%------------------------------------------------------------------------------
% 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 : n027.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 06:58:57 PM UTC 2026
% Result : Theorem 87.89s 13.84s
% Output : Refutation 87.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 6
% Syntax : Number of formulae : 121 ( 69 unt; 0 typ; 4 def)
% Number of atoms : 7639 (1216 equ; 4 cnn)
% Maximal formula atoms : 33 ( 63 avg)
% Number of connectives : 39000 (5312 ~;4981 |; 920 &;22298 @)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 3 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 4824 (4824 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 65 usr; 13 con; 0-5 aty)
% (5419 !!; 36 ??; 0 @@+; 0 @@-)
% Number of variables : 6979 (6377 ^; 600 !; 2 ?;6979 :)
% 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_55,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
sK2: $i > $i > $o ).
thf(func_def_57,type,
sK3: $i > d_unsorted ).
thf(func_def_58,type,
sK4: ( $i > $i > $o ) > $i ).
thf(func_def_59,type,
sK5: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_60,type,
sK6: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_61,type,
sK7: ( $i > $i > $o ) > $i ).
thf(func_def_62,type,
sK8: ( $i > $i > $o ) > $i ).
thf(func_def_63,type,
sK9: ( $i > $i > $o ) > $i ).
thf(func_def_64,type,
sK10: $i > ( $i > $i > $o ) > $i > $i > $i > $o ).
thf(func_def_68,type,
sK14: ( $i > $i > $o ) > $i ).
thf(func_def_69,type,
sK15: ( $i > $i > $o ) > $i ).
thf(func_def_70,type,
sK16: ( $i > $i > $o ) > $i > $i ).
thf(func_def_71,type,
sK17: ( $i > $i > $o ) > $i ).
thf(func_def_72,type,
sK18: ( $i > $i > $o ) > $i > $o ).
thf(func_def_73,type,
sK19: ( $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK20: ( $i > $i > $o ) > $i > $i ).
thf(func_def_75,type,
sK21: ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK22: ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK23: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_78,type,
sK24: ( $i > $i > $o ) > $i ).
thf(func_def_79,type,
sK25: $i > $i > $o ).
thf(func_def_80,type,
sK26: ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK27: ( $i > $i > $o ) > $i ).
thf(func_def_82,type,
sK28: ( $i > $i > $o ) > $i ).
thf(func_def_83,type,
sK29: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_84,type,
sK30: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(f5875,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f148,f4810,f4819,f4823,f5873]) ).
thf(f5873,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f5872]) ).
thf(f5872,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f5789]) ).
thf(f5789,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f4848,f5753]) ).
thf(f5753,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( join @ X1 @ X2 @ X3 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f5752,f152]) ).
thf(f152,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f141,f141]) ).
thf(f141,plain,
! [X1: $i] :
( ( d2unsorted @ d_unsorted_0 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X1: $i] :
( ( ( d2unsorted @ d_unsorted_0 )
= X1 )
= $true ),
inference(forward_demodulation,[status(thm)],[f139,f110]) ).
