)
% 2.14/1.51 % (3186)------------------------------
% 2.14/1.51 % (3186)------------------------------
% 2.14/1.52 % (3188)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/30Mi)
% 2.14/1.52 % (3189)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/127Mi)
% 2.14/1.53 % (3188)Instruction limit reached!
% 2.14/1.53 % (3188)------------------------------
% 2.14/1.53 % (3188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.53 % (3188)Termination reason: Unknown
% 2.14/1.53 % (3188)Termination phase: Property scanning
% 2.14/1.53
% 2.14/1.53 % (3188)Memory used [KB]: 1535
% 2.14/1.53 % (3188)Time elapsed: 0.009 s
% 2.14/1.53 % (3188)Instructions burned: 33 (million)
% 2.14/1.53 % (3188)------------------------------
% 2.14/1.53 % (3188)------------------------------
% 2.14/1.54 % (3190)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/100Mi)
% 2.14/1.56 % (3189)Instruction limit reached!
% 2.14/1.56 % (3189)------------------------------
% 2.14/1.56 % (3189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.56 % (3189)Termination reason: Unknown
% 2.14/1.56 % (3189)Termination phase: Saturation
% 2.14/1.56
% 2.14/1.56 % (3189)Memory used [KB]: 6652
% 2.14/1.56 % (3189)Time elapsed: 0.039 s
% 2.14/1.56 % (3189)Instructions burned: 130 (million)
% 2.14/1.56 % (3189)------------------------------
% 2.14/1.56 % (3189)------------------------------
% 2.14/1.56 % (3190)Instruction limit reached!
% 2.14/1.56 % (3190)------------------------------
% 2.14/1.56 % (3190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.56 % (3190)Termination reason: Unknown
% 2.14/1.56 % (3190)Termination phase: Saturation
% 2.14/1.56
% 2.14/1.56 % (3190)Memory used [KB]: 6012
% 2.14/1.56 % (3190)Time elapsed: 0.026 s
% 2.14/1.56 % (3190)Instructions burned: 103 (million)
% 2.14/1.56 % (3190)------------------------------
% 2.14/1.56 % (3190)------------------------------
% 2.14/1.57 % (3191)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/3Mi)
% 2.14/1.57 % (3192)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/20Mi)
% 2.14/1.57 % (3191)Instruction limit reached!
% 2.14/1.57 % (3191)------------------------------
% 2.14/1.57 % (3191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.57 % (3191)Termination reason: Unknown
% 2.14/1.57 % (3191)Termination phase: shuffling
% 2.14/1.57
% 2.14/1.57 % (3191)Memory used [KB]: 1151
% 2.14/1.57 % (3191)Time elapsed: 0.003 s
% 2.14/1.57 % (3191)Instructions burned: 4 (million)
% 2.14/1.57 % (3191)------------------------------
% 2.14/1.57 % (3191)------------------------------
% 2.14/1.58 % (3192)Instruction limit reached!
% 2.14/1.58 % (3192)------------------------------
% 2.14/1.58 % (3192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.58 % (3192)Termination reason: Unknown
% 2.14/1.58 % (3192)Termination phase: Property scanning
% 2.14/1.58
% 2.14/1.58 % (3192)Memory used [KB]: 1535
% 2.14/1.58 % (3192)Time elapsed: 0.007 s
% 2.14/1.58 % (3192)Instructions burned: 24 (million)
% 2.14/1.58 % (3192)------------------------------
% 2.14/1.58 % (3192)------------------------------
% 2.14/1.58 % (3193)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/86Mi)
% 2.14/1.59 % (3194)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_3057 for (2998ds/107Mi)
% 2.14/1.60 % (3182)Instruction limit reached!
% 2.14/1.60 % (3182)------------------------------
% 2.14/1.60 % (3182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.60 % (3182)Termination reason: Unknown
% 2.14/1.60 % (3182)Termination phase: Saturation
% 2.14/1.60
% 2.14/1.60 % (3182)Memory used [KB]: 7036
% 2.14/1.60 % (3182)Time elapsed: 0.113 s
% 2.14/1.60 % (3182)Instructions burned: 378 (million)
% 2.14/1.60 % (3182)------------------------------
% 2.14/1.60 % (3182)------------------------------
% 2.14/1.61 % (3193)Instruction limit reached!
% 2.14/1.61 % (3193)------------------------------
% 2.14/1.61 % (3193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.61 % (3193)Termination reason: Unknown
% 2.14/1.61 % (3193)Termination phase: Saturation
% 2.14/1.61
% 2.14/1.61 % (3193)Memory used [KB]: 6140
% 2.14/1.61 % (3193)Time elapsed: 0.025 s
% 2.14/1.61 % (3193)Instructions burned: 88 (million)
% 2.14/1.61 % (3193)------------------------------
% 2.14/1.61 % (3193)------------------------------
% 2.14/1.61 % (3195)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/39Mi)
% 2.14/1.62 % (3194)Instruction limit reached!
% 2.14/1.62 % (3194)------------------------------
% 2.14/1.62 % (3194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.62 % (3194)Termination reason: Unknown
% 2.14/1.62 % (3194)Termination phase: Saturation
% 2.14/1.62
% 2.14/1.62 % (3194)Memory used [KB]: 6268
% 2.14/1.62 % (3194)Time elapsed: 0.029 s
% 2.14/1.62 % (3194)Instructions burned: 108 (million)
% 2.14/1.62 % (3194)------------------------------
% 2.14/1.62 % (3194)------------------------------
% 2.14/1.62 % (3196)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/448Mi)
% 2.14/1.62 % (3195)Instruction limit reached!
% 2.14/1.62 % (3195)------------------------------
% 2.14/1.62 % (3195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.62 % (3195)Termination reason: Unknown
% 2.14/1.62 % (3195)Termination phase: Saturation
% 2.14/1.62
% 2.14/1.62 % (3195)Memory used [KB]: 6012
% 2.14/1.62 % (3195)Time elapsed: 0.011 s
% 2.14/1.62 % (3195)Instructions burned: 40 (million)
% 2.14/1.62 % (3195)------------------------------
% 2.14/1.62 % (3195)------------------------------
% 2.14/1.63 % (3197)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/46Mi)
% 2.14/1.63 % (3198)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/98Mi)
% 2.14/1.64 % (3197)Instruction limit reached!
% 2.14/1.64 % (3197)------------------------------
% 2.14/1.64 % (3197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.64 % (3197)Termination reason: Unknown
% 2.14/1.64 % (3197)Termination phase: Saturation
% 2.14/1.64
% 2.14/1.64 % (3197)Memory used [KB]: 6012
% 2.14/1.64 % (3197)Time elapsed: 0.013 s
% 2.14/1.64 % (3197)Instructions burned: 47 (million)
% 2.14/1.64 % (3197)------------------------------
% 2.14/1.64 % (3197)------------------------------
% 2.14/1.65 % (3199)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/507Mi)
% 2.14/1.65 % (3198)Instruction limit reached!
% 2.14/1.65 % (3198)------------------------------
% 2.14/1.65 % (3198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.65 % (3198)Termination reason: Unknown
% 2.14/1.65 % (3198)Termination phase: Saturation
% 2.14/1.65
% 2.14/1.65 % (3198)Memory used [KB]: 1535
% 2.14/1.65 % (3198)Time elapsed: 0.025 s
% 2.14/1.65 % (3198)Instructions burned: 101 (million)
% 2.14/1.65 % (3198)------------------------------
% 2.14/1.65 % (3198)------------------------------
% 2.14/1.66 % (3200)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/149Mi)
% 2.14/1.69 % (3199)Refutation not found, incomplete strategy
% 2.14/1.69 % (3199)------------------------------
% 2.14/1.69 % (3199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.69 % (3199)Termination reason: Refutation not found, incomplete strategy
% 2.14/1.69
% 2.14/1.69
% 2.14/1.69 % (3199)Memory used [KB]: 6140
% 2.14/1.69 % (3199)Time elapsed: 0.040 s
% 2.14/1.69 % (3199)Instructions burned: 143 (million)
% 2.14/1.69 % (3199)------------------------------
% 2.14/1.69 % (3199)------------------------------
% 2.14/1.69 % (3185)First to succeed.
% 2.14/1.69 % (3176)Instruction limit reached!
% 2.14/1.69 % (3176)------------------------------
% 2.14/1.69 % (3176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.69 % (3176)Termination reason: Unknown
% 2.14/1.69 % (3176)Termination phase: Saturation
% 2.14/1.69
% 2.14/1.69 % (3176)Memory used [KB]: 7547
% 2.14/1.69 % (3176)Time elapsed: 0.251 s
% 2.14/1.69 % (3176)Instructions burned: 711 (million)
% 2.14/1.69 % (3176)------------------------------
% 2.14/1.69 % (3176)------------------------------
% 2.14/1.70 % (3201)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/39Mi)
% 2.14/1.70 % (3167)Instruction limit reached!
% 2.14/1.70 % (3167)------------------------------
% 2.14/1.70 % (3167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.70 % (3167)Termination reason: Unknown
% 2.14/1.70 % (3167)Termination phase: Saturation
% 2.14/1.70
% 2.14/1.70 % (3167)Memory used [KB]: 7547
% 2.14/1.70 % (3167)Time elapsed: 0.275 s
% 2.14/1.70 % (3167)Instructions burned: 1044 (million)
% 2.14/1.70 % (3167)------------------------------
% 2.14/1.70 % (3167)------------------------------
% 2.14/1.71 % (3202)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/6Mi)
% 2.14/1.71 % (3200)Instruction limit reached!
% 2.14/1.71 % (3200)------------------------------
% 2.14/1.71 % (3200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.71 % (3200)Termination reason: Unknown
% 2.14/1.71 % (3200)Termination phase: Saturation
% 2.14/1.71
% 2.14/1.71 % (3200)Memory used [KB]: 6396
% 2.14/1.71 % (3200)Time elapsed: 0.044 s
% 2.14/1.71 % (3200)Instructions burned: 151 (million)
% 2.14/1.71 % (3200)------------------------------
% 2.14/1.71 % (3200)------------------------------
% 2.14/1.71 % (3201)Instruction limit reached!
% 2.14/1.71 % (3201)------------------------------
% 2.14/1.71 % (3201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.71 % (3201)Termination reason: Unknown
% 2.14/1.71 % (3201)Termination phase: Function definition elimination
% 2.14/1.71
% 2.14/1.71 % (3201)Memory used [KB]: 1535
% 2.14/1.71 % (3201)Time elapsed: 0.011 s
% 2.14/1.71 % (3201)Instructions burned: 39 (million)
% 2.14/1.71 % (3201)------------------------------
% 2.14/1.71 % (3201)------------------------------
% 2.14/1.71 % (3202)Instruction limit reached!
% 2.14/1.71 % (3202)------------------------------
% 2.14/1.71 % (3202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.71 % (3202)Termination reason: Unknown
% 2.14/1.71 % (3202)Termination phase: shuffling
% 2.14/1.71
% 2.14/1.71 % (3202)Memory used [KB]: 1279
% 2.14/1.71 % (3202)Time elapsed: 0.003 s
% 2.14/1.71 % (3202)Instructions burned: 7 (million)
% 2.14/1.71 % (3202)------------------------------
% 2.14/1.71 % (3202)------------------------------
% 2.14/1.71 % (3203)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_3057 for (2997ds/1087Mi)
% 2.14/1.72 % (3204)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3057 for (2996ds/47Mi)
% 2.14/1.72 % (3205)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_3057 for (2996ds/44Mi)
% 2.14/1.72 % (3206)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_3057 for (2996ds/432Mi)
% 2.14/1.72 % (3185)Refutation found. Thanks to Tanya!
% 2.14/1.72 % SZS status Theorem for DTF2THF_3057
% 2.14/1.72 % SZS output start Proof for DTF2THF_3057
% 2.14/1.72 thf(type_def_6, type, d_unsorted: $tType).
% 2.14/1.72 thf(func_def_0, type, unsorted: $tType).
% 2.14/1.72 thf(func_def_1, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 2.14/1.72 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 2.14/1.72 thf(func_def_30, type, d_unsorted: $tType).
% 2.14/1.72 thf(func_def_31, type, d2unsorted: d_unsorted > $i).
% 2.14/1.72 thf(func_def_32, type, d_unsorted_0: d_unsorted).
% 2.14/1.72 thf(func_def_53, type, sK0: $i > d_unsorted).
% 2.14/1.72 thf(func_def_55, type, ph2: !>[X0: $tType]:(X0)).
% 2.14/1.72 thf(func_def_56, type, sK3: $i > $i > $o).
% 2.14/1.72 thf(func_def_58, type, sK5: $i > $o).
% 2.14/1.72 thf(func_def_59, type, sK6: $i > $o).
% 2.14/1.72 thf(func_def_60, type, sK7: $i > $i).
% 2.14/1.72 thf(func_def_61, type, sK8: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_62, type, sK9: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_63, type, sK10: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_64, type, sK11: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_65, type, sK12: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_67, type, sK14: $i > $o).
% 2.14/1.72 thf(func_def_68, type, sK15: $i > $i).
% 2.14/1.72 thf(func_def_69, type, sK16: $i > $i).
% 2.14/1.72 thf(func_def_70, type, sK17: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_71, type, sK18: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_72, type, sK19: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_73, type, sK20: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_74, type, sK21: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_76, type, sK23: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_77, type, sK24: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_78, type, sK25: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_79, type, sK26: $i > $i).
% 2.14/1.72 thf(func_def_80, type, sK27: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_81, type, sK28: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_82, type, sK29: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_83, type, sK30: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_84, type, sK31: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_85, type, sK32: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_86, type, sK33: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_87, type, sK34: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_88, type, sK35: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_89, type, sK36: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_90, type, sK37: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_91, type, sK38: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_92, type, sK39: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_93, type, sK40: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_94, type, sK41: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_95, type, sK42: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_96, type, sK43: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_97, type, sK44: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_98, type, sK45: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_99, type, sK46: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_100, type, sK47: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_101, type, sK48: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_102, type, sK49: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_103, type, sK50: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_104, type, sK51: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_105, type, sK52: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_106, type, sK53: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_107, type, sK54: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_108, type, sK55: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_109, type, sK56: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_110, type, sK57: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_111, type, sK58: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_112, type, sK59: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_113, type, sK60: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_114, type, sK61: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_115, type, sK62: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_116, type, sK63: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_117, type, sK64: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_118, type, sK65: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_119, type, sK66: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_120, type, sK67: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_121, type, sK68: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_122, type, sK69: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_123, type, sK70: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_125, type, sK72: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_126, type, sK73: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_127, type, sK74: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_128, type, sK75: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_129, type, sK76: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_130, type, sK77: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_131, type, sK78: ($i > $i > $o) > $i).
% 2.14/1.72 thf(func_def_132, type, sK79: ($i > $o) > $i).
% 2.14/1.72 thf(func_def_133, type, sK80: ($i > $o) > $i).
% 2.14/1.72 thf(func_def_134, type, sK81: $i > ($i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_135, type, sK82: $i > ($i > $o) > $i > $i > $o).
% 2.14/1.72 thf(func_def_136, type, sK83: ($i > $o) > $i > $i > $i > $o).
% 2.14/1.72 thf(func_def_137, type, sK84: ($i > $o) > $i > $i > $i > $o).
% 2.14/1.72 thf(func_def_138, type, sK85: ($i > $o) > $i > $i > $i > $o).
% 2.14/1.72 thf(func_def_139, type, sK86: ($i > $o) > $i).
% 2.14/1.72 thf(func_def_140, type, sK87: ($i > $o) > $i > $i > $i > $o).
% 2.14/1.72 thf(f2994,plain,(
% 2.14/1.72 $false),
% 2.14/1.72 inference(avatar_sat_refutation,[status(thm)],[f681,f689,f695,f707,f712,f777,f969,f1245,f1270,f1639,f1666,f2212,f2253,f2349,f2381,f2563,f2869,f2975])).
% 2.14/1.72 thf(f2975,plain,(
% 2.14/1.72 ~spl1_35 | ~spl1_38),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f2974])).
% 2.14/1.72 thf(f2974,plain,(
% 2.14/1.72 $false | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(subsumption_resolution,[status(thm)],[f2970,f1310])).
% 2.14/1.72 thf(f1310,plain,(
% 2.14/1.72 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 2.14/1.72 inference(superposition,[status(thm)],[f50,f50])).