thf(f110,plain,
! [X1: d_unsorted] : ( d_unsorted_0 = X1 ),
inference(equality_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X1: d_unsorted] :
( ( d_unsorted_0 = X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= trans )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= trans )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= trans )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= trans )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] : ( d_unsorted_0 = Y0 ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= trans )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] : ( d_unsorted_0 = Y0 ) )
& ( trsc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( subrel
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) )
& ( trsc
= ( ^ [X4: $i > $i > $o,X5: $i,X6: $i] :
( ! [X7: $i > $i > $o] :
( ~ ! [X8: $i,X9: $i] :
( ( X7 @ X9 @ X8 )
| ~ ( X4 @ X9 @ X8 ) )
| ~ ! [X10: $i,X11: $i,X12: $i] :
( ~ ( X7 @ X10 @ X11 )
| ~ ( X7 @ X12 @ X10 )
| ( X7 @ X12 @ X11 ) )
| ( X7 @ X6 @ X5 ) )
| ( X5 = X6 )
| ! [X13: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X15 @ X14 )
| ( X13 @ X15 @ X14 ) )
| ~ ! [X16: $i,X17: $i,X18: $i] :
( ( X13 @ X16 @ X18 )
| ~ ( X13 @ X16 @ X17 )
| ~ ( X13 @ X17 @ X18 ) )
| ( X13 @ X5 @ X6 ) ) ) ) )
& ! [X19: d_unsorted] : ( d_unsorted_0 = X19 )
& ( ( ^ [X20: $i > $i > $o,X21: $i,X22: $i] : ( X20 @ X22 @ X21 ) )
= inv )
& ( ( ^ [X23: $i > $i > $o] :
! [X24: $i,X25: $i,X26: $i] :
( ~ ( X23 @ X24 @ X25 )
| ~ ( X23 @ X26 @ X24 )
| ( X23 @ X26 @ X25 ) ) )
= trans )
& ( nfof
= ( ^ [X27: $i > $i > $o,X28: $i,X29: $i] :
( ! [X30: $i] :
~ ( X27 @ X28 @ X30 )
& ( ! [X31: $i > $i > $o] :
( ~ ! [X32: $i,X33: $i,X34: $i] :
( ( X31 @ X32 @ X33 )
| ~ ( X31 @ X34 @ X33 )
| ~ ( X31 @ X32 @ X34 ) )
| ~ ! [X35: $i,X36: $i] :
( ~ ( X27 @ X36 @ X35 )
| ( X31 @ X36 @ X35 ) )
| ( X31 @ X29 @ X28 ) )
| ( X28 = X29 ) ) ) ) )
& ( total
= ( ^ [X37: $i > $i > $o] :
! [X38: $i,X39: $i] :
( ( X38 = X39 )
| ( X37 @ X39 @ X38 )
| ( X37 @ X38 @ X39 ) ) ) )
& ! [X40: d_unsorted,X41: d_unsorted] :
( ( ( d2unsorted @ X41 )
= ( d2unsorted @ X40 ) )
=> ( X40 = X41 ) )
& ( ind
= ( ^ [X42: $i > $i > $o] :
! [X43: $i > $o,X44: $i] :
( ( X43 @ X44 )
| ~ ! [X45: $i] :
( ( X43 @ X45 )
| ~ ! [X46: $i] :
( ( X43 @ X46 )
| ~ ! [X47: $i > $i > $o] :
( ~ ! [X48: $i,X49: $i,X50: $i] :
( ( X47 @ X49 @ X48 )
| ~ ( X47 @ X49 @ X50 )
| ~ ( X47 @ X50 @ X48 ) )
| ~ ! [X51: $i,X52: $i] :
( ( X47 @ X52 @ X51 )
| ~ ( X42 @ X52 @ X51 ) )
| ( X47 @ X45 @ X46 ) ) ) ) ) ) )
& ( confl
= ( ^ [X53: $i > $i > $o] :
! [X54: $i > $i > $o,X55: $i,X56: $i > $i > $o,X57: $i,X58: $i] :
( ( X56 @ X55 @ X57 )
| ~ ! [X59: $i,X60: $i] :
( ( X56 @ X59 @ X60 )
| ~ ( X53 @ X59 @ X60 ) )