% 2.14/1.72 thf(f50,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((d2unsorted @ d_unsorted_0) = X0)) )),
% 2.14/1.72 inference(backward_demodulation,[status(thm)],[f45,f44])).
% 2.14/1.72 thf(f44,plain,(
% 2.14/1.72 ( ! [X2 : d_unsorted] : ((d_unsorted_0 = X2)) )),
% 2.14/1.72 inference(cnf_transformation,[status(thm)],[f14])).
% 2.14/1.72 thf(f14,plain,(
% 2.14/1.72 (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & ! [X0 : $i] : ((d2unsorted @ (sK0 @ X0)) = X0) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y2 @ Y4) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y5 = Y4)))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y7 @ Y9))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (Y6 @ Y5 @ Y2))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y8 @ Y7))) | (Y1 @ Y8 @ Y6)))))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y10 @ Y8))) | (Y7 @ Y10 @ Y9))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))))))))))))))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y1 @ Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) != (d2unsorted @ X4)) | (X3 = X4)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) | (~ (Y4 @ Y5 @ Y6))) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2)))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y7)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y7 @ Y6)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y1 @ Y4))))) & (~ (Y4 = Y1))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y2 @ Y5 @ Y6)))))))) | (Y3 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (Y2 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y1 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (~ (Y2 @ Y5 @ Y7))) | (Y2 @ Y5 @ Y6)))))))))) | (Y4 = Y1)))))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y3 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (~ (Y0 @ Y1 @ Y2))) | (Y5 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y7))) | (Y5 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7)))))))))))))) & (~ (Y4 = Y1)))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y8 @ Y7))) | (Y3 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y0 @ Y1 @ Y2 @ Y3) | (~ (Y0 @ Y4 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y6))))))))))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y1 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y9) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))))))) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y8 @ Y6))) | (Y2 @ Y8 @ Y7)))))))))) | (Y5 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y7)))))))))))))))))))))))),
% 2.14/1.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13])).
% 2.14/1.72 thf(f13,plain,(
% 2.14/1.72 ! [X0 : $i] : (? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) => ((d2unsorted @ (sK0 @ X0)) = X0))),
% 2.14/1.72 introduced(definition,[],[choice_axiom])).
% 2.14/1.72 thf(f12,plain,(
% 2.14/1.72 (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y2 @ Y4) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y5 = Y4)))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y7 @ Y9))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (Y6 @ Y5 @ Y2))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y8 @ Y7))) | (Y1 @ Y8 @ Y6)))))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y10 @ Y8))) | (Y7 @ Y10 @ Y9))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))))))))))))))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y1 @ Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : (((d2unsorted @ X3) != (d2unsorted @ X4)) | (X3 = X4)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) | (~ (Y4 @ Y5 @ Y6))) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2)))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y7)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y7 @ Y6)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y1 @ Y4))))) & (~ (Y4 = Y1))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y2 @ Y5 @ Y6)))))))) | (Y3 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (Y2 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y1 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (~ (Y2 @ Y5 @ Y7))) | (Y2 @ Y5 @ Y6)))))))))) | (Y4 = Y1)))))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y3 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (~ (Y0 @ Y1 @ Y2))) | (Y5 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y7))) | (Y5 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7)))))))))))))) & (~ (Y4 = Y1)))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y8 @ Y7))) | (Y3 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y0 @ Y1 @ Y2 @ Y3) | (~ (Y0 @ Y4 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y6))))))))))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y1 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y9) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))))))) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y8 @ Y6))) | (Y2 @ Y8 @ Y7)))))))))) | (Y5 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y7)))))))))))))))))))))))),
% 2.14/1.72 inference(rectify,[status(thm)],[f11])).
% 2.14/1.72 thf(f11,plain,(
% 2.14/1.72 (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y2 @ Y4) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y5 = Y4)))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y7 @ Y9))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (Y6 @ Y5 @ Y2))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y8 @ Y7))) | (Y1 @ Y8 @ Y6)))))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y10 @ Y8))) | (Y7 @ Y10 @ Y9))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))))))))))))))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y1 @ Y2)))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! 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@ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y3 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (~ (Y0 @ Y1 @ Y2))) | (Y5 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y7))) | (Y5 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7)))))))))))))) & (~ (Y4 = Y1)))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y8 @ Y7))) | (Y3 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! 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@ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))))))) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y8 @ Y6))) | (Y2 @ Y8 @ Y7)))))))))) | (Y5 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y7)))))))))))))))))))))))),
% 2.14/1.72 inference(ennf_transformation,[status(thm)],[f10])).
% 2.14/1.72 thf(f10,plain,(
% 2.14/1.72 (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : ((d2unsorted @ X3) = X2) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y0 @ Y1 @ Y2 @ Y3) | (~ (Y0 @ Y4 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y6))))))))))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y7)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y7 @ Y6)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y1 @ Y4))))) & (~ (Y4 = Y1))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y2 @ Y5 @ Y6)))))))) | (Y3 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (Y2 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y1 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (~ (Y2 @ Y5 @ Y7))) | (Y2 @ Y5 @ Y6)))))))))) | (Y4 = Y1)))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y3 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (~ (Y0 @ Y1 @ Y2))) | (Y5 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y7))) | (Y5 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7)))))))))))))) & (~ (Y4 = Y1)))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y8 @ Y7))) | (Y3 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))))))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y1 @ Y2)))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) | (~ (Y4 @ Y5 @ Y6))) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : (((d2unsorted @ X1) = (d2unsorted @ X0)) => (X0 = X1)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y1 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y9) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))))))) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y8 @ Y6))) | (Y2 @ Y8 @ Y7)))))))))) | (Y5 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y7))))))))))))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y2 @ Y4) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y5 = Y4)))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y7 @ Y9))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (Y6 @ Y5 @ Y2))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y8 @ Y7))) | (Y1 @ Y8 @ Y6)))))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y10 @ Y8))) | (Y7 @ Y10 @ Y9))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))))))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 2.14/1.72 inference(rectify,[status(thm)],[f6])).
% 2.14/1.72 thf(f6,plain,(
% 2.14/1.72 (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y1 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y10 @ Y9) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y10 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))))))) | (~ (Y0 @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (~ (Y2 @ Y8 @ Y6))) | (Y2 @ Y8 @ Y7)))))))))) | (Y5 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y7))))))))))))))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y2 @ Y1))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & ! [X53 : d_unsorted,X54 : d_unsorted] : (((d2unsorted @ X54) = (d2unsorted @ X53)) => (X53 = X54)) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((~ (Y3 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y1 @ Y2)))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((Y3 @ Y4 @ Y2) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y8)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))))))))))) | (~ (Y0 @ Y1 @ Y2))) | (Y5 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y7))) | (Y5 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7)))))))))))))) & (~ (Y4 = Y1)))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y8)) | (~ (Y3 @ Y8 @ Y7))) | (Y3 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))))))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) | (~ (Y4 @ Y5 @ Y6))) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))) | (~ (Y0 @ Y1 @ Y2))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y0 @ Y1 @ Y2 @ Y3) | (~ (Y0 @ Y4 @ Y2 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (Y4 @ Y5 @ Y6))))))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))))))))))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & ! [X160 : $i] : ? [X161 : d_unsorted] : ((d2unsorted @ X161) = X160) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y7)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y7 @ Y6)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y7 @ Y6)))))))))) | (Y5 @ Y1 @ Y4))))) & (~ (Y4 = Y1))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7)))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y2 @ Y5 @ Y6)))))))) | (Y3 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (Y2 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y7 @ Y9))) | (Y6 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y1 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (~ (Y2 @ Y5 @ Y7))) | (Y2 @ Y5 @ Y6)))))))))) | (Y4 = Y1)))))))))))) & ! [X202 : d_unsorted] : (d_unsorted_0 = X202) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))) | (Y3 @ Y2 @ Y1)))) | (Y1 = Y2)) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2)))) | (Y1 = Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 @ Y2 @ Y4) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y5 = Y4)))) | ((~ (Y5 = Y2)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y7 @ Y9))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (Y6 @ Y5 @ Y2))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7)))))))) | (Y1 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y8 @ Y7))) | (Y1 @ Y8 @ Y6)))))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y9 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y10 @ Y8))) | (Y7 @ Y10 @ Y9))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))))))))))))))))))))))))),
% 2.14/1.72 inference(fool_elimination,[status(thm)],[f5])).
% 2.14/1.72 thf(f5,plain,(
% 2.14/1.72 (irrefl = (^[X0 : $i > $i > $o] : (! [X1 : $i] : ~(X0 @ X1 @ X1)))) & (tc = (^[X2 : $i > $i > $o, X3 : $i, X4 : $i] : (! [X5 : $i > $i > $o] : ((X5 @ X3 @ X4) | ~! [X6 : $i,X7 : $i] : (~(X2 @ X6 @ X7) | (X5 @ X6 @ X7)) | ~! [X8 : $i,X9 : $i,X10 : $i] : (~(X5 @ X10 @ X8) | (X5 @ X10 @ X9) | ~(X5 @ X8 @ X9)))))) & (lconfl = (^[X11 : $i > $i > $o] : (! [X12 : $i > $i > $o,X13 : $i,X14 : $i,X15 : $i > $i > $o,X16 : $i] : (~! [X17 : $i,X18 : $i,X19 : $i] : (~(X12 @ X17 @ X18) | (X12 @ X19 @ X18) | ~(X12 @ X19 @ X17)) | (X12 @ X16 @ X13) | ~! [X20 : $i,X21 : $i,X22 : $i] : ((X15 @ X20 @ X21) | ~(X15 @ X20 @ X22) | ~(X15 @ X22 @ X21)) | ~! [X23 : $i,X24 : $i] : (~(X11 @ X24 @ X23) | (X12 @ X24 @ X23)) | ~(X11 @ X14 @ X16) | (X15 @ X13 @ X16) | (X13 = X16) | ~! [X25 : $i,X26 : $i] : (~(X11 @ X26 @ X25) | (X15 @ X26 @ X25)) | ~(X11 @ X14 @ X13) | ~! [X27 : $i] : (~! [X28 : $i > $i > $o] : (~! [X29 : $i,X30 : $i] : ((X28 @ X29 @ X30) | ~(X11 @ X29 @ X30)) | ~! [X31 : $i,X32 : $i,X33 : $i] : (~(X28 @ X32 @ X31) | ~(X28 @ X33 @ X32) | (X28 @ X33 @ X31)) | (X28 @ X13 @ X27)) | ~! [X34 : $i > $i > $o] : (~! [X35 : $i,X36 : $i] : (~(X11 @ X36 @ X35) | (X34 @ X36 @ X35)) | ~! [X37 : $i,X38 : $i,X39 : $i] : (~(X34 @ X37 @ X39) | ~(X34 @ X39 @ X38) | (X34 @ X37 @ X38)) | (X34 @ X16 @ X27))))))) & ((^[X40 : $i > $i > $o] : (! [X41 : $i,X42 : $i] : (~(X40 @ X41 @ X42) | (X40 @ X42 @ X41)))) = symm) & ((^[X43 : $i > $i > $o] : (! [X44 : $i,X45 : $i,X46 : $i] : (~(X43 @ X44 @ X45) | (X43 @ X46 @ X45) | ~(X43 @ X46 @ X44)))) = trans) & ((^[X47 : $i > $i > $o] : (! [X48 : $i,X49 : $i] : (~(X47 @ X49 @ X48) | (X48 = X49) | ~(X47 @ X48 @ X49)))) = antisymm) & (total = (^[X50 : $i > $i > $o] : (! [X51 : $i,X52 : $i] : ((X50 @ X51 @ X52) | (X50 @ X52 @ X51) | (X51 = X52))))) & ! [X53 : d_unsorted,X54 : d_unsorted] : (((d2unsorted @ X54) = (d2unsorted @ X53)) => (X53 = X54)) & ((^[X55 : ($i > $i > $o) > $i > $i > $o] : (! [X56 : $i > $i > $o,X57 : $i,X58 : $i] : ((X55 @ X56 @ X58 @ X57) | ~(X56 @ X58 @ X57)))) = infl) & (sconfl = (^[X59 : $i > $i > $o] : (! [X60 : $i > $i > $o,X61 : $i,X62 : $i > $i > $o,X63 : $i,X64 : $i] : (~! [X65 : $i,X66 : $i] : ((X62 @ X66 @ X65) | ~(X59 @ X66 @ X65)) | ~! [X67 : $i,X68 : $i,X69 : $i] : ((X62 @ X69 @ X68) | ~(X62 @ X67 @ X68) | ~(X62 @ X69 @ X67)) | (X61 = X63) | ((X61 != X64) & ~! [X70 : $i > $i > $o] : (~! [X71 : $i,X72 : $i,X73 : $i] : (~(X70 @ X72 @ X73) | (X70 @ X71 @ X73) | ~(X70 @ X71 @ X72)) | ~! [X74 : $i,X75 : $i] : ((X70 @ X75 @ X74) | ~(X59 @ X75 @ X74)) | (X70 @ X64 @ X61))) | ~! [X76 : $i,X77 : $i] : ((X60 @ X76 @ X77) | ~(X59 @ X76 @ X77)) | ~! [X78 : $i,X79 : $i,X80 : $i] : ((X60 @ X80 @ X78) | ~(X60 @ X80 @ X79) | ~(X60 @ X79 @ X78)) | (X60 @ X63 @ X61) | ~(X59 @ X64 @ X63) | ~! [X81 : $i] : (~! [X82 : $i > $i > $o] : (~! [X83 : $i,X84 : $i] : ((X82 @ X83 @ X84) | ~(X59 @ X83 @ X84)) | ~! [X85 : $i,X86 : $i,X87 : $i] : (~(X82 @ X86 @ X85) | (X82 @ X87 @ X85) | ~(X82 @ X87 @ X86)) | (X82 @ X61 @ X81)) | ~! [X88 : $i > $i > $o] : (~! [X89 : $i,X90 : $i] : ((X88 @ X90 @ X89) | ~(X59 @ X90 @ X89)) | (X88 @ X63 @ X81) | ~! [X91 : $i,X92 : $i,X93 : $i] : (~(X88 @ X92 @ X93) | (X88 @ X91 @ X93) | ~(X88 @ X91 @ X92)))) | (X62 @ X61 @ X63))))) & (inv = (^[X94 : $i > $i > $o, X95 : $i, X96 : $i] : (X94 @ X96 @ X95))) & (norm = (^[X97 : $i > $i > $o] : (! [X98 : $i,X99 : $i] : (~(X97 @ X99 @ X98) | ~! [X100 : $i] : (~! [X101 : $i] : ~(X97 @ X100 @ X101) | ~! [X102 : $i > $i > $o] : (~! [X103 : $i,X104 : $i] : (~(X97 @ X104 @ X103) | (X102 @ X104 @ X103)) | ~! [X105 : $i,X106 : $i,X107 : $i] : (~(X102 @ X105 @ X107) | ~(X102 @ X107 @ X106) | (X102 @ X105 @ X106)) | (X102 @ X99 @ X100))))))) & ((^[X108 : $i > $i > $o, X109 : $i, X110 : $i] : ((X108 @ X110 @ X109) | (X108 @ X109 @ X110))) = sc) & (join = (^[X111 : $i > $i > $o, X112 : $i, X113 : $i] : (~(~! [X114 : $i > $i > $o] : (~! [X115 : $i,X116 : $i] : ((X114 @ X115 @ X116) | ~(X111 @ X115 @ X116)) | (X114 @ X112 @ X113) | ~! [X117 : $i,X118 : $i,X119 : $i] : (~(X114 @ X117 @ X119) | ~(X114 @ X118 @ X117) | (X114 @ X118 @ X119))) & (X112 != X113) & ! [X120 : $i] : (~! [X121 : $i > $i > $o] : ((X121 @ X112 @ X120) | ~! [X122 : $i,X123 : $i] : ((X121 @ X122 @ X123) | ~(X111 @ X122 @ X123)) | ~! [X124 : $i,X125 : $i,X126 : $i] : ((X121 @ X126 @ X125) | ~(X121 @ X124 @ X125) | ~(X121 @ X126 @ X124))) | ~! [X127 : $i > $i > $o] : (~! [X128 : $i,X129 : $i,X130 : $i] : ((X127 @ X130 @ X128) | ~(X127 @ X130 @ X129) | ~(X127 @ X129 @ X128)) | (X127 @ X113 @ X120) | ~! [X131 : $i,X132 : $i] : ((X127 @ X132 @ X131) | ~(X111 @ X132 @ X131)))) & ~! [X133 : $i > $i > $o] : (~! [X134 : $i,X135 : $i] : (~(X111 @ X135 @ X134) | (X133 @ X135 @ X134)) | ~! [X136 : $i,X137 : $i,X138 : $i] : ((X133 @ X138 @ X136) | ~(X133 @ X137 @ X136) | ~(X133 @ X138 @ X137)) | (X133 @ X113 @ X112)))))) & (mono = (^[X139 : ($i > $i > $o) > $i > $i > $o] : (! [X140 : $i > $i > $o,X141 : $i,X142 : $i,X143 : $i > $i > $o] : (~! [X144 : $i,X145 : $i] : (~(X140 @ X145 @ X144) | (X143 @ X145 @ X144)) | ~(X139 @ X140 @ X142 @ X141) | (X139 @ X143 @ X142 @ X141))))) & (ind = (^[X146 : $i > $i > $o] : (! [X147 : $i > $o,X148 : $i] : (~! [X149 : $i] : (~! [X150 : $i] : (~! [X151 : $i > $i > $o] : (~! [X152 : $i,X153 : $i] : (~(X146 @ X152 @ X153) | (X151 @ X152 @ X153)) | (X151 @ X149 @ X150) | ~! [X154 : $i,X155 : $i,X156 : $i] : ((X151 @ X154 @ X156) | ~(X151 @ X155 @ X156) | ~(X151 @ X154 @ X155))) | (X147 @ X150)) | (X147 @ X149)) | (X147 @ X148))))) & ((^[X157 : $i > $i > $o] : (! [X158 : $i,X159 : $i] : (~(X157 @ X159 @ X158) | ~(X157 @ X158 @ X159)))) = asymm) & ! [X160 : $i] : ? [X161 : d_unsorted] : ((d2unsorted @ X161) = X160) & (cr = (^[X162 : $i > $i > $o] : (! [X163 : $i,X164 : $i > $i > $o,X165 : $i > $i > $o,X166 : $i] : ((X163 = X166) | ~! [X167 : $i,X168 : $i,X169 : $i] : ((X165 @ X169 @ X168) | ~(X165 @ X169 @ X167) | ~(X165 @ X167 @ X168)) | ~! [X170 : $i] : (~! [X171 : $i > $i > $o] : (~! [X172 : $i,X173 : $i] : (~(X162 @ X172 @ X173) | (X171 @ X172 @ X173)) | ~! [X174 : $i,X175 : $i,X176 : $i] : (~(X171 @ X174 @ X175) | ~(X171 @ X175 @ X176) | (X171 @ X174 @ X176)) | (X171 @ X163 @ X170)) | ~! [X177 : $i > $i > $o] : ((X177 @ X166 @ X170) | ~! [X178 : $i,X179 : $i] : (~(X162 @ X178 @ X179) | (X177 @ X178 @ X179)) | ~! [X180 : $i,X181 : $i,X182 : $i] : ((X177 @ X181 @ X180) | ~(X177 @ X182 @ X180) | ~(X177 @ X181 @ X182)))) | (X165 @ X166 @ X163) | ~! [X183 : $i,X184 : $i] : ((X164 @ X184 @ X183) | ~(X162 @ X184 @ X183)) | (X164 @ X163 @ X166) | ~! [X185 : $i,X186 : $i] : ((X165 @ X186 @ X185) | ~(X162 @ X186 @ X185)) | (~! [X187 : $i > $i > $o] : (~! [X188 : $i,X189 : $i,X190 : $i] : (~(X187 @ X190 @ X189) | (X187 @ X188 @ X189) | ~(X187 @ X188 @ X190)) | ~! [X191 : $i,X192 : $i] : ((X187 @ X192 @ X191) | ~(X162 @ X192 @ X191)) | (X187 @ X163 @ X166)) & (X163 != X166) & ~! [X193 : $i > $i > $o] : ((X193 @ X166 @ X163) | ~! [X194 : $i,X195 : $i,X196 : $i] : ((X193 @ X195 @ X196) | ~(X193 @ X195 @ X194) | ~(X193 @ X194 @ X196)) | ~! [X197 : $i,X198 : $i] : (~(X162 @ X198 @ X197) | (X193 @ X198 @ X197)))) | ~! [X199 : $i,X200 : $i,X201 : $i] : (~(X164 @ X199 @ X200) | (X164 @ X201 @ X200) | ~(X164 @ X201 @ X199)))))) & ! [X202 : d_unsorted] : (d_unsorted_0 = X202) & (nfof = (^[X203 : $i > $i > $o, X204 : $i, X205 : $i] : (! [X206 : $i] : ~(X203 @ X204 @ X206) & ((X204 = X205) | ! [X207 : $i > $i > $o] : ((X207 @ X205 @ X204) | ~! [X208 : $i,X209 : $i,X210 : $i] : (~(X207 @ X209 @ X210) | (X207 @ X209 @ X208) | ~(X207 @ X210 @ X208)) | ~! [X211 : $i,X212 : $i] : (~(X203 @ X211 @ X212) | (X207 @ X211 @ X212))))))) & (po = (^[X213 : $i > $i > $o] : (! [X214 : $i,X215 : $i] : ((X214 = X215) | ~(X213 @ X215 @ X214) | ~(X213 @ X214 @ X215)) & ! [X216 : $i,X217 : $i,X218 : $i] : ((X213 @ X217 @ X218) | ~(X213 @ X216 @ X218) | ~(X213 @ X217 @ X216)) & ! [X219 : $i] : (X213 @ X219 @ X219)))) & (subrel = (^[X220 : $i > $i > $o, X221 : $i > $i > $o] : (! [X222 : $i,X223 : $i] : ((X221 @ X223 @ X222) | ~(X220 @ X223 @ X222))))) & (trc = (^[X224 : $i > $i > $o, X225 : $i, X226 : $i] : ((X225 = X226) | ! [X227 : $i > $i > $o] : ((X227 @ X225 @ X226) | ~! [X228 : $i,X229 : $i] : ((X227 @ X229 @ X228) | ~(X224 @ X229 @ X228)) | ~! [X230 : $i,X231 : $i,X232 : $i] : ((X227 @ X232 @ X230) | ~(X227 @ X231 @ X230) | ~(X227 @ X232 @ X231)))))) & (rc = (^[X233 : $i > $i > $o, X234 : $i, X235 : $i] : ((X234 = X235) | (X233 @ X234 @ X235)))) & ((^[X236 : $i > $i > $o, X237 : $i, X238 : $i] : (! [X239 : $i > $i > $o] : ((X239 @ X237 @ X238) | ~! [X240 : $i,X241 : $i] : (~(X236 @ X240 @ X241) | (X239 @ X240 @ X241)) | ~! [X242 : $i,X243 : $i,X244 : $i] : (~(X239 @ X244 @ X242) | (X239 @ X243 @ X242) | ~(X239 @ X243 @ X244))) | (X237 = X238) | ! [X245 : $i > $i > $o] : (~! [X246 : $i,X247 : $i] : ((X245 @ X246 @ X247) | ~(X236 @ X246 @ X247)) | ~! [X248 : $i,X249 : $i,X250 : $i] : (~(X245 @ X249 @ X250) | ~(X245 @ X248 @ X249) | (X245 @ X248 @ X250)) | (X245 @ X238 @ X237)))) = trsc) & ((^[X251 : $i > $i > $o] : (! [X252 : $i] : (X251 @ X252 @ X252))) = refl) & (idem = (^[X253 : ($i > $i > $o) > $i > $i > $o] : (! [X254 : $i > $i > $o] : ((X253 @ (X253 @ X254)) = (X253 @ X254))))) & ((^[X255 : $i > $i > $o, X256 : $i] : (! [X257 : $i] : ~(X255 @ X256 @ X257))) = innf) & ((^[X258 : $i > $i > $o] : (! [X259 : $i,X260 : $i,X261 : $i] : (~(X258 @ X259 @ X261) | (X258 @ X260 @ X261) | ~(X258 @ X260 @ X259)) & ! [X262 : $i,X263 : $i] : (~(X258 @ X263 @ X262) | ~(X258 @ X262 @ X263)))) = so) & (term = (^[X264 : $i > $i > $o] : (! [X265 : $i > $o,X266 : $i] : (~(X265 @ X266) | ~! [X267 : $i] : (~! [X268 : $i] : (~(X264 @ X267 @ X268) | ~(X265 @ X268)) | ~(X265 @ X267)))))) & (confl = (^[X269 : $i > $i > $o] : (! [X270 : $i,X271 : $i,X272 : $i > $i > $o,X273 : $i,X274 : $i > $i > $o] : (~! [X275 : $i] : (~! [X276 : $i > $i > $o] : (~! [X277 : $i,X278 : $i] : (~(X269 @ X278 @ X277) | (X276 @ X278 @ X277)) | (X276 @ X271 @ X275) | ~! [X279 : $i,X280 : $i,X281 : $i] : ((X276 @ X279 @ X280) | ~(X276 @ X279 @ X281) | ~(X276 @ X281 @ X280))) | ~! [X282 : $i > $i > $o] : ((X282 @ X273 @ X275) | ~! [X283 : $i,X284 : $i] : (~(X269 @ X284 @ X283) | (X282 @ X284 @ X283)) | ~! [X285 : $i,X286 : $i,X287 : $i] : (~(X282 @ X286 @ X285) | (X282 @ X287 @ X285) | ~(X282 @ X287 @ X286)))) | ~! [X288 : $i,X289 : $i] : ((X274 @ X288 @ X289) | ~(X269 @ X288 @ X289)) | (X271 = X273) | ~! [X290 : $i,X291 : $i,X292 : $i] : ((X274 @ X290 @ X292) | ~(X274 @ X290 @ X291) | ~(X274 @ X291 @ X292)) | ~! [X293 : $i,X294 : $i,X295 : $i] : (~(X272 @ X293 @ X295) | (X272 @ X293 @ X294) | ~(X272 @ X295 @ X294)) | (X274 @ X271 @ X273) | ~! [X296 : $i,X297 : $i] : ((X272 @ X297 @ X296) | ~(X269 @ X297 @ X296)) | (~! [X298 : $i > $i > $o] : ((X298 @ X270 @ X273) | ~! [X299 : $i,X300 : $i,X301 : $i] : (~(X298 @ X299 @ X300) | ~(X298 @ X301 @ X299) | (X298 @ X301 @ X300)) | ~! [X302 : $i,X303 : $i] : ((X298 @ X302 @ X303) | ~(X269 @ X302 @ X303))) & (X270 != X273)) | ((X270 != X271) & ~! [X304 : $i > $i > $o] : (~! [X305 : $i,X306 : $i] : ((X304 @ X306 @ X305) | ~(X269 @ X306 @ X305)) | (X304 @ X270 @ X271) | ~! [X307 : $i,X308 : $i,X309 : $i] : (~(X304 @ X307 @ X308) | ~(X304 @ X308 @ X309) | (X304 @ X307 @ X309)))) | (X272 @ X273 @ X271)))))),
% 2.14/1.72 inference(rectify,[status(thm)],[f1])).
% 2.14/1.72 thf(f1,axiom,(
% 2.14/1.72 (irrefl = (^[X4 : $i > $i > $o] : (! [X6 : $i] : ~(X4 @ X6 @ X6)))) & (tc = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (! [X5 : $i > $i > $o] : ((X5 @ X6 @ X7) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X11) | ~(X5 @ X13 @ X11)))))) & (lconfl = (^[X4 : $i > $i > $o] : (! [X29 : $i > $i > $o,X7 : $i,X6 : $i,X28 : $i > $i > $o,X11 : $i] : (~! [X13 : $i,X26 : $i,X12 : $i] : (~(X29 @ X13 @ X26) | (X29 @ X12 @ X26) | ~(X29 @ X12 @ X13)) | (X29 @ X11 @ X7) | ~! [X12 : $i,X25 : $i,X13 : $i] : ((X28 @ X12 @ X25) | ~(X28 @ X12 @ X13) | ~(X28 @ X13 @ X25)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X29 @ X14 @ X15)) | ~(X4 @ X6 @ X11) | (X28 @ X7 @ X11) | (X7 = X11) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X28 @ X14 @ X15)) | ~(X4 @ X6 @ X7) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X25)) | (X5 @ X7 @ X27)) | ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X26 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26) | (X5 @ X12 @ X26)) | (X5 @ X11 @ X27))))))) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : (~(X4 @ X6 @ X7) | (X4 @ X7 @ X6)))) = symm) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X11 : $i,X6 : $i] : (~(X4 @ X7 @ X11) | (X4 @ X6 @ X11) | ~(X4 @ X6 @ X7)))) = trans) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : (~(X4 @ X7 @ X6) | (X6 = X7) | ~(X4 @ X6 @ X7)))) = antisymm) & (total = (^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7) | (X6 = X7))))) & ! [X3 : d_unsorted,X2 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & ((^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X4 : $i > $i > $o,X7 : $i,X6 : $i] : ((X8 @ X4 @ X6 @ X7) | ~(X4 @ X6 @ X7)))) = infl) & (sconfl = (^[X4 : $i > $i > $o] : (! [X31 : $i > $i > $o,X7 : $i,X30 : $i > $i > $o,X11 : $i,X6 : $i] : (~! [X15 : $i,X14 : $i] : ((X30 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X25 : $i,X12 : $i] : ((X30 @ X12 @ X25) | ~(X30 @ X13 @ X25) | ~(X30 @ X12 @ X13)) | (X7 = X11) | ((X6 != X7) & ~! [X5 : $i > $i > $o] : (~! [X12 : $i,X13 : $i,X32 : $i] : (~(X5 @ X13 @ X32) | (X5 @ X12 @ X32) | ~(X5 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X7))) | ~! [X14 : $i,X15 : $i] : ((X31 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X26 : $i,X13 : $i,X12 : $i] : ((X31 @ X12 @ X26) | ~(X31 @ X12 @ X13) | ~(X31 @ X13 @ X26)) | (X31 @ X11 @ X7) | ~(X4 @ X6 @ X11) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X25) | (X5 @ X12 @ X25) | ~(X5 @ X12 @ X13)) | (X5 @ X7 @ X27)) | ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X11 @ X27) | ~! [X12 : $i,X13 : $i,X26 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)))) | (X30 @ X7 @ X11))))) & (inv = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (X4 @ X7 @ X6))) & (norm = (^[X4 : $i > $i > $o] : (! [X23 : $i,X6 : $i] : (~(X4 @ X6 @ X23) | ~! [X24 : $i] : (~! [X22 : $i] : ~(X4 @ X24 @ X22) | ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X11 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11) | (X5 @ X12 @ X11)) | (X5 @ X6 @ X24))))))) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7))) = sc) & (join = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (~(~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X7) | ~! [X13 : $i,X12 : $i,X26 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26))) & (X6 != X7) & ! [X27 : $i] : (~! [X5 : $i > $i > $o] : ((X5 @ X6 @ X27) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X26 : $i,X12 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13))) | ~! [X5 : $i > $i > $o] : (~! [X25 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25)) | (X5 @ X7 @ X27) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)))) & ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X25 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)) | (X5 @ X7 @ X6)))))) & (mono = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X4 : $i > $i > $o,X10 : $i,X9 : $i,X5 : $i > $i > $o] : (~! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | (X5 @ X6 @ X7)) | ~(X8 @ X4 @ X9 @ X10) | (X8 @ X5 @ X9 @ X10))))) & (ind = (^[X4 : $i > $i > $o] : (! [X20 : $i > $o,X21 : $i] : (~! [X6 : $i] : (~! [X7 : $i] : (~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X7) | ~! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) | (X20 @ X7)) | (X20 @ X6)) | (X20 @ X21))))) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : (~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)))) = asymm) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (cr = (^[X4 : $i > $i > $o] : (! [X6 : $i,X37 : $i > $i > $o,X36 : $i > $i > $o,X7 : $i] : ((X6 = X7) | ~! [X13 : $i,X25 : $i,X12 : $i] : ((X36 @ X12 @ X25) | ~(X36 @ X12 @ X13) | ~(X36 @ X13 @ X25)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X26 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26) | (X5 @ X12 @ X26)) | (X5 @ X6 @ X27)) | ~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X27) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X25 : $i,X12 : $i,X13 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)))) | (X36 @ X7 @ X6) | ~! [X15 : $i,X14 : $i] : ((X37 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X37 @ X6 @ X7) | ~! [X15 : $i,X14 : $i] : ((X36 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (~! [X5 : $i > $i > $o] : (~! [X12 : $i,X11 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X7)) & (X6 != X7) & ~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X13 : $i,X12 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | ~! [X13 : $i,X26 : $i,X12 : $i] : (~(X37 @ X13 @ X26) | (X37 @ X12 @ X26) | ~(X37 @ X12 @ X13)))))) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & (nfof = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (! [X22 : $i] : ~(X4 @ X6 @ X22) & ((X6 = X7) | ! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X11) | ~(X5 @ X13 @ X11)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))))))) & (po = (^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : ((X6 = X7) | ~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)) & ! [X7 : $i,X6 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X7 @ X11) | ~(X4 @ X6 @ X7)) & ! [X6 : $i] : (X4 @ X6 @ X6)))) & (subrel = (^[X4 : $i > $i > $o, X5 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & (trc = (^[X4 : $i > $i > $o, X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : $i > $i > $o] : ((X5 @ X16 @ X17) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X11 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13)))))) & (rc = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X6 = X7) | (X4 @ X6 @ X7)))) & ((^[X4 : $i > $i > $o, X16 : $i, X17 : $i] : (! [X5 : $i > $i > $o] : ((X5 @ X16 @ X17) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13))) | (X16 = X17) | ! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X11 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)) | (X5 @ X17 @ X16)))) = trsc) & ((^[X4 : $i > $i > $o] : (! [X6 : $i] : (X4 @ X6 @ X6))) = refl) & (idem = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X4 : $i > $i > $o] : ((X8 @ X4) = (X8 @ (X8 @ X4)))))) & ((^[X4 : $i > $i > $o, X6 : $i] : (! [X7 : $i] : ~(X4 @ X6 @ X7))) = innf) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i,X11 : $i] : (~(X4 @ X7 @ X11) | (X4 @ X6 @ X11) | ~(X4 @ X6 @ X7)) & ! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6)))) = so) & (term = (^[X4 : $i > $i > $o] : (! [X18 : $i > $o,X19 : $i] : (~(X18 @ X19) | ~! [X6 : $i] : (~! [X7 : $i] : (~(X4 @ X6 @ X7) | ~(X18 @ X7)) | ~(X18 @ X6)))))) & (confl = (^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i,X34 : $i > $i > $o,X11 : $i,X33 : $i > $i > $o] : (~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X7 @ X27) | ~! [X12 : $i,X25 : $i,X13 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25))) | ~! [X5 : $i > $i > $o] : ((X5 @ X11 @ X27) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X26 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)))) | ~! [X14 : $i,X15 : $i] : ((X33 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X7 = X11) | ~! [X12 : $i,X13 : $i,X25 : $i] : ((X33 @ X12 @ X25) | ~(X33 @ X12 @ X13) | ~(X33 @ X13 @ X25)) | ~! [X12 : $i,X26 : $i,X13 : $i] : (~(X34 @ X12 @ X13) | (X34 @ X12 @ X26) | ~(X34 @ X13 @ X26)) | (X33 @ X7 @ X11) | ~! [X15 : $i,X14 : $i] : ((X34 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (~! [X5 : $i > $i > $o] : ((X5 @ X6 @ X11) | ~! [X13 : $i,X26 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26)) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))) & (X6 != X11)) | ((X6 != X7) & ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X7) | ~! [X12 : $i,X13 : $i,X35 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X35) | (X5 @ X12 @ X35)))) | (X34 @ X11 @ X7)))))),
% 2.14/1.72 file('/export/starexec/sandbox2/tmp/tmp.Z8wGJ6wj6z/DTF2THF_3057.p',sev441_1)).