| ( ~ ! [X61: $i > $i > $o] :
( ~ ! [X62: $i,X63: $i,X64: $i] :
( ( X61 @ X64 @ X63 )
| ~ ( X61 @ X62 @ X63 )
| ~ ( X61 @ X64 @ X62 ) )
| ( X61 @ X58 @ X55 )
| ~ ! [X65: $i,X66: $i] :
( ~ ( X53 @ X65 @ X66 )
| ( X61 @ X65 @ X66 ) ) )
& ( X55 != X58 ) )
| ( X55 = X57 )
| ~ ! [X67: $i,X68: $i,X69: $i] :
( ( X54 @ X67 @ X68 )
| ~ ( X54 @ X67 @ X69 )
| ~ ( X54 @ X69 @ X68 ) )
| ~ ! [X70: $i,X71: $i] :
( ~ ( X53 @ X71 @ X70 )
| ( X54 @ X71 @ X70 ) )
| ~ ! [X72: $i,X73: $i,X74: $i] :
( ( X56 @ X74 @ X72 )
| ~ ( X56 @ X73 @ X72 )
| ~ ( X56 @ X74 @ X73 ) )
| ( ( X57 != X58 )
& ~ ! [X75: $i > $i > $o] :
( ~ ! [X76: $i,X77: $i,X78: $i] :
( ( X75 @ X78 @ X76 )
| ~ ( X75 @ X77 @ X76 )
| ~ ( X75 @ X78 @ X77 ) )
| ( X75 @ X58 @ X57 )
| ~ ! [X79: $i,X80: $i] :
( ~ ( X53 @ X80 @ X79 )
| ( X75 @ X80 @ X79 ) ) ) )
| ( X54 @ X57 @ X55 )
| ~ ! [X81: $i] :
( ~ ! [X82: $i > $i > $o] :
( ~ ! [X83: $i,X84: $i] :
( ( X82 @ X84 @ X83 )
| ~ ( X53 @ X84 @ X83 ) )
| ( X82 @ X57 @ X81 )
| ~ ! [X85: $i,X86: $i,X87: $i] :
( ( X82 @ X85 @ X87 )
| ~ ( X82 @ X85 @ X86 )
| ~ ( X82 @ X86 @ X87 ) ) )
| ~ ! [X88: $i > $i > $o] :
( ~ ! [X89: $i,X90: $i] :
( ( X88 @ X89 @ X90 )
| ~ ( X53 @ X89 @ X90 ) )
| ~ ! [X91: $i,X92: $i,X93: $i] :
( ~ ( X88 @ X93 @ X92 )
| ( X88 @ X91 @ X92 )
| ~ ( X88 @ X91 @ X93 ) )
| ( X88 @ X55 @ X81 ) ) ) ) ) )
& ( ( ^ [X94: $i > $i > $o,X95: $i,X96: $i] :
~ ( ! [X97: $i] :
( ~ ! [X98: $i > $i > $o] :
( ~ ! [X99: $i,X100: $i] :
( ( X98 @ X100 @ X99 )
| ~ ( X94 @ X100 @ X99 ) )
| ~ ! [X101: $i,X102: $i,X103: $i] :
( ~ ( X98 @ X103 @ X102 )
| ( X98 @ X103 @ X101 )
| ~ ( X98 @ X102 @ X101 ) )
| ( X98 @ X96 @ X97 ) )
| ~ ! [X104: $i > $i > $o] :
( ~ ! [X105: $i,X106: $i,X107: $i] :
( ( X104 @ X106 @ X107 )
| ~ ( X104 @ X106 @ X105 )
| ~ ( X104 @ X105 @ X107 ) )
| ( X104 @ X95 @ X97 )
| ~ ! [X108: $i,X109: $i] :
( ~ ( X94 @ X109 @ X108 )
| ( X104 @ X109 @ X108 ) ) ) )
& ~ ! [X110: $i > $i > $o] :
( ~ ! [X111: $i,X112: $i] :
( ( X110 @ X112 @ X111 )
| ~ ( X94 @ X112 @ X111 ) )
| ~ ! [X113: $i,X114: $i,X115: $i] :
( ~ ( X110 @ X113 @ X114 )
| ( X110 @ X115 @ X114 )
| ~ ( X110 @ X115 @ X113 ) )
| ( X110 @ X95 @ X96 ) )
& ~ ! [X116: $i > $i > $o] :
( ( X116 @ X96 @ X95 )
| ~ ! [X117: $i,X118: $i,X119: $i] :
( ~ ( X116 @ X118 @ X117 )
| ~ ( X116 @ X117 @ X119 )
| ( X116 @ X118 @ X119 ) )
| ~ ! [X120: $i,X121: $i] :
( ~ ( X94 @ X120 @ X121 )
| ( X116 @ X120 @ X121 ) ) )
& ( X95 != X96 ) ) )
= join )
& ( sc
= ( ^ [X122: $i > $i > $o,X123: $i,X124: $i] :
( ( X122 @ X123 @ X124 )
| ( X122 @ X124 @ X123 ) ) ) )
& ( trc
= ( ^ [X125: $i > $i > $o,X126: $i,X127: $i] :
( ! [X128: $i > $i > $o] :
( ( X128 @ X126 @ X127 )
| ~ ! [X129: $i,X130: $i] :
( ~ ( X125 @ X129 @ X130 )
| ( X128 @ X129 @ X130 ) )
| ~ ! [X131: $i,X132: $i,X133: $i] :