% 2.14/1.72 thf(f45,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((d2unsorted @ (sK0 @ X0)) = X0)) )),
% 2.14/1.72 inference(cnf_transformation,[status(thm)],[f14])).
% 2.14/1.72 thf(f2970,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((sK7 @ X1) != X1)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(equality_proxy_clausification,[status(thm)],[f2969])).
% 2.14/1.72 thf(f2969,plain,(
% 2.14/1.72 ( ! [X1 : $i] : ((((sK7 @ X1) = X1) = $false)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(not_proxy_clausification,[status(thm)],[f2968])).
% 2.14/1.72 thf(f2968,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((~ ((sK7 @ X1) = X1)) = $true)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2967])).
% 2.14/1.72 thf(f2967,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((~ ((sK7 @ X1) = X1)) = $true) | ($false = $true)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(boolean_simplification,[status(thm)],[f2966])).
% 2.14/1.72 thf(f2966,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (($true = (~ $true)) | ((~ ((sK7 @ X1) = X1)) = $true)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(boolean_simplification,[status(thm)],[f2965])).
% 2.14/1.72 thf(f2965,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((~ ((sK7 @ X1) = X1)) = $true) | ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))) = $true)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f2897])).
% 2.14/1.72 thf(f2897,plain,(
% 2.14/1.72 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ X1 @ (sK7 @ X1)) = $true)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(primitive_instantiation,[status(thm)],[f2884])).
% 2.14/1.72 thf(f2884,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((X2 @ X1 @ (sK7 @ X1)) = $true)) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2882])).
% 2.14/1.72 thf(f2882,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((X2 @ X1 @ (sK7 @ X1)) = $true) | ($false = $true) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) ) | (~spl1_35 | ~spl1_38)),
% 2.14/1.72 inference(backward_demodulation,[status(thm)],[f1256,f2875])).
% 2.14/1.72 thf(f2875,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (($false = (sK6 @ X0))) ) | ~spl1_35),
% 2.14/1.72 inference(superposition,[status(thm)],[f1240,f1310])).
% 2.14/1.72 thf(f1240,plain,(
% 2.14/1.72 ((sK6 @ sK13) = $false) | ~spl1_35),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f1238])).
% 2.14/1.72 thf(f1238,definition,(
% 2.14/1.72 spl1_35 <=> ((sK6 @ sK13) = $false)),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_35])],[avatar_definition])).
% 2.14/1.72 thf(f1256,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) ) | ~spl1_38),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f1255])).
% 2.14/1.72 thf(f1255,definition,(
% 2.14/1.72 spl1_38 <=> ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((X2 @ X1 @ (sK7 @ X1)) = $true))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_38])],[avatar_definition])).
% 2.14/1.72 thf(f2869,plain,(
% 2.14/1.72 ~spl1_2 | ~spl1_21 | ~spl1_26),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f2868])).
% 2.14/1.72 thf(f2868,plain,(
% 2.14/1.72 $false | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(subsumption_resolution,[status(thm)],[f2819,f1310])).
% 2.14/1.72 thf(f2819,plain,(
% 2.14/1.72 ( ! [X3 : $i] : (((sK26 @ X3) != X3)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(equality_proxy_clausification,[status(thm)],[f2818])).
% 2.14/1.72 thf(f2818,plain,(
% 2.14/1.72 ( ! [X3 : $i] : ((((sK26 @ X3) = X3) = $false)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(not_proxy_clausification,[status(thm)],[f2817])).
% 2.14/1.72 thf(f2817,plain,(
% 2.14/1.72 ( ! [X3 : $i] : (((~ ((sK26 @ X3) = X3)) = $true)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2816])).
% 2.14/1.72 thf(f2816,plain,(
% 2.14/1.72 ( ! [X3 : $i] : (($false = $true) | ((~ ((sK26 @ X3) = X3)) = $true)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(boolean_simplification,[status(thm)],[f2815])).
% 2.14/1.72 thf(f2815,plain,(
% 2.14/1.72 ( ! [X3 : $i] : (((~ ((sK26 @ X3) = X3)) = $true) | ($true = (~ $true))) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(boolean_simplification,[status(thm)],[f2814])).
% 2.14/1.72 thf(f2814,plain,(
% 2.14/1.72 ( ! [X3 : $i] : (((~ ((sK26 @ X3) = X3)) = $true) | ((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))) = $true)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f2760])).
% 2.14/1.72 thf(f2760,plain,(
% 2.14/1.72 ( ! [X3 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ X3 @ (sK26 @ X3)) = $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(primitive_instantiation,[status(thm)],[f2574])).
% 2.14/1.72 thf(f2574,plain,(
% 2.14/1.72 ( ! [X3 : $i,X4 : $i > $i > $o] : (((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2573])).
% 2.14/1.72 thf(f2573,plain,(
% 2.14/1.72 ( ! [X3 : $i,X4 : $i > $i > $o] : (((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ($false = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true)) ) | (~spl1_2 | ~spl1_21 | ~spl1_26)),
% 2.14/1.72 inference(backward_demodulation,[status(thm)],[f826,f2572])).
% 2.14/1.72 thf(f2572,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((sK14 @ X0) = $false)) ) | (~spl1_2 | ~spl1_21)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2569])).
% 2.14/1.72 thf(f2569,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (($false = $true) | ((sK14 @ X0) = $false)) ) | (~spl1_2 | ~spl1_21)),
% 2.14/1.72 inference(superposition,[status(thm)],[f759,f1311])).
% 2.14/1.72 thf(f1311,plain,(
% 2.14/1.72 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X2) = $true) | ((X1 @ X0) = $false)) ) | ~spl1_2),
% 2.14/1.72 inference(superposition,[status(thm)],[f666,f50])).
% 2.14/1.72 thf(f666,plain,(
% 2.14/1.72 ( ! [X2 : $i > $o,X4 : $i] : (($false = (X2 @ (d2unsorted @ d_unsorted_0))) | ((X2 @ X4) = $true)) ) | ~spl1_2),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f665])).
% 2.14/1.72 thf(f665,definition,(
% 2.14/1.72 spl1_2 <=> ! [X4 : $i,X2 : $i > $o] : (((X2 @ X4) = $true) | ($false = (X2 @ (d2unsorted @ d_unsorted_0))))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 2.14/1.72 thf(f759,plain,(
% 2.14/1.72 ((sK14 @ sK71) = $false) | ~spl1_21),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f757])).
% 2.14/1.72 thf(f757,definition,(
% 2.14/1.72 spl1_21 <=> ((sK14 @ sK71) = $false)),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_21])],[avatar_definition])).
% 2.14/1.72 thf(f826,plain,(
% 2.14/1.72 ( ! [X3 : $i,X4 : $i > $i > $o] : (((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((sK14 @ X3) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true)) ) | ~spl1_26),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f825])).
% 2.14/1.72 thf(f825,definition,(
% 2.14/1.72 spl1_26 <=> ! [X4 : $i > $i > $o,X3 : $i] : (((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK14 @ X3) = $true) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_26])],[avatar_definition])).
% 2.14/1.72 thf(f2563,plain,(
% 2.14/1.72 ~spl1_23 | ~spl1_36),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f2562])).
% 2.14/1.72 thf(f2562,plain,(
% 2.14/1.72 $false | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(subsumption_resolution,[status(thm)],[f2553,f1310])).
% 2.14/1.72 thf(f2553,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((sK15 @ X1) != X1)) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(equality_proxy_clausification,[status(thm)],[f2552])).
% 2.14/1.72 thf(f2552,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (($false = ((sK15 @ X1) = X1))) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(not_proxy_clausification,[status(thm)],[f2551])).
% 2.14/1.72 thf(f2551,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((~ ((sK15 @ X1) = X1)) = $true)) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2550])).
% 2.14/1.72 thf(f2550,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (($false = $true) | ((~ ((sK15 @ X1) = X1)) = $true)) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(boolean_simplification,[status(thm)],[f2549])).
% 2.14/1.72 thf(f2549,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((~ ((sK15 @ X1) = X1)) = $true) | ($true = (~ $true))) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(boolean_simplification,[status(thm)],[f2548])).
% 2.14/1.72 thf(f2548,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((~ ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))) = $true) | ((~ ((sK15 @ X1) = X1)) = $true)) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f2482])).
% 2.14/1.72 thf(f2482,plain,(
% 2.14/1.72 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ X1 @ (sK15 @ X1)) = $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (~ (Y1 = Y0))))) @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(primitive_instantiation,[status(thm)],[f2385])).
% 2.14/1.72 thf(f2385,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ($true = (X2 @ X1 @ (sK15 @ X1)))) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2384])).
% 2.14/1.72 thf(f2384,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ($false = $true) | ($true = (X2 @ X1 @ (sK15 @ X1)))) ) | (~spl1_23 | ~spl1_36)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f771,f1320])).
% 2.14/1.72 thf(f1320,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (($false = (sK5 @ X0))) ) | ~spl1_36),
% 2.14/1.72 inference(superposition,[status(thm)],[f1244,f1310])).
% 2.14/1.72 thf(f1244,plain,(
% 2.14/1.72 ((sK5 @ sK4) = $false) | ~spl1_36),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f1242])).
% 2.14/1.72 thf(f1242,definition,(
% 2.14/1.72 spl1_36 <=> ((sK5 @ sK4) = $false)),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_36])],[avatar_definition])).
% 2.14/1.72 thf(f771,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ($true = (sK5 @ X1)) | ($true = (X2 @ X1 @ (sK15 @ X1)))) ) | ~spl1_23),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f770])).
% 2.14/1.72 thf(f770,definition,(
% 2.14/1.72 spl1_23 <=> ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ($true = (X2 @ X1 @ (sK15 @ X1))))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_23])],[avatar_definition])).
% 2.14/1.72 thf(f2381,plain,(
% 2.14/1.72 ~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22 | ~spl1_36),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f2380])).
% 2.14/1.72 thf(f2380,plain,(
% 2.14/1.72 $false | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2379])).
% 2.14/1.72 thf(f2379,plain,(
% 2.14/1.72 ($false = $true) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f2378,f1320])).
% 2.14/1.72 thf(f2378,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((sK5 @ X0) = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2377])).
% 2.14/1.72 thf(f2377,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((sK5 @ X0) = $true) | ($false = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f2359,f1320])).
% 2.14/1.72 thf(f2359,plain,(
% 2.14/1.72 ( ! [X0 : $i,X1 : $i] : (($true = (sK5 @ X1)) | ((sK5 @ X0) = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2320])).
% 2.14/1.72 thf(f2320,plain,(
% 2.14/1.72 ( ! [X0 : $i,X1 : $i] : (($true = (sK5 @ X1)) | ($false = $true) | ((sK5 @ X0) = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(superposition,[status(thm)],[f1244,f2285])).
% 2.14/1.72 thf(f2285,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true = (X1 @ X3)) | ((X1 @ X0) = $true) | ((X1 @ X2) = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2284])).
% 2.14/1.72 thf(f2284,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true = (X1 @ X3)) | ((X1 @ X0) = $true) | ($false = $true) | ((X1 @ X2) = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(duplicate_literal_removal,[status(thm)],[f2265])).
% 2.14/1.72 thf(f2265,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X0) = $true) | ((X1 @ X2) = $true) | ((X1 @ X0) = $true) | ($true = (X1 @ X3)) | ($false = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(superposition,[status(thm)],[f688,f2255])).
% 2.14/1.72 thf(f2255,plain,(
% 2.14/1.72 ( ! [X2 : $i > $o,X8 : $i,X9 : $i,X4 : $i,X5 : $i] : (((sK82 @ X5 @ X2 @ X9 @ X8) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true)) ) | (~spl1_2 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2254])).
% 2.14/1.72 thf(f2254,plain,(
% 2.14/1.72 ( ! [X2 : $i > $o,X8 : $i,X9 : $i,X4 : $i,X5 : $i] : (($false = $true) | ((sK82 @ X5 @ X2 @ X9 @ X8) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true)) ) | (~spl1_2 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f703,f1524])).
% 2.14/1.72 thf(f1524,plain,(
% 2.14/1.72 ( ! [X0 : $i,X1 : $i] : (((sK3 @ X0 @ X1) = $true)) ) | (~spl1_2 | ~spl1_22)),
% 2.14/1.72 inference(superposition,[status(thm)],[f1385,f1310])).
% 2.14/1.72 thf(f1385,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((sK3 @ (d2unsorted @ d_unsorted_0) @ X0) = $true)) ) | (~spl1_2 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1382])).
% 2.14/1.72 thf(f1382,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((sK3 @ (d2unsorted @ d_unsorted_0) @ X0) = $true) | ($false = $true)) ) | (~spl1_2 | ~spl1_22)),
% 2.14/1.72 inference(superposition,[status(thm)],[f763,f666])).
% 2.14/1.72 thf(f763,plain,(
% 2.14/1.72 ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ~spl1_22),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f761])).
% 2.14/1.72 thf(f761,definition,(
% 2.14/1.72 spl1_22 <=> ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_22])],[avatar_definition])).