( ( X128 @ X132 @ X131 )
| ~ ( X128 @ X133 @ X131 )
| ~ ( X128 @ X132 @ X133 ) ) )
| ( X126 = X127 ) ) ) )
& ( ( ^ [X134: $i > $i > $o] :
( ! [X135: $i,X136: $i] :
( ~ ( X134 @ X135 @ X136 )
| ~ ( X134 @ X136 @ X135 ) )
& ! [X137: $i,X138: $i,X139: $i] :
( ~ ( X134 @ X137 @ X139 )
| ( X134 @ X138 @ X139 )
| ~ ( X134 @ X138 @ X137 ) ) ) )
= so )
& ( lconfl
= ( ^ [X140: $i > $i > $o] :
! [X141: $i > $i > $o,X142: $i,X143: $i,X144: $i,X145: $i > $i > $o] :
( ~ ! [X146: $i,X147: $i,X148: $i] :
( ~ ( X145 @ X148 @ X147 )
| ( X145 @ X148 @ X146 )
| ~ ( X145 @ X147 @ X146 ) )
| ~ ! [X149: $i] :
( ~ ! [X150: $i > $i > $o] :
( ( X150 @ X144 @ X149 )
| ~ ! [X151: $i,X152: $i] :
( ~ ( X140 @ X152 @ X151 )
| ( X150 @ X152 @ X151 ) )
| ~ ! [X153: $i,X154: $i,X155: $i] :
( ~ ( X150 @ X155 @ X153 )
| ~ ( X150 @ X154 @ X155 )
| ( X150 @ X154 @ X153 ) ) )
| ~ ! [X156: $i > $i > $o] :
( ~ ! [X157: $i,X158: $i,X159: $i] :
( ~ ( X156 @ X157 @ X159 )
| ( X156 @ X158 @ X159 )
| ~ ( X156 @ X158 @ X157 ) )
| ~ ! [X160: $i,X161: $i] :
( ( X156 @ X161 @ X160 )
| ~ ( X140 @ X161 @ X160 ) )
| ( X156 @ X142 @ X149 ) ) )
| ~ ! [X162: $i,X163: $i] :
( ~ ( X140 @ X163 @ X162 )
| ( X141 @ X163 @ X162 ) )
| ( X142 = X144 )
| ~ ( X140 @ X143 @ X144 )
| ( X141 @ X142 @ X144 )
| ~ ! [X164: $i,X165: $i] :
( ( X145 @ X164 @ X165 )
| ~ ( X140 @ X164 @ X165 ) )
| ~ ! [X166: $i,X167: $i,X168: $i] :
( ( X141 @ X166 @ X168 )
| ~ ( X141 @ X167 @ X168 )
| ~ ( X141 @ X166 @ X167 ) )
| ( X145 @ X144 @ X142 )
| ~ ( X140 @ X143 @ X142 ) ) ) )
& ( ( ^ [X169: $i > $i > $o] :
! [X170: $i,X171: $i > $i > $o,X172: $i > $i > $o,X173: $i] :
( ~ ! [X174: $i,X175: $i,X176: $i] :
( ~ ( X172 @ X175 @ X174 )
| ( X172 @ X175 @ X176 )
| ~ ( X172 @ X174 @ X176 ) )
| ~ ! [X177: $i,X178: $i,X179: $i] :
( ~ ( X171 @ X179 @ X177 )
| ( X171 @ X178 @ X177 )
| ~ ( X171 @ X178 @ X179 ) )
| ~ ! [X180: $i,X181: $i] :
( ~ ( X169 @ X181 @ X180 )
| ( X172 @ X181 @ X180 ) )
| ( ~ ! [X182: $i > $i > $o] :
( ( X182 @ X170 @ X173 )
| ~ ! [X183: $i,X184: $i] :
( ( X182 @ X184 @ X183 )
| ~ ( X169 @ X184 @ X183 ) )
| ~ ! [X185: $i,X186: $i,X187: $i] :
( ~ ( X182 @ X185 @ X186 )
| ~ ( X182 @ X187 @ X185 )
| ( X182 @ X187 @ X186 ) ) )
& ~ ! [X188: $i > $i > $o] :
( ~ ! [X189: $i,X190: $i] :
( ( X188 @ X189 @ X190 )
| ~ ( X169 @ X189 @ X190 ) )
| ~ ! [X191: $i,X192: $i,X193: $i] :
( ~ ( X188 @ X192 @ X191 )
| ( X188 @ X192 @ X193 )
| ~ ( X188 @ X191 @ X193 ) )
| ( X188 @ X173 @ X170 ) )
& ( X170 != X173 ) )
| ~ ! [X194: $i] :
( ~ ! [X195: $i > $i > $o] :
( ~ ! [X196: $i,X197: $i,X198: $i] :
( ~ ( X195 @ X198 @ X196 )
| ( X195 @ X197 @ X196 )
| ~ ( X195 @ X197 @ X198 ) )
| ~ ! [X199: $i,X200: $i] :
( ( X195 @ X199 @ X200 )
| ~ ( X169 @ X199 @ X200 ) )
| ( X195 @ X173 @ X194 ) )
| ~ ! [X201: $i > $i > $o] :
( ~ ! [X202: $i,X203: $i] :
( ( X201 @ X202 @ X203 )
| ~ ( X169 @ X202 @ X203 ) )
| ~ ! [X204: $i,X205: $i,X206: $i] :
( ~ ( X201 @ X205 @ X206 )
| ( X201 @ X204 @ X206 )
| ~ ( X201 @ X204 @ X205 ) )
| ( X201 @ X170 @ X194 ) ) )
| ( X172 @ X170 @ X173 )
| ( X170 = X173 )
| ~ ! [X207: $i,X208: $i] :
( ~ ( X169 @ X208 @ X207 )
| ( X171 @ X208 @ X207 ) )
| ( X171 @ X173 @ X170 ) ) )
= cr )
& ( ( ^ [X209: $i > $i > $o] :
! [X210: $i] : ( X209 @ X210 @ X210 ) )
= refl )
& ( infl
= ( ^ [X211: ( $i > $i > $o ) > $i > $i > $o] :
! [X212: $i > $i > $o,X213: $i,X214: $i] :
( ( X211 @ X212 @ X214 @ X213 )
| ~ ( X212 @ X214 @ X213 ) ) ) )
& ( po
= ( ^ [X215: $i > $i > $o] :
( ! [X216: $i] : ( X215 @ X216 @ X216 )
& ! [X217: $i,X218: $i] :
( ( X217 = X218 )
| ~ ( X215 @ X217 @ X218 )
| ~ ( X215 @ X218 @ X217 ) )
& ! [X219: $i,X220: $i,X221: $i] :
( ~ ( X215 @ X219 @ X220 )
| ~ ( X215 @ X221 @ X219 )
| ( X215 @ X221 @ X220 ) ) ) ) )
& ( tc
= ( ^ [X222: $i > $i > $o,X223: $i,X224: $i] :
! [X225: $i > $i > $o] :
( ( X225 @ X223 @ X224 )
| ~ ! [X226: $i,X227: $i] :
( ~ ( X222 @ X226 @ X227 )
| ( X225 @ X226 @ X227 ) )
| ~ ! [X228: $i,X229: $i,X230: $i] :
( ~ ( X225 @ X228 @ X229 )
| ( X225 @ X230 @ X229 )
| ~ ( X225 @ X230 @ X228 ) ) ) ) )
& ( ( ^ [X231: ( $i > $i > $o ) > $i > $i > $o] :
! [X232: $i,X233: $i > $i > $o,X234: $i,X235: $i > $i > $o] :
( ( X231 @ X235 @ X234 @ X232 )
| ~ ! [X236: $i,X237: $i] :
( ( X235 @ X236 @ X237 )
| ~ ( X233 @ X236 @ X237 ) )
| ~ ( X231 @ X233 @ X234 @ X232 ) ) )
= mono )
& ( norm
= ( ^ [X238: $i > $i > $o] :
! [X239: $i,X240: $i] :
( ~ ! [X241: $i] :
( ~ ! [X242: $i] :
~ ( X238 @ X241 @ X242 )
| ~ ! [X243: $i > $i > $o] :
( ~ ! [X244: $i,X245: $i,X246: $i] :
( ~ ( X243 @ X246 @ X244 )
| ( X243 @ X245 @ X244 )
| ~ ( X243 @ X245 @ X246 ) )
| ~ ! [X247: $i,X248: $i] :
( ~ ( X238 @ X248 @ X247 )
| ( X243 @ X248 @ X247 ) )
| ( X243 @ X240 @ X241 ) ) )
| ~ ( X238 @ X240 @ X239 ) ) ) )
& ( ( ^ [X249: $i > $i > $o] :
! [X250: $i,X251: $i] :
( ~ ( X249 @ X251 @ X250 )
| ~ ( X249 @ X250 @ X251 ) ) )
= asymm )
& ( ( ^ [X252: $i > $i > $o,X253: $i] :
! [X254: $i] :
~ ( X252 @ X253 @ X254 ) )
= innf )
& ( sconfl
= ( ^ [X255: $i > $i > $o] :
! [X256: $i,X257: $i > $i > $o,X258: $i,X259: $i > $i > $o,X260: $i] :
( ~ ! [X261: $i,X262: $i,X263: $i] :
( ~ ( X257 @ X261 @ X262 )
| ~ ( X257 @ X262 @ X263 )
| ( X257 @ X261 @ X263 ) )
| ( X257 @ X260 @ X256 )
| ( X259 @ X256 @ X260 )
| ~ ! [X264: $i,X265: $i,X266: $i] :
( ~ ( X259 @ X265 @ X264 )
| ( X259 @ X266 @ X264 )
| ~ ( X259 @ X266 @ X265 ) )
| ~ ! [X267: $i] :
( ~ ! [X268: $i > $i > $o] :
( ~ ! [X269: $i,X270: $i] :
( ~ ( X255 @ X269 @ X270 )
| ( X268 @ X269 @ X270 ) )