% 2.14/1.72 thf(f703,plain,(
% 2.14/1.72 ( ! [X2 : $i > $o,X8 : $i,X9 : $i,X4 : $i,X5 : $i] : (((sK82 @ X5 @ X2 @ X9 @ X8) = $true) | ((sK3 @ X9 @ X8) = $false) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true)) ) | ~spl1_9),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f702])).
% 2.14/1.72 thf(f702,definition,(
% 2.14/1.72 spl1_9 <=> ! [X5 : $i,X4 : $i,X8 : $i,X9 : $i,X2 : $i > $o] : (((sK3 @ X9 @ X8) = $false) | ((sK82 @ X5 @ X2 @ X9 @ X8) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 2.14/1.72 thf(f688,plain,(
% 2.14/1.72 ( ! [X2 : $i > $o,X4 : $i,X5 : $i] : (($false = (sK82 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true)) ) | ~spl1_6),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f687])).
% 2.14/1.72 thf(f687,definition,(
% 2.14/1.72 spl1_6 <=> ! [X2 : $i > $o,X5 : $i,X4 : $i] : (((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ($false = (sK82 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 2.14/1.72 thf(f2349,plain,(
% 2.14/1.72 ~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f2348])).
% 2.14/1.72 thf(f2348,plain,(
% 2.14/1.72 $false | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2347])).
% 2.14/1.72 thf(f2347,plain,(
% 2.14/1.72 ($false = $true) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(duplicate_literal_removal,[status(thm)],[f2346])).
% 2.14/1.72 thf(f2346,plain,(
% 2.14/1.72 ($false = $true) | ($false = $true) | ($false = $true) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f2299])).
% 2.14/1.72 thf(f2299,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i] : ((((^[Y0 : $i]: ($false)) @ X3) = $true) | (((^[Y0 : $i]: ($false)) @ X2) = $true) | (((^[Y0 : $i]: ($false)) @ X0) = $true)) ) | (~spl1_2 | ~spl1_6 | ~spl1_9 | ~spl1_22)),
% 2.14/1.72 inference(primitive_instantiation,[status(thm)],[f2285])).
% 2.14/1.72 thf(f2253,plain,(
% 2.14/1.72 ~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22 | ~spl1_36),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f2252])).
% 2.14/1.72 thf(f2252,plain,(
% 2.14/1.72 $false | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2251])).
% 2.14/1.72 thf(f2251,plain,(
% 2.14/1.72 ($false = $true) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f2250,f1320])).
% 2.14/1.72 thf(f2250,plain,(
% 2.14/1.72 ( ! [X2 : $i] : (((sK5 @ X2) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2249])).
% 2.14/1.72 thf(f2249,plain,(
% 2.14/1.72 ( ! [X2 : $i] : (($false = $true) | ((sK5 @ X2) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f2222,f1320])).
% 2.14/1.72 thf(f2222,plain,(
% 2.14/1.72 ( ! [X2 : $i,X1 : $i] : (($true = (sK5 @ X1)) | ((sK5 @ X2) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2193])).
% 2.14/1.72 thf(f2193,plain,(
% 2.14/1.72 ( ! [X2 : $i,X1 : $i] : (($true = (sK5 @ X1)) | ((sK5 @ X2) = $true) | ($false = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(superposition,[status(thm)],[f1320,f2166])).
% 2.14/1.72 thf(f2166,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X3) = $true) | ((X0 @ X2) = $true) | ((X0 @ X1) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2165])).
% 2.14/1.72 thf(f2165,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X1) = $true) | ($false = $true) | ((X0 @ X3) = $true) | ((X0 @ X2) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22)),
% 2.14/1.72 inference(duplicate_literal_removal,[status(thm)],[f2142])).
% 2.14/1.72 thf(f2142,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = $true) | ((X0 @ X2) = $true) | ((X0 @ X1) = $true) | ((X0 @ X3) = $true) | ((X0 @ X1) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22)),
% 2.14/1.72 inference(superposition,[status(thm)],[f711,f1668])).
% 2.14/1.72 thf(f1668,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X10 : $i,X1 : $i,X6 : $i,X7 : $i] : (((sK84 @ X3 @ X6 @ X10 @ X7) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1667])).
% 2.14/1.72 thf(f1667,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X10 : $i,X1 : $i,X6 : $i,X7 : $i] : (((sK84 @ X3 @ X6 @ X10 @ X7) = $true) | ((X3 @ X1) = $true) | ($false = $true) | ((X3 @ X6) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_22)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f706,f1524])).
% 2.14/1.72 thf(f706,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X10 : $i,X1 : $i,X6 : $i,X7 : $i] : (((sK84 @ X3 @ X6 @ X10 @ X7) = $true) | ((sK3 @ X10 @ X7) = $false) | ((X3 @ X1) = $true) | ((X3 @ X6) = $true)) ) | ~spl1_10),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f705])).
% 2.14/1.72 thf(f705,definition,(
% 2.14/1.72 spl1_10 <=> ! [X10 : $i,X7 : $i,X6 : $i,X3 : $i > $o,X1 : $i] : (((X3 @ X6) = $true) | ((sK3 @ X10 @ X7) = $false) | ((X3 @ X1) = $true) | ((sK84 @ X3 @ X6 @ X10 @ X7) = $true))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition])).
% 2.14/1.72 thf(f711,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X1 : $i,X6 : $i] : (((sK84 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6) = $false) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true)) ) | ~spl1_11),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f710])).
% 2.14/1.72 thf(f710,definition,(
% 2.14/1.72 spl1_11 <=> ! [X6 : $i,X1 : $i,X3 : $i > $o] : (((X3 @ X6) = $true) | ((X3 @ X1) = $true) | ((sK84 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6) = $false))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 2.14/1.72 thf(f2212,plain,(
% 2.14/1.72 ~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f2211])).
% 2.14/1.72 thf(f2211,plain,(
% 2.14/1.72 $false | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f2210])).
% 2.14/1.72 thf(f2210,plain,(
% 2.14/1.72 ($false = $true) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22)),
% 2.14/1.72 inference(duplicate_literal_removal,[status(thm)],[f2209])).
% 2.14/1.72 thf(f2209,plain,(
% 2.14/1.72 ($false = $true) | ($false = $true) | ($false = $true) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22)),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f2171])).
% 2.14/1.72 thf(f2171,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X2) = $true) | (((^[Y0 : $i]: ($false)) @ X3) = $true) | (((^[Y0 : $i]: ($false)) @ X1) = $true)) ) | (~spl1_2 | ~spl1_10 | ~spl1_11 | ~spl1_22)),
% 2.14/1.72 inference(primitive_instantiation,[status(thm)],[f2166])).
% 2.14/1.72 thf(f1666,plain,(
% 2.14/1.72 ~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22 | ~spl1_36),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f1665])).
% 2.14/1.72 thf(f1665,plain,(
% 2.14/1.72 $false | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1664])).
% 2.14/1.72 thf(f1664,plain,(
% 2.14/1.72 ($false = $true) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f1663,f1320])).
% 2.14/1.72 thf(f1663,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((sK5 @ X0) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1662])).
% 2.14/1.72 thf(f1662,plain,(
% 2.14/1.72 ( ! [X0 : $i] : (((sK5 @ X0) = $true) | ($false = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f1635,f1320])).
% 2.14/1.72 thf(f1635,plain,(
% 2.14/1.72 ( ! [X0 : $i,X1 : $i] : (($true = (sK5 @ X1)) | ((sK5 @ X0) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1609])).
% 2.14/1.72 thf(f1609,plain,(
% 2.14/1.72 ( ! [X0 : $i,X1 : $i] : (((sK5 @ X0) = $true) | ($false = $true) | ($true = (sK5 @ X1))) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22 | ~spl1_36)),
% 2.14/1.72 inference(superposition,[status(thm)],[f1574,f1244])).
% 2.14/1.72 thf(f1574,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X3) = $true) | ((X0 @ X1) = $true) | ((X0 @ X2) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1573])).
% 2.14/1.72 thf(f1573,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ((X0 @ X3) = $true) | ($false = $true) | ((X0 @ X1) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22)),
% 2.14/1.72 inference(duplicate_literal_removal,[status(thm)],[f1563])).
% 2.14/1.72 thf(f1563,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X1) = $true) | ((X0 @ X3) = $true) | ((X0 @ X2) = $true) | ($false = $true) | ((X0 @ X1) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22)),
% 2.14/1.72 inference(superposition,[status(thm)],[f694,f1537])).
% 2.14/1.72 thf(f1537,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i] : (((sK85 @ X3 @ X6 @ X8 @ X7) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1533])).
% 2.14/1.72 thf(f1533,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i] : (((X3 @ X1) = $true) | ($false = $true) | ((X3 @ X6) = $true) | ((sK85 @ X3 @ X6 @ X8 @ X7) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_22)),
% 2.14/1.72 inference(backward_demodulation,[status(thm)],[f685,f1524])).
% 2.14/1.72 thf(f685,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i] : (((sK85 @ X3 @ X6 @ X8 @ X7) = $true) | ($false = (sK3 @ X8 @ X7)) | ((X3 @ X1) = $true) | ((X3 @ X6) = $true)) ) | ~spl1_5),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f684])).
% 2.14/1.72 thf(f684,definition,(
% 2.14/1.72 spl1_5 <=> ! [X7 : $i,X8 : $i,X6 : $i,X3 : $i > $o,X1 : $i] : (((X3 @ X6) = $true) | ((sK85 @ X3 @ X6 @ X8 @ X7) = $true) | ((X3 @ X1) = $true) | ($false = (sK3 @ X8 @ X7)))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 2.14/1.72 thf(f694,plain,(
% 2.14/1.72 ( ! [X3 : $i > $o,X1 : $i,X6 : $i] : (($false = (sK85 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true)) ) | ~spl1_7),
% 2.14/1.72 inference(avatar_component_clause,[status(thm)],[f693])).
% 2.14/1.72 thf(f693,definition,(
% 2.14/1.72 spl1_7 <=> ! [X6 : $i,X1 : $i,X3 : $i > $o] : (($false = (sK85 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true))),
% 2.14/1.72 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 2.14/1.72 thf(f1639,plain,(
% 2.14/1.72 ~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22),
% 2.14/1.72 inference(avatar_contradiction_clause,[status(thm)],[f1638])).
% 2.14/1.72 thf(f1638,plain,(
% 2.14/1.72 $false | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22)),
% 2.14/1.72 inference(trivial_inequality_removal,[status(thm)],[f1637])).
% 2.14/1.72 thf(f1637,plain,(
% 2.14/1.72 ($false = $true) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22)),
% 2.14/1.72 inference(duplicate_literal_removal,[status(thm)],[f1636])).
% 2.14/1.72 thf(f1636,plain,(
% 2.14/1.72 ($false = $true) | ($false = $true) | ($false = $true) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22)),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f1607])).
% 2.14/1.72 thf(f1607,plain,(
% 2.14/1.72 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X3) = $true) | (((^[Y0 : $i]: ($false)) @ X2) = $true) | (((^[Y0 : $i]: ($false)) @ X1) = $true)) ) | (~spl1_2 | ~spl1_5 | ~spl1_7 | ~spl1_22)),
% 2.14/1.72 inference(primitive_instantiation,[status(thm)],[f1574])).
% 2.14/1.72 thf(f1270,plain,(
% 2.14/1.72 spl1_36 | spl1_22 | spl1_38),
% 2.14/1.72 inference(avatar_split_clause,[status(thm)],[f1269,f1255,f761,f1242])).
% 2.14/1.72 thf(f1269,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((sK5 @ sK4) = $false) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((X2 @ X1 @ (sK7 @ X1)) = $true)) )),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f1268,f50])).
% 2.14/1.72 thf(f1268,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((X2 @ X1 @ (sK7 @ X1)) = $true) | ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK11 @ X2)) = $true) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)) )),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f1267,f50])).
% 2.14/1.72 thf(f1267,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK5 @ sK4) = $false) | ((X2 @ (sK12 @ X2) @ (sK11 @ X2)) = $true) | ((sK6 @ X1) = $true) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((X2 @ X1 @ (sK7 @ X1)) = $true)) )),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f1266,f50])).
% 2.14/1.72 thf(f1266,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK3 @ (d2unsorted @ d_unsorted_0) @ (sK8 @ X2))) | ((sK6 @ X1) = $true) | ((X2 @ (sK12 @ X2) @ (sK11 @ X2)) = $true) | ((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true)) )),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f101,f50])).
% 2.14/1.72 thf(f101,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK3 @ (sK9 @ X2) @ (sK8 @ X2)) = $true) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((X2 @ (sK12 @ X2) @ (sK11 @ X2)) = $true)) )),
% 2.14/1.72 inference(not_proxy_clausification,[status(thm)],[f100])).
% 2.14/1.72 thf(f100,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ($false = (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2)))) | ((sK6 @ X1) = $true) | ((X2 @ (sK12 @ X2) @ (sK11 @ X2)) = $true)) )),
% 2.14/1.72 inference(not_proxy_clausification,[status(thm)],[f99])).
% 2.14/1.72 thf(f99,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((~ (X2 @ (sK12 @ X2) @ (sK11 @ X2))) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ($false = (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) )),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 2.14/1.72 thf(f97,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : ((((~ (X2 @ (sK12 @ X2) @ (sK11 @ X2))) | (X2 @ (sK10 @ X2) @ (sK11 @ X2))) = $false) | ($false = (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2)))) | ((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK6 @ X1) = $true)) )),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f88])).
% 2.14/1.72 thf(f88,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((X2 @ X1 @ (sK7 @ X1)) = $true) | ($false = (((~ (X2 @ (sK12 @ X2) @ (sK11 @ X2))) | (X2 @ (sK10 @ X2) @ (sK11 @ X2))) | (~ (X2 @ (sK10 @ X2) @ (sK12 @ X2))))) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ($false = (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) )),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 2.14/1.72 thf(f87,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ($false = ((X2 @ (sK9 @ X2) @ (sK8 @ X2)) | (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK5 @ sK4) = $false) | ($false = (((~ (X2 @ (sK12 @ X2) @ (sK11 @ X2))) | (X2 @ (sK10 @ X2) @ (sK11 @ X2))) | (~ (X2 @ (sK10 @ X2) @ (sK12 @ X2)))))) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f86])).
% 2.14/1.72 thf(f86,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($false = ((^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK11 @ X2))) | (X2 @ (sK10 @ X2) @ (sK11 @ X2))) | (~ (X2 @ (sK10 @ X2) @ Y0)))) @ (sK12 @ X2))) | ($false = ((X2 @ (sK9 @ X2) @ (sK8 @ X2)) | (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true)) )),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f85])).
% 2.14/1.72 thf(f85,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK11 @ X2))) | (X2 @ (sK10 @ X2) @ (sK11 @ X2))) | (~ (X2 @ (sK10 @ X2) @ Y0)))))) | ($false = ((X2 @ (sK9 @ X2) @ (sK8 @ X2)) | (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) | ((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true)) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f84])).
% 2.14/1.72 thf(f84,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK5 @ sK4) = $false) | ((sK6 @ X1) = $true) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (X2 @ (sK10 @ X2) @ Y0)) | (~ (X2 @ (sK10 @ X2) @ Y1)))))) @ (sK11 @ X2))) | ($false = ((X2 @ (sK9 @ X2) @ (sK8 @ X2)) | (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) | ((X2 @ X1 @ (sK7 @ X1)) = $true)) )),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f83])).
% 2.14/1.72 thf(f83,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (X2 @ (sK10 @ X2) @ Y0)) | (~ (X2 @ (sK10 @ X2) @ Y1)))))))) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK6 @ X1) = $true) | ($false = ((X2 @ (sK9 @ X2) @ (sK8 @ X2)) | (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) | ((sK5 @ sK4) = $false)) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f82])).
% 2.14/1.72 thf(f82,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($false = ((X2 @ (sK9 @ X2) @ (sK8 @ X2)) | (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2)))))))) @ (sK10 @ X2)) = $false)) )),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f81])).
% 2.14/1.72 thf(f81,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2))))))))) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK5 @ sK4) = $false) | ($false = ((X2 @ (sK9 @ X2) @ (sK8 @ X2)) | (~ (sK3 @ (sK9 @ X2) @ (sK8 @ X2))))) | ((sK6 @ X1) = $true)) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f80])).
% 2.14/1.72 thf(f80,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($false = ((^[Y0 : $i]: ((X2 @ Y0 @ (sK8 @ X2)) | (~ (sK3 @ Y0 @ (sK8 @ X2))))) @ (sK9 @ X2))) | ((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK6 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2))))))))) = $false)) )),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f79])).