| ( X268 @ X256 @ X267 )
| ~ ! [X271: $i,X272: $i,X273: $i] :
( ~ ( X268 @ X273 @ X272 )
| ( X268 @ X271 @ X272 )
| ~ ( X268 @ X271 @ X273 ) ) )
| ~ ! [X274: $i > $i > $o] :
( ( X274 @ X260 @ X267 )
| ~ ! [X275: $i,X276: $i] :
( ~ ( X255 @ X276 @ X275 )
| ( X274 @ X276 @ X275 ) )
| ~ ! [X277: $i,X278: $i,X279: $i] :
( ~ ( X274 @ X279 @ X278 )
| ( X274 @ X279 @ X277 )
| ~ ( X274 @ X278 @ X277 ) ) ) )
| ~ ( X255 @ X258 @ X260 )
| ~ ! [X280: $i,X281: $i] :
( ~ ( X255 @ X280 @ X281 )
| ( X257 @ X280 @ X281 ) )
| ~ ! [X282: $i,X283: $i] :
( ~ ( X255 @ X282 @ X283 )
| ( X259 @ X282 @ X283 ) )
| ( ( X256 != X258 )
& ~ ! [X284: $i > $i > $o] :
( ~ ! [X285: $i,X286: $i,X287: $i] :
( ~ ( X284 @ X287 @ X285 )
| ~ ( X284 @ X286 @ X287 )
| ( X284 @ X286 @ X285 ) )
| ( X284 @ X258 @ X256 )
| ~ ! [X288: $i,X289: $i] :
( ~ ( X255 @ X288 @ X289 )
| ( X284 @ X288 @ X289 ) ) ) )
| ( X256 = X260 ) ) ) )
& ( ( ^ [X290: $i > $i > $o] :
! [X291: $i] :
~ ( X290 @ X291 @ X291 ) )
= irrefl )
& ( symm
= ( ^ [X292: $i > $i > $o] :
! [X293: $i,X294: $i] :
( ( X292 @ X293 @ X294 )
| ~ ( X292 @ X294 @ X293 ) ) ) )
& ( rc
= ( ^ [X295: $i > $i > $o,X296: $i,X297: $i] :
( ( X296 = X297 )
| ( X295 @ X296 @ X297 ) ) ) )
& ( idem
= ( ^ [X298: ( $i > $i > $o ) > $i > $i > $o] :
! [X299: $i > $i > $o] :
( ( X298 @ X299 )
= ( X298 @ ( X298 @ X299 ) ) ) ) )
& ( antisymm
= ( ^ [X300: $i > $i > $o] :
! [X301: $i,X302: $i] :
( ( X301 = X302 )
| ~ ( X300 @ X302 @ X301 )
| ~ ( X300 @ X301 @ X302 ) ) ) )
& ( ( ^ [X303: $i > $i > $o] :
! [X304: $i,X305: $i > $o] :
( ~ ( X305 @ X304 )
| ~ ! [X306: $i] :
( ~ ! [X307: $i] :
( ~ ( X305 @ X307 )
| ~ ( X303 @ X306 @ X307 ) )
| ~ ( X305 @ X306 ) ) ) )
= term )
& ! [X308: $i] :
? [X309: d_unsorted] :
( ( d2unsorted @ X309 )
= X308 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( subrel
= ( ^ [X4: $i > $i > $o,X5: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ( X5 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( trsc
= ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X11: $i,X12: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) )
| ( X5 @ X17 @ X16 ) )
| ( X16 = X17 )
| ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X11: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) )
| ( X5 @ X16 @ X17 ) ) ) ) )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] : ( X4 @ X7 @ X6 ) )
= inv )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X11: $i,X6: $i] :
( ~ ( X4 @ X7 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ( X4 @ X6 @ X11 ) ) )
= trans )
& ( nfof
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ! [X22: $i] :
~ ( X4 @ X6 @ X22 )
& ( ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X11: $i,X13: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X6 ) )