% 2.14/1.72 thf(f79,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK5 @ sK4) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK8 @ X2)) | (~ (sK3 @ Y0 @ (sK8 @ X2)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2))))))))) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK6 @ X1) = $true)) )),
% 2.14/1.72 inference(not_proxy_clausification,[status(thm)],[f78])).
% 2.14/1.72 thf(f78,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2)))))))))) = $true) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK8 @ X2)) | (~ (sK3 @ Y0 @ (sK8 @ X2)))))) = $false)) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f77])).
% 2.14/1.72 thf(f77,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK5 @ sK4) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2)))))))))) = $true) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ (sK8 @ X2))) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK6 @ X1) = $true)) )),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f76])).
% 2.14/1.72 thf(f76,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2)))))))))) = $true)) )),
% 2.14/1.72 inference(not_proxy_clausification,[status(thm)],[f75])).
% 2.14/1.72 thf(f75,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2)))))))))) = $true) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK5 @ sK4) = $false)) )),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 2.14/1.72 thf(f74,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) = $true) | ((X2 @ X1 @ (sK7 @ X1)) = $true) | ((sK5 @ sK4) = $false)) )),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 2.14/1.72 thf(f73,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK6 @ X1) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (X2 @ Y0 @ Y1)) | (~ (X2 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) | (X2 @ X1 @ (sK7 @ X1))) = $true) | ((sK5 @ sK4) = $false)) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f72])).
% 2.14/1.72 thf(f72,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X1 : $i] : ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X1 @ (sK7 @ X1)))) @ X2) = $true) | ((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false)) )),
% 2.14/1.72 inference(pi_clausification,[status(thm)],[f71])).
% 2.14/1.72 thf(f71,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((sK6 @ X1) = $true) | ((sK5 @ sK4) = $false) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X1 @ (sK7 @ X1))))) = $true)) )),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 2.14/1.72 thf(f69,plain,(
% 2.14/1.72 ( ! [X1 : $i] : ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X1 @ (sK7 @ X1))))) => (sK6 @ (sK7 @ X1))) = $false) | ((sK5 @ sK4) = $false) | ((sK6 @ X1) = $true)) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f68])).
% 2.14/1.72 thf(f68,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((sK5 @ sK4) = $false) | ($false = ((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X1 @ Y0)))) => (sK6 @ Y0))) @ (sK7 @ X1))) | ((sK6 @ X1) = $true)) )),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f67])).
% 2.14/1.72 thf(f67,plain,(
% 2.14/1.72 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X1 @ Y0)))) => (sK6 @ Y0)))) = $false) | ((sK5 @ sK4) = $false) | ((sK6 @ X1) = $true)) )),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 2.14/1.72 thf(f66,plain,(
% 2.14/1.72 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X1 @ Y0)))) => (sK6 @ Y0)))) => (sK6 @ X1)) = $true) | ((sK5 @ sK4) = $false)) )),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f65])).
% 2.14/1.72 thf(f65,plain,(
% 2.14/1.72 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK6 @ Y1)))) => (sK6 @ Y0))) @ X1) = $true) | ((sK5 @ sK4) = $false)) )),
% 2.14/1.72 inference(pi_clausification,[status(thm)],[f64])).
% 2.14/1.72 thf(f64,plain,(
% 2.14/1.72 ((sK5 @ sK4) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK6 @ Y1)))) => (sK6 @ Y0)))) = $true)),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 2.14/1.72 thf(f62,plain,(
% 2.14/1.72 ((sK5 @ sK4) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK6 @ Y1)))) => (sK6 @ Y0)))) => (!! @ $i @ sK6)))),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f61])).
% 2.14/1.72 thf(f61,plain,(
% 2.14/1.72 (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ sK6) = $false) | ((sK5 @ sK4) = $false)),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f60])).
% 2.14/1.72 thf(f60,plain,(
% 2.14/1.72 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))) | ((sK5 @ sK4) = $false)),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 2.14/1.72 thf(f58,plain,(
% 2.14/1.72 (((sK5 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))))))))))))) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f57])).
% 2.14/1.72 thf(f57,plain,(
% 2.14/1.72 (((^[Y0 : $i > $o]: ((Y0 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4)))))))))))))))))))))) @ sK5) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f56])).
% 2.14/1.72 thf(f56,plain,(
% 2.14/1.72 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4)))))))))))))))))))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f55])).
% 2.14/1.72 thf(f55,plain,(
% 2.14/1.72 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (sK3 @ Y6 @ Y5)))))))))))))))))))))))) @ sK4) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f54])).
% 2.14/1.72 thf(f54,plain,(
% 2.14/1.72 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (sK3 @ Y6 @ Y5)))))))))))))))))))))))))) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 2.14/1.72 thf(f52,plain,(
% 2.14/1.72 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (sK3 @ Y6 @ Y5))))))))))))))))))))))))) != (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f51])).
% 2.14/1.72 thf(f51,plain,(
% 2.14/1.72 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))))))))) @ sK3) != ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) @ sK3))),
% 2.14/1.72 inference(negative_extensionality,[status(thm)],[f49])).
% 2.14/1.72 thf(f49,plain,(
% 2.14/1.72 ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y3)))) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ Y1))))) != (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))))))))))),
% 2.14/1.72 inference(beta_eta_normalization,[status(thm)],[f48])).
% 2.14/1.72 thf(f48,plain,(
% 2.14/1.72 ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y4 @ Y9 @ Y8))))))))) | (Y7 @ Y5 @ Y6))))))))) @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))) != (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))))))))))),
% 2.14/1.72 inference(definition_unfolding,[status(thm)],[f47,f40,f27])).
% 2.14/1.72 thf(f27,plain,(
% 2.14/1.72 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))),
% 2.14/1.72 inference(cnf_transformation,[status(thm)],[f14])).
% 2.14/1.72 thf(f40,plain,(
% 2.14/1.72 (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))))))))))),
% 2.14/1.72 inference(cnf_transformation,[status(thm)],[f14])).
% 2.14/1.72 thf(f47,plain,(
% 2.14/1.72 (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 2.14/1.72 inference(cnf_transformation,[status(thm)],[f9])).
% 2.14/1.72 thf(f9,plain,(
% 2.14/1.72 (ind != (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 2.14/1.72 inference(flattening,[status(thm)],[f8])).
% 2.14/1.72 thf(f8,plain,(
% 2.14/1.72 ~(ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 2.14/1.72 inference(fool_elimination,[status(thm)],[f7])).
% 2.14/1.72 thf(f7,plain,(
% 2.14/1.72 ~((^[X0 : $i > $i > $o] : (! [X1 : $i > $o] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X4 : $i] : (X1 @ X4)))) = ind)),
% 2.14/1.72 inference(rectify,[status(thm)],[f3])).
% 2.14/1.72 thf(f3,negated_conjecture,(
% 2.14/1.72 ~((^[X4 : $i > $i > $o] : (! [X20 : $i > $o] : (! [X6 : $i] : (! [X7 : $i] : ((tc @ X4 @ X6 @ X7) => (X20 @ X7)) => (X20 @ X6)) => ! [X6 : $i] : (X20 @ X6)))) = ind)),
% 2.14/1.72 inference(negated_conjecture,[status(cth)],[f2])).
% 2.14/1.72 thf(f2,conjecture,(
% 2.14/1.72 ((^[X4 : $i > $i > $o] : (! [X20 : $i > $o] : (! [X6 : $i] : (! [X7 : $i] : ((tc @ X4 @ X6 @ X7) => (X20 @ X7)) => (X20 @ X6)) => ! [X6 : $i] : (X20 @ X6)))) = ind)),
% 2.14/1.72 file('/export/starexec/sandbox2/tmp/tmp.Z8wGJ6wj6z/DTF2THF_3057.p',satisfying_the_induction_principle)).
% 2.14/1.72 thf(f1245,plain,(
% 2.14/1.72 spl1_35 | spl1_36),
% 2.14/1.72 inference(avatar_split_clause,[status(thm)],[f105,f1242,f1238])).
% 2.14/1.72 thf(f105,plain,(
% 2.14/1.72 ((sK6 @ sK13) = $false) | ((sK5 @ sK4) = $false)),
% 2.14/1.72 inference(sigma_clausification,[status(thm)],[f63])).
% 2.14/1.72 thf(f63,plain,(
% 2.14/1.72 ($false = (!! @ $i @ sK6)) | ((sK5 @ sK4) = $false)),
% 2.14/1.72 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 2.14/1.72 thf(f969,plain,(
% 2.14/1.72 spl1_23 | spl1_26 | spl1_22),
% 2.14/1.72 inference(avatar_split_clause,[status(thm)],[f968,f761,f825,f770])).
% 2.14/1.72 thf(f968,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((sK14 @ X3) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.72 inference(duplicate_literal_removal,[status(thm)],[f967])).
% 2.14/1.72 thf(f967,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (sK5 @ X1)) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((sK14 @ X3) = $true) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)) )),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f966,f50])).
% 2.14/1.72 thf(f966,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ X3) = $true) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ($true = (sK5 @ X1)) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK23 @ X2)) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)) )),
% 2.14/1.72 inference(forward_demodulation,[status(thm)],[f965,f50])).
% 2.14/1.72 thf(f965,plain,(
% 2.14/1.72 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK51 @ X4)) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK23 @ X2)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((sK14 @ X3) = $true) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f964,f50])).
% 2.14/1.73 thf(f964,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (sK5 @ X1)) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK51 @ X4)) = $true) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f963,f50])).
% 2.14/1.73 thf(f963,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((sK14 @ X3) = $true) | ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK27 @ X2)) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK51 @ X4)) = $true) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f962,f50])).
% 2.14/1.73 thf(f962,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((sK14 @ X3) = $true) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (sK5 @ X1)) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK51 @ X4)) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f961,f50])).
% 2.14/1.73 thf(f961,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X4 @ (d2unsorted @ d_unsorted_0) @ (sK57 @ X4)) = $true) | ($true = (sK5 @ X1)) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK14 @ X3) = $true) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK51 @ X4)) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f960,f50])).
% 2.14/1.73 thf(f960,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X4 @ (d2unsorted @ d_unsorted_0) @ (sK57 @ X4)) = $true) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f342,f50])).
% 2.14/1.73 thf(f342,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X4 @ (sK58 @ X4) @ (sK57 @ X4)) = $true) | ((sK14 @ X3) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((X4 @ X3 @ (sK26 @ X3)) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f341])).
% 2.14/1.73 thf(f341,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ((~ (X4 @ (sK58 @ X4) @ (sK57 @ X4))) = $false) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f339])).
% 2.14/1.73 thf(f339,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | (((~ (X4 @ (sK58 @ X4) @ (sK57 @ X4))) | (X4 @ (sK56 @ X4) @ (sK57 @ X4))) = $false) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4)))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f337])).
% 2.14/1.73 thf(f337,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((sK14 @ X3) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (sK5 @ X1)) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($false = (((~ (X4 @ (sK58 @ X4) @ (sK57 @ X4))) | (X4 @ (sK56 @ X4) @ (sK57 @ X4))) | (~ (X4 @ (sK56 @ X4) @ (sK58 @ X4))))) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f336])).
% 2.14/1.73 thf(f336,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($false = ((^[Y0 : $i]: (((~ (X4 @ Y0 @ (sK57 @ X4))) | (X4 @ (sK56 @ X4) @ (sK57 @ X4))) | (~ (X4 @ (sK56 @ X4) @ Y0)))) @ (sK58 @ X4))) | ((sK14 @ X3) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ($true = (sK5 @ X1)) | ((X4 @ X3 @ (sK26 @ X3)) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f335])).
% 2.14/1.73 thf(f335,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((!! @ $i @ (^[Y0 : $i]: (((~ (X4 @ Y0 @ (sK57 @ X4))) | (X4 @ (sK56 @ X4) @ (sK57 @ X4))) | (~ (X4 @ (sK56 @ X4) @ Y0))))) = $false)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f334])).
% 2.14/1.73 thf(f334,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ((sK14 @ X3) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ Y1 @ Y0)) | (X4 @ (sK56 @ X4) @ Y0)) | (~ (X4 @ (sK56 @ X4) @ Y1)))))) @ (sK57 @ X4))) | ($true = (sK5 @ X1)) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f333])).
% 2.14/1.73 thf(f333,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((sK14 @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ Y1 @ Y0)) | (X4 @ (sK56 @ X4) @ Y0)) | (~ (X4 @ (sK56 @ X4) @ Y1)))))))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f332])).
% 2.14/1.73 thf(f332,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((~ (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X4 @ Y1 @ Y0)) | (X4 @ (sK56 @ X4) @ Y0)) | (~ (X4 @ (sK56 @ X4) @ Y1)))))))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ((sK14 @ X3) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f331])).
% 2.14/1.73 thf(f331,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((~ (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) = $false) | ($true = (sK5 @ X1)) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK14 @ X3) = $true) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))) @ (sK56 @ X4))) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f330])).
% 2.14/1.73 thf(f330,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))) | ($true = (sK5 @ X1)) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((~ (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) = $false) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f315])).
% 2.14/1.73 thf(f315,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2))))))))))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (sK5 @ X1)) | ((sK14 @ X3) = $true) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ((~ (sK3 @ (sK52 @ X4) @ (sK51 @ X4))) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f314])).
% 2.14/1.73 thf(f314,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | (((X4 @ (sK52 @ X4) @ (sK51 @ X4)) | (~ (sK3 @ (sK52 @ X4) @ (sK51 @ X4)))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2))))))))))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f313])).
% 2.14/1.73 thf(f313,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2))))))))))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | (((^[Y0 : $i]: ((X4 @ Y0 @ (sK51 @ X4)) | (~ (sK3 @ Y0 @ (sK51 @ X4))))) @ (sK52 @ X4)) = $false) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f312])).
% 2.14/1.73 thf(f312,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X4 @ Y0 @ (sK51 @ X4)) | (~ (sK3 @ Y0 @ (sK51 @ X4))))))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2))))))))))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (sK5 @ X1)) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f311])).
% 2.14/1.73 thf(f311,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((X4 @ X3 @ (sK26 @ X3)) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (sK5 @ X1)) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ((sK14 @ X3) = $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ (sK51 @ X4)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f310])).
% 2.14/1.73 thf(f310,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (sK5 @ X1)) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((sK14 @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))))) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f309])).
% 2.14/1.73 thf(f309,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2))))))))))) | ($true = (sK5 @ X1)) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f308])).
% 2.14/1.73 thf(f308,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ X1 @ (sK15 @ X1))) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) = $true) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ((X2 @ (sK50 @ X2) @ (sK27 @ X2)) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f307])).
% 2.14/1.73 thf(f307,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | ($false = (~ (X2 @ (sK50 @ X2) @ (sK27 @ X2)))) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f305])).
% 2.14/1.73 thf(f305,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ X3) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((X4 @ X3 @ (sK26 @ X3)) = $true) | (((~ (X2 @ (sK50 @ X2) @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f304])).
% 2.14/1.73 thf(f304,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) | (X4 @ X3 @ (sK26 @ X3))) = $true) | ($true = (sK5 @ X1)) | ((sK14 @ X3) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | (((~ (X2 @ (sK50 @ X2) @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f302])).
% 2.14/1.73 thf(f302,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (((sK14 @ X3) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($false = (((~ (X2 @ (sK50 @ X2) @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ (sK50 @ X2) @ (sK25 @ X2)))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X4 @ Y2 @ Y1)) | (X4 @ Y0 @ Y1)) | (~ (X4 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X4 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) | (X4 @ X3 @ (sK26 @ X3))) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f301])).
% 2.14/1.73 thf(f301,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i,X4 : $i > $i > $o] : (($false = (((~ (X2 @ (sK50 @ X2) @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ (sK50 @ X2) @ (sK25 @ X2)))) | (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3)))) @ X4) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f300])).
% 2.14/1.73 thf(f300,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((sK14 @ X3) = $true) | ($true = (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) | ($false = (((~ (X2 @ (sK50 @ X2) @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ (sK50 @ X2) @ (sK25 @ X2))))) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f299])).
% 2.14/1.73 thf(f299,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) = $false) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) = $true) | ((sK14 @ X3) = $true) | ($false = (((~ (X2 @ (sK50 @ X2) @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ (sK50 @ X2) @ (sK25 @ X2))))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f297])).