| ( X6 = X7 ) ) ) ) )
& ( total
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X6 = X7 )
| ( X4 @ X6 @ X7 )
| ( X4 @ X7 @ X6 ) ) ) )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( ind
= ( ^ [X4: $i > $i > $o] :
! [X20: $i > $o,X21: $i] :
( ( X20 @ X21 )
| ~ ! [X6: $i] :
( ( X20 @ X6 )
| ~ ! [X7: $i] :
( ( X20 @ X7 )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X12: $i,X13: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 ) ) ) ) ) ) )
& ( confl
= ( ^ [X4: $i > $i > $o] :
! [X33: $i > $i > $o,X11: $i,X34: $i > $i > $o,X7: $i,X6: $i] :
( ( X34 @ X11 @ X7 )
| ~ ! [X14: $i,X15: $i] :
( ( X34 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X26: $i,X12: $i] :
( ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X6 @ X11 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) )
& ( X6 != X11 ) )
| ( X7 = X11 )
| ~ ! [X12: $i,X25: $i,X13: $i] :
( ( X33 @ X12 @ X25 )
| ~ ( X33 @ X12 @ X13 )
| ~ ( X33 @ X13 @ X25 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X33 @ X14 @ X15 ) )
| ~ ! [X26: $i,X13: $i,X12: $i] :
( ( X34 @ X12 @ X26 )
| ~ ( X34 @ X13 @ X26 )
| ~ ( X34 @ X12 @ X13 ) )
| ( ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X35: $i,X13: $i,X12: $i] :
( ( X5 @ X12 @ X35 )
| ~ ( X5 @ X13 @ X35 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) )
| ( X33 @ X7 @ X11 )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X12: $i,X13: $i,X25: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X11 @ X27 ) ) ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
~ ( ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 ) )
| ( X5 @ X7 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X12: $i,X26: $i] :
( ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 ) )
| ( X5 @ X6 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X26: $i,X12: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X6 @ X7 ) )
& ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X13: $i,X12: $i,X25: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) )
& ( X6 != X7 ) ) )
= join )
& ( sc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X4 @ X6 @ X7 )
| ( X4 @ X7 @ X6 ) ) ) )
& ( trc
= ( ^ [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 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ( X16 = X17 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
( ! [X6: $i,X7: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) )
& ! [X7: $i,X6: $i,X11: $i] :
( ~ ( X4 @ X7 @ X11 )
| ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
= so )
& ( lconfl
= ( ^ [X4: $i > $i > $o] :
! [X29: $i > $i > $o,X11: $i,X6: $i,X7: $i,X28: $i > $i > $o] :
( ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X28 @ X12 @ X13 )
| ( X28 @ X12 @ X