% 2.14/1.73 thf(f297,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (sK5 @ X1)) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) => (sK14 @ (sK26 @ X3))) = $false) | ($false = (((~ (X2 @ (sK50 @ X2) @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ (sK50 @ X2) @ (sK25 @ X2)))) | ((~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f296])).
% 2.14/1.73 thf(f296,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (sK5 @ X1)) | ((sK14 @ X3) = $true) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) => (sK14 @ (sK26 @ X3))) = $false) | (((^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ Y0 @ (sK25 @ X2)))) @ (sK50 @ X2)) = $false) | ((~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f180])).
% 2.14/1.73 thf(f180,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((sK14 @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ Y0 @ (sK25 @ X2)))))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) => (sK14 @ (sK26 @ X3))) = $false) | ((~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2))) = $false) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f179])).
% 2.14/1.73 thf(f179,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) => (sK14 @ (sK26 @ X3))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK27 @ X2))) | (~ (X2 @ (sK27 @ X2) @ (sK25 @ X2)))) | (X2 @ Y0 @ (sK25 @ X2)))))) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f178])).
% 2.14/1.73 thf(f178,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) => (sK14 @ (sK26 @ X3))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK25 @ X2)))) | (X2 @ Y1 @ (sK25 @ X2)))))) @ (sK27 @ X2)) = $false) | ($true = (sK5 @ X1)) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f177])).
% 2.14/1.73 thf(f177,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK25 @ X2)))) | (X2 @ Y1 @ (sK25 @ X2))))))) = $false) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ X3 @ (sK26 @ X3))))) => (sK14 @ (sK26 @ X3))) = $false) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f176])).
% 2.14/1.73 thf(f176,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0))) @ (sK26 @ X3))) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ X3) = $true) | ($true = (sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK25 @ X2)))) | (X2 @ Y1 @ (sK25 @ X2))))))) = $false)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f175])).
% 2.14/1.73 thf(f175,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) = $false) | ((sK14 @ X3) = $true) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ($true = (sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK25 @ X2)))) | (X2 @ Y1 @ (sK25 @ X2))))))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f174])).
% 2.14/1.73 thf(f174,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((sK14 @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) = $false) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ($true = (sK5 @ X1)) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))) @ (sK25 @ X2))) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f173])).
% 2.14/1.73 thf(f173,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) = $false) | ((sK14 @ X3) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f172])).
% 2.14/1.73 thf(f172,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((sK14 @ X3) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) = $true) | ($true = (sK5 @ X1)) | ($true = (X2 @ X1 @ (sK15 @ X1))) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f171])).
% 2.14/1.73 thf(f171,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((sK14 @ X3) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) = $false) | (((X2 @ (sK24 @ X2) @ (sK23 @ X2)) | (~ (sK3 @ (sK24 @ X2) @ (sK23 @ X2)))) = $false) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f170])).
% 2.14/1.73 thf(f170,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((sK14 @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ($true = (sK5 @ X1)) | ($false = ((^[Y0 : $i]: ((X2 @ Y0 @ (sK23 @ X2)) | (~ (sK3 @ Y0 @ (sK23 @ X2))))) @ (sK24 @ X2)))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f169])).
% 2.14/1.73 thf(f169,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK23 @ X2)) | (~ (sK3 @ Y0 @ (sK23 @ X2)))))) = $false) | ((sK14 @ X3) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) = $false) | ($true = (sK5 @ X1)) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f168])).
% 2.14/1.73 thf(f168,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) => (sK14 @ X3)) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK23 @ X2)) | (~ (sK3 @ Y0 @ (sK23 @ X2)))))) = $false) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f167])).
% 2.14/1.73 thf(f167,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ($true = (sK5 @ X1)) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ (sK23 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) => (sK14 @ X3)) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f166])).
% 2.14/1.73 thf(f166,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (sK5 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) => (sK14 @ X3)) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f165])).
% 2.14/1.73 thf(f165,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ($true = (sK5 @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ X3 @ Y0)))) => (sK14 @ Y0)))) => (sK14 @ X3)) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f164])).
% 2.14/1.73 thf(f164,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X3 : $i,X1 : $i] : (($true = (sK5 @ X1)) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $true) | ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0))) @ X3))) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f163])).
% 2.14/1.73 thf(f163,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 2.14/1.73 thf(f162,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) = $true) | ($true = (sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f161])).
% 2.14/1.73 thf(f161,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) = $true) | (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))) @ X2) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f160])).
% 2.14/1.73 thf(f160,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 2.14/1.73 thf(f158,plain,(
% 2.14/1.73 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false) | ($true = (sK5 @ X1)) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f115])).
% 2.14/1.73 thf(f115,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (($false = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))))) | ($true = (sK5 @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 2.14/1.73 thf(f114,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (($true = (sK5 @ X1)) | ($false = ((sK5 @ (sK15 @ X1)) | (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))))))) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f113])).
% 2.14/1.73 thf(f113,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (($true = (sK5 @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false) | (((^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2)))))))))))))) @ (sK15 @ X1)) = $false)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f112])).
% 2.14/1.73 thf(f112,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f111])).
% 2.14/1.73 thf(f111,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2)))))))))))))))) = $true) | ($true = (sK5 @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 2.14/1.73 thf(f110,plain,(
% 2.14/1.73 ( ! [X1 : $i] : ((((sK5 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f109])).
% 2.14/1.73 thf(f109,plain,(
% 2.14/1.73 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))) @ X1) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f108])).
% 2.14/1.73 thf(f108,plain,(
% 2.14/1.73 ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))))))))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (sK14 @ Y1)))) => (sK14 @ Y0)))) => (!! @ $i @ sK14)) = $false)),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f107])).
% 2.14/1.73 thf(f107,plain,(
% 2.14/1.73 ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))))))))))) = $true) | (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ sK14) = $false)),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f106])).
% 2.14/1.73 thf(f106,plain,(
% 2.14/1.73 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))))))))))) = $true)),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f59])).
% 2.14/1.73 thf(f59,plain,(
% 2.14/1.73 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))) = $false) | ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))))),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 2.14/1.73 thf(f777,plain,(
% 2.14/1.73 spl1_23 | spl1_21 | spl1_22),
% 2.14/1.73 inference(avatar_split_clause,[status(thm)],[f776,f761,f757,f770])).
% 2.14/1.73 thf(f776,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ($true = (X2 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((sK14 @ sK71) = $false)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f775,f50])).
% 2.14/1.73 thf(f775,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK14 @ sK71) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) = $true) | ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK77 @ X2)) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f774,f50])).
% 2.14/1.73 thf(f774,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((sK14 @ sK71) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK72 @ X2)) = $true) | ((X2 @ (d2unsorted @ d_unsorted_0) @ (sK77 @ X2)) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f773,f50])).
% 2.14/1.73 thf(f773,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((X2 @ (sK78 @ X2) @ (sK77 @ X2)) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((sK3 @ (d2unsorted @ d_unsorted_0) @ (sK72 @ X2)) = $true) | ((sK14 @ sK71) = $false)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f447,f50])).
% 2.14/1.73 thf(f447,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true) | ((X2 @ (sK78 @ X2) @ (sK77 @ X2)) = $true) | ((sK14 @ sK71) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f446])).
% 2.14/1.73 thf(f446,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((~ (X2 @ (sK78 @ X2) @ (sK77 @ X2))) = $false) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true) | ((sK14 @ sK71) = $false) | ($true = (sK5 @ X1)) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f444])).
% 2.14/1.73 thf(f444,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : ((((~ (X2 @ (sK78 @ X2) @ (sK77 @ X2))) | (~ (X2 @ (sK77 @ X2) @ (sK73 @ X2)))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true) | ((sK14 @ sK71) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f442])).
% 2.14/1.73 thf(f442,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK14 @ sK71) = $false) | ($false = (((~ (X2 @ (sK78 @ X2) @ (sK77 @ X2))) | (~ (X2 @ (sK77 @ X2) @ (sK73 @ X2)))) | (X2 @ (sK78 @ X2) @ (sK73 @ X2)))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f441])).
% 2.14/1.73 thf(f441,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ sK71) = $false) | ($true = (sK5 @ X1)) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true) | (((^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK77 @ X2))) | (~ (X2 @ (sK77 @ X2) @ (sK73 @ X2)))) | (X2 @ Y0 @ (sK73 @ X2)))) @ (sK78 @ X2)) = $false)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f440])).
% 2.14/1.73 thf(f440,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((~ (X2 @ Y0 @ (sK77 @ X2))) | (~ (X2 @ (sK77 @ X2) @ (sK73 @ X2)))) | (X2 @ Y0 @ (sK73 @ X2))))) = $false) | ($true = (sK5 @ X1)) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true) | ((sK14 @ sK71) = $false)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f439])).
% 2.14/1.73 thf(f439,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK14 @ sK71) = $false) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true) | ($true = (sK5 @ X1)) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK73 @ X2)))) | (X2 @ Y1 @ (sK73 @ X2)))))) @ (sK77 @ X2)) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f438])).
% 2.14/1.73 thf(f438,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK14 @ sK71) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK73 @ X2)))) | (X2 @ Y1 @ (sK73 @ X2))))))) = $false) | ($true = (sK5 @ X1)) | ((sK3 @ (sK74 @ X2) @ (sK72 @ X2)) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f426])).
% 2.14/1.73 thf(f426,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($false = (~ (sK3 @ (sK74 @ X2) @ (sK72 @ X2)))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ sK71) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK73 @ X2)))) | (X2 @ Y1 @ (sK73 @ X2))))))) = $false) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f425])).
% 2.14/1.73 thf(f425,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((sK14 @ sK71) = $false) | (((X2 @ (sK74 @ X2) @ (sK72 @ X2)) | (~ (sK3 @ (sK74 @ X2) @ (sK72 @ X2)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK73 @ X2)))) | (X2 @ Y1 @ (sK73 @ X2))))))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f424])).
% 2.14/1.73 thf(f424,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((sK14 @ sK71) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | (((^[Y0 : $i]: ((X2 @ Y0 @ (sK72 @ X2)) | (~ (sK3 @ Y0 @ (sK72 @ X2))))) @ (sK74 @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK73 @ X2)))) | (X2 @ Y1 @ (sK73 @ X2))))))) = $false)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f423])).
% 2.14/1.73 thf(f423,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((sK14 @ sK71) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK72 @ X2)) | (~ (sK3 @ Y0 @ (sK72 @ X2)))))) = $false) | ($true = (sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (X2 @ Y1 @ Y0)) | (~ (X2 @ Y0 @ (sK73 @ X2)))) | (X2 @ Y1 @ (sK73 @ X2))))))) = $false)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f422])).
% 2.14/1.73 thf(f422,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (X2 @ X1 @ (sK15 @ X1))) | ($true = (sK5 @ X1)) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))) @ (sK73 @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK72 @ X2)) | (~ (sK3 @ Y0 @ (sK72 @ X2)))))) = $false) | ((sK14 @ sK71) = $false)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f421])).
% 2.14/1.73 thf(f421,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | ((sK14 @ sK71) = $false) | ($true = (sK5 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK72 @ X2)) | (~ (sK3 @ Y0 @ (sK72 @ X2)))))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1)))) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f420])).
% 2.14/1.73 thf(f420,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0 @ (sK72 @ X2)) | (~ (sK3 @ Y0 @ (sK72 @ X2)))))) = $false) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ sK71) = $false)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f419])).
% 2.14/1.73 thf(f419,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((sK14 @ sK71) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) = $true) | ($true = (X2 @ X1 @ (sK15 @ X1))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ (sK72 @ X2)) = $false)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f418])).
% 2.14/1.73 thf(f418,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) | ($true = (X2 @ X1 @ (sK15 @ X1))) | ((sK14 @ sK71) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f417])).
% 2.14/1.73 thf(f417,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((sK14 @ sK71) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f416])).
% 2.14/1.73 thf(f416,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) = $true) | ((sK14 @ sK71) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f415])).
% 2.14/1.73 thf(f415,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (X2 @ Y2 @ Y1)) | (~ (X2 @ Y1 @ Y0))) | (X2 @ Y2 @ Y0))))))))) | (X2 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) = $true) | ((sK14 @ sK71) = $false) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f414])).
% 2.14/1.73 thf(f414,plain,(
% 2.14/1.73 ( ! [X2 : $i > $i > $o,X1 : $i] : (($true = (sK5 @ X1)) | ((sK14 @ sK71) = $false) | (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))) @ X2) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f413])).
% 2.14/1.73 thf(f413,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (((sK14 @ sK71) = $false) | ($true = (sK5 @ X1)) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f159])).
% 2.14/1.73 thf(f159,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (((!! @ $i @ sK14) = $false) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ X1 @ (sK15 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) = $true) | ($true = (sK5 @ X1))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 2.14/1.73 thf(f712,plain,(
% 2.14/1.73 spl1_9 | spl1_11),
% 2.14/1.73 inference(avatar_split_clause,[status(thm)],[f708,f710,f702])).
% 2.14/1.73 thf(f708,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ($false = (sK3 @ X8 @ X7)) | ((X2 @ X4) = $true) | ((X2 @ X5) = $true) | ((sK82 @ X5 @ X2 @ X8 @ X7) = $true) | ((sK84 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6) = $false) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f585,f50])).
% 2.14/1.73 thf(f585,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ($false = (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6)) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((sK82 @ X5 @ X2 @ X8 @ X7) = $true) | ($false = (sK3 @ X8 @ X7)) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f584])).
% 2.14/1.73 thf(f584,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6)) | ((X2 @ X5) = $true) | ((X3 @ X1) = $true) | ((X3 @ X6) = $true) | ((X2 @ X4) = $true) | ((~ (sK3 @ X8 @ X7)) = $true) | ((sK82 @ X5 @ X2 @ X8 @ X7) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f583])).
% 2.14/1.73 thf(f583,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK82 @ X5 @ X2 @ X8 @ X7) | (~ (sK3 @ X8 @ X7))) = $true) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true) | ((X3 @ X6) = $true) | ((X2 @ X4) = $true) | ($false = (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f582])).
% 2.14/1.73 thf(f582,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ($false = (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6)) | ((X2 @ X5) = $true) | (((^[Y0 : $i]: ((sK82 @ X5 @ X2 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7)))) @ X8) = $true) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f565])).
% 2.14/1.73 thf(f565,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6)) | ((X2 @ X5) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK82 @ X5 @ X2 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7))))) = $true) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f564])).
% 2.14/1.73 thf(f564,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK84 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK84 @ X3 @ X6 @ Y1 @ Y0))) | (sK84 @ X3 @ X6 @ Y2 @ Y0))))))))) | (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6))) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true) | ((X3 @ X6) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK82 @ X5 @ X2 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7))))) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f563])).
% 2.14/1.73 thf(f563,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X1) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK84 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK84 @ X3 @ X6 @ Y1 @ Y0))) | (sK84 @ X3 @ X6 @ Y2 @ Y0))))))))) | (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6))) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((X2 @ X5) = $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ X7) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f562])).
% 2.14/1.73 thf(f562,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X2 @ X5) = $true) | ((X3 @ X6) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true) | ((X3 @ X1) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK84 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK84 @ X3 @ X6 @ Y1 @ Y0))) | (sK84 @ X3 @ X6 @ Y2 @ Y0))))))))) | (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6)))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f560])).
% 2.14/1.73 thf(f560,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK84 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK84 @ X3 @ X6 @ Y1 @ Y0))) | (sK84 @ X3 @ X6 @ Y2 @ Y0))))))))) | (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK84 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))))) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f559])).
% 2.14/1.73 thf(f559,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $false) | ((X2 @ X5) = $true) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK84 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK84 @ X3 @ X6 @ Y1 @ Y0))) | (sK84 @ X3 @ X6 @ Y2 @ Y0))))))))) | (sK84 @ X3 @ X6 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK84 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f558])).
% 2.14/1.73 thf(f558,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))) @ (sK84 @ X3 @ X6)) = $false) | ((X2 @ X4) = $true) | ((X2 @ X5) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $false)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f557])).
% 2.14/1.73 thf(f557,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) = $false) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $false)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f503])).
% 2.14/1.73 thf(f503,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((X2 @ X4) = $true) | ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))))) = $true) | ((X2 @ X5) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $false) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f502])).
% 2.14/1.73 thf(f502,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK82 @ X5 @ X2 @ Y2 @ Y1)) | (sK82 @ X5 @ X2 @ Y0 @ Y1)) | (~ (sK82 @ X5 @ X2 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))))) | ((X3 @ X1) = $true) | ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))))) = $true) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f501])).
% 2.14/1.73 thf(f501,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | (((X3 @ X6) | (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK82 @ X5 @ X2 @ Y2 @ Y1)) | (sK82 @ X5 @ X2 @ Y0 @ Y1)) | (~ (sK82 @ X5 @ X2 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))))) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f500])).
% 2.14/1.73 thf(f500,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X3 @ X1) = $true) | (((^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2)))))))))))))) @ X6) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK82 @ X5 @ X2 @ Y2 @ Y1)) | (sK82 @ X5 @ X2 @ Y0 @ Y1)) | (~ (sK82 @ X5 @ X2 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))))) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f499])).
% 2.14/1.73 thf(f499,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK82 @ X5 @ X2 @ Y2 @ Y1)) | (sK82 @ X5 @ X2 @ Y0 @ Y1)) | (~ (sK82 @ X5 @ X2 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))))) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f497])).
% 2.14/1.73 thf(f497,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK82 @ X5 @ X2 @ Y2 @ Y1)) | (sK82 @ X5 @ X2 @ Y0 @ Y1)) | (~ (sK82 @ X5 @ X2 @ Y0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) | (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5))) | ((X2 @ X5) = $true) | ((X3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f496])).
% 2.14/1.73 thf(f496,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))) = $true) | ((X2 @ X4) = $true) | (((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ (sK79 @ X2) @ X5))) @ (sK82 @ X5 @ X2)) = $false) | ((X2 @ X5) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f495])).
% 2.14/1.73 thf(f495,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ (sK79 @ X2) @ X5)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))) = $true) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f494])).
% 2.14/1.73 thf(f494,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ((X3 @ X1) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))))) | ((X2 @ X4) = $true) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ (sK79 @ X2) @ X5)))) = $false)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f467])).
% 2.14/1.73 thf(f467,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ (sK79 @ X2) @ X5)))) => (X2 @ X5)) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))))) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f466])).
% 2.14/1.73 thf(f466,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : ((((X3 @ (sK80 @ X3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))))) = $false) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))) | (Y0 @ (sK79 @ X2) @ X5)))) => (X2 @ X5)) = $true) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f465])).
% 2.14/1.73 thf(f465,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : ((((X3 @ (sK80 @ X3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))))) = $false) | (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ (sK79 @ X2) @ Y0)))) => (X2 @ Y0))) @ X5) = $true) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f464])).
% 2.14/1.73 thf(f464,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (((X3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ (sK79 @ X2) @ Y0)))) => (X2 @ Y0)))) = $true) | ((X2 @ X4) = $true) | (((X3 @ (sK80 @ X3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))))) = $false)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f463])).
% 2.14/1.73 thf(f463,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (((X2 @ X4) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ (sK79 @ X2) @ Y0)))) => (X2 @ Y0)))) = $true) | ((X3 @ X1) = $true) | ($false = ((^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))) @ (sK80 @ X3)))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f462])).
% 2.14/1.73 thf(f462,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ (sK79 @ X2) @ Y0)))) => (X2 @ Y0)))) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f460])).
% 2.14/1.73 thf(f460,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))) | (Y1 @ (sK79 @ X2) @ Y0)))) => (X2 @ Y0)))) => (X2 @ (sK79 @ X2))) = $false) | ((X3 @ X1) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f459])).
% 2.14/1.73 thf(f459,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))) | (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))) @ (sK79 @ X2)) = $false) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f458])).
% 2.14/1.73 thf(f458,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))))) | ((X3 @ X1) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f457])).
% 2.14/1.73 thf(f457,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))) = $true) | ((X2 @ X4) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0))))) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f456])).
% 2.14/1.73 thf(f456,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i] : (((X3 @ X1) = $true) | ((!! @ $i @ X2) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f455])).
% 2.14/1.73 thf(f455,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i] : (($true = ((X3 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))))))) | ((!! @ $i @ X2) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f454])).
% 2.14/1.73 thf(f454,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))) => (!! @ $i @ X2)) = $true) | ($true = ((X3 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))))))))))))))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f453])).
% 2.14/1.73 thf(f453,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4)))))))))))))))))))))) @ X3) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))) => (!! @ $i @ X2)) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f452])).
% 2.14/1.73 thf(f452,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))))))))))))))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))) | (Y2 @ Y0 @ Y1)))) => (X2 @ Y1)))) => (X2 @ Y0)))) => (!! @ $i @ X2)) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f451])).
% 2.14/1.73 thf(f451,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ X2) = $true) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))))))))))))))))) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f450])).
% 2.14/1.73 thf(f450,plain,(
% 2.14/1.73 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))) = $true) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y5 @ Y4))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))))))))))))))))) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f449])).
% 2.14/1.73 thf(f449,plain,(
% 2.14/1.73 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (sK3 @ Y6 @ Y5)))))))))))))))))))))))) @ X1) = $true) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f53])).
% 2.14/1.73 thf(f53,plain,(
% 2.14/1.73 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y6 @ Y5))) | (Y4 @ Y7 @ Y5))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (sK3 @ Y6 @ Y5))))))))))))))))))))))))) = $true) | ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (sK3 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0)))) = $true)),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 2.14/1.73 thf(f707,plain,(
% 2.14/1.73 spl1_9 | spl1_10),
% 2.14/1.73 inference(avatar_split_clause,[status(thm)],[f598,f705,f702])).
% 2.14/1.73 thf(f598,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((sK3 @ X9 @ X8) = $false) | ((sK84 @ X3 @ X6 @ X10 @ X7) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((sK82 @ X5 @ X2 @ X9 @ X8) = $true) | ((sK3 @ X10 @ X7) = $false)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f597])).
% 2.14/1.73 thf(f597,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((sK3 @ X10 @ X7) = $false) | ((X2 @ X4) = $true) | ((sK84 @ X3 @ X6 @ X10 @ X7) = $true) | ((sK82 @ X5 @ X2 @ X9 @ X8) = $true) | ((X2 @ X5) = $true) | ((~ (sK3 @ X9 @ X8)) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f596])).
% 2.14/1.73 thf(f596,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((sK82 @ X5 @ X2 @ X9 @ X8) | (~ (sK3 @ X9 @ X8))) = $true) | ((X2 @ X5) = $true) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((sK3 @ X10 @ X7) = $false) | ((sK84 @ X3 @ X6 @ X10 @ X7) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f595])).
% 2.14/1.73 thf(f595,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((~ (sK3 @ X10 @ X7)) = $true) | ((X2 @ X4) = $true) | ((sK84 @ X3 @ X6 @ X10 @ X7) = $true) | (((sK82 @ X5 @ X2 @ X9 @ X8) | (~ (sK3 @ X9 @ X8))) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f594])).
% 2.14/1.73 thf(f594,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true) | (((sK84 @ X3 @ X6 @ X10 @ X7) | (~ (sK3 @ X10 @ X7))) = $true) | (((sK82 @ X5 @ X2 @ X9 @ X8) | (~ (sK3 @ X9 @ X8))) = $true) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f593])).
% 2.14/1.73 thf(f593,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X10 : $i,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((X2 @ X5) = $true) | (((^[Y0 : $i]: ((sK84 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7)))) @ X10) = $true) | (((sK82 @ X5 @ X2 @ X9 @ X8) | (~ (sK3 @ X9 @ X8))) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f592])).
% 2.14/1.73 thf(f592,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK84 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7))))) = $true) | (((sK82 @ X5 @ X2 @ X9 @ X8) | (~ (sK3 @ X9 @ X8))) = $true) | ((X3 @ X6) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f591])).
% 2.14/1.73 thf(f591,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((X2 @ X5) = $true) | (((^[Y0 : $i]: ((sK82 @ X5 @ X2 @ Y0 @ X8) | (~ (sK3 @ Y0 @ X8)))) @ X9) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK84 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7))))) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f590])).
% 2.14/1.73 thf(f590,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK82 @ X5 @ X2 @ Y0 @ X8) | (~ (sK3 @ Y0 @ X8))))) = $true) | ((X2 @ X4) = $true) | ((X2 @ X5) = $true) | ((X3 @ X1) = $true) | ((X3 @ X6) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK84 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7))))) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f589])).
% 2.14/1.73 thf(f589,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((X2 @ X5) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK84 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7))))) = $true) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ X8) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f588])).
% 2.14/1.73 thf(f588,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK84 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7))))) = $true) | ((X3 @ X6) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f587])).
% 2.14/1.73 thf(f587,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((X2 @ X5) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK84 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ X7) = $true) | ((X3 @ X6) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f586])).
% 2.14/1.73 thf(f586,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((X2 @ X4) = $true) | ((X2 @ X5) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK84 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f561])).
% 2.14/1.73 thf(f561,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK84 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK82 @ X5 @ X2 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true) | ((X3 @ X1) = $true) | ((X3 @ X6) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f560])).
% 2.14/1.73 thf(f695,plain,(
% 2.14/1.73 spl1_7 | spl1_6),
% 2.14/1.73 inference(avatar_split_clause,[status(thm)],[f691,f687,f693])).
% 2.14/1.73 thf(f691,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = (sK85 @ X3 @ X6 @ (d2unsorted @ d_unsorted_0) @ X6)) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ($false = (sK82 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) | ((X3 @ X1) = $true) | ((X3 @ X6) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f690,f50])).
% 2.14/1.73 thf(f690,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ($false = (sK82 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) | ((sK85 @ X3 @ X6 @ (sK80 @ X3) @ X6) = $false) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f607,f50])).
% 2.14/1.73 thf(f607,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((sK85 @ X3 @ X6 @ (sK80 @ X3) @ X6) = $false) | ((X3 @ X6) = $true) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f606])).
% 2.14/1.73 thf(f606,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X5) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK85 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK85 @ X3 @ X6 @ Y1 @ Y0))) | (sK85 @ X3 @ X6 @ Y2 @ Y0))))))))) | (sK85 @ X3 @ X6 @ (sK80 @ X3) @ X6)) = $false) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f604])).
% 2.14/1.73 thf(f604,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK85 @ X3 @ X6 @ Y2 @ Y1)) | (~ (sK85 @ X3 @ X6 @ Y1 @ Y0))) | (sK85 @ X3 @ X6 @ Y2 @ Y0))))))))) | (sK85 @ X3 @ X6 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK85 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) = $false) | ((X3 @ X6) = $true) | ((X2 @ X4) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f603])).
% 2.14/1.73 thf(f603,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X5) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ($false = ((^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))) @ (sK85 @ X3 @ X6)))) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f602])).
% 2.14/1.73 thf(f602,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))) = $false) | ((X3 @ X1) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X5) = $true) | ((X3 @ X6) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f601])).
% 2.14/1.73 thf(f601,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X3 @ X1) = $true) | ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1)))))))))))) = $true) | ((X2 @ X4) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X5) = $true) | ((X3 @ X6) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f600])).
% 2.14/1.73 thf(f600,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((X3 @ X6) | (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y0 @ Y3 @ Y1))))))))) | (Y0 @ (sK80 @ X3) @ X6)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (sK3 @ Y2 @ Y1))))))))))))) = $true) | ((X3 @ X1) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f599])).
% 2.14/1.73 thf(f599,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X5) = $true) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true) | (((^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2)))))))))))))) @ X6) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f498])).
% 2.14/1.73 thf(f498,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK80 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2))))))))))))))) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f497])).
% 2.14/1.73 thf(f689,plain,(
% 2.14/1.73 spl1_5 | spl1_6),
% 2.14/1.73 inference(avatar_split_clause,[status(thm)],[f682,f687,f684])).
% 2.14/1.73 thf(f682,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((X2 @ X5) = $true) | ($false = (sK3 @ X8 @ X7)) | ((X3 @ X1) = $true) | ($false = (sK82 @ X5 @ X2 @ (d2unsorted @ d_unsorted_0) @ X5)) | ((sK85 @ X3 @ X6 @ X8 @ X7) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f626,f50])).
% 2.14/1.73 thf(f626,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ((X3 @ X1) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ($false = (sK3 @ X8 @ X7)) | ((sK85 @ X3 @ X6 @ X8 @ X7) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f625])).
% 2.14/1.73 thf(f625,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ((sK85 @ X3 @ X6 @ X8 @ X7) = $true) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((~ (sK3 @ X8 @ X7)) = $true) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f624])).
% 2.14/1.73 thf(f624,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X4) = $true) | ((X2 @ X5) = $true) | (((sK85 @ X3 @ X6 @ X8 @ X7) | (~ (sK3 @ X8 @ X7))) = $true) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f623])).
% 2.14/1.73 thf(f623,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | (((^[Y0 : $i]: ((sK85 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7)))) @ X8) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f622])).
% 2.14/1.73 thf(f622,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((X3 @ X6) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK85 @ X3 @ X6 @ Y0 @ X7) | (~ (sK3 @ Y0 @ X7)))))) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((X2 @ X5) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5))) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f621])).
% 2.14/1.73 thf(f621,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK85 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0)))))) @ X7)) | ((X3 @ X6) = $true) | ((X2 @ X5) = $true) | ((X2 @ X4) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(pi_clausification,[status(thm)],[f620])).
% 2.14/1.73 thf(f620,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X2 @ X5) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ((X2 @ X4) = $true) | ((X3 @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK85 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))) = $true) | ((X3 @ X6) = $true)) )),
% 2.14/1.73 inference(not_proxy_clausification,[status(thm)],[f605])).
% 2.14/1.73 thf(f605,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((X3 @ X6) = $true) | ($false = (sK82 @ X5 @ X2 @ (sK79 @ X2) @ X5)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK85 @ X3 @ X6 @ Y1 @ Y0) | (~ (sK3 @ Y1 @ Y0))))))))) | ((X2 @ X5) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f604])).
% 2.14/1.73 thf(f681,plain,(
% 2.14/1.73 spl1_2 | spl1_2),
% 2.14/1.73 inference(avatar_split_clause,[status(thm)],[f680,f665,f665])).
% 2.14/1.73 thf(f680,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (((X3 @ X1) = $true) | ((X2 @ X4) = $true) | ((X3 @ (d2unsorted @ d_unsorted_0)) = $false) | ($false = (X2 @ (d2unsorted @ d_unsorted_0)))) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f679,f50])).
% 2.14/1.73 thf(f679,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (((X2 @ X4) = $true) | ((X3 @ (sK86 @ X3)) = $false) | ($false = (X2 @ (d2unsorted @ d_unsorted_0))) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(forward_demodulation,[status(thm)],[f630,f50])).
% 2.14/1.73 thf(f630,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (($false = (X2 @ (sK79 @ X2))) | ((X3 @ X1) = $true) | ((X3 @ (sK86 @ X3)) = $false) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f628])).
% 2.14/1.73 thf(f628,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (($false = ((X3 @ (sK86 @ X3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y3 @ Y2))) | (Y1 @ Y4 @ Y2))))))))) | (Y1 @ (sK86 @ X3) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (sK3 @ Y3 @ Y2)))))))))))))))))) | ($false = (X2 @ (sK79 @ X2))) | ((X3 @ X1) = $true) | ((X2 @ X4) = $true)) )),
% 2.14/1.73 inference(beta_eta_normalization,[status(thm)],[f627])).
% 2.14/1.73 thf(f627,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (($false = (X2 @ (sK79 @ X2))) | ((X2 @ X4) = $true) | (((^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3)))))))))))))))))) @ (sK86 @ X3)) = $false) | ((X3 @ X1) = $true)) )),
% 2.14/1.73 inference(sigma_clausification,[status(thm)],[f461])).
% 2.14/1.73 thf(f461,plain,(
% 2.14/1.73 ( ! [X2 : $i > $o,X3 : $i > $o,X1 : $i,X4 : $i] : (((X3 @ X1) = $true) | ($false = (X2 @ (sK79 @ X2))) | ((X2 @ X4) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X3 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((X3 @ Y1) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y4 @ Y3))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (sK3 @ Y4 @ Y3))))))))))))))))))))) )),
% 2.14/1.73 inference(binary_proxy_clausification,[status(thm)],[f460])).
% 2.14/1.73 % SZS output end Proof for DTF2THF_3057
% 2.14/1.73 % (3185)------------------------------
% 2.14/1.73 % (3185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.73 % (3185)Termination reason: Refutation
% 2.14/1.73
% 2.14/1.73 % (3185)Memory used [KB]: 8187
% 2.14/1.73 % (3185)Time elapsed: 0.217 s
% 2.14/1.73 % (3185)Instructions burned: 575 (million)
% 2.14/1.73 % (3185)------------------------------
% 2.14/1.73 % (3185)------------------------------
% 2.14/1.73 % (3155)Success in time 0.319 s
%------------------------------------------------------------------------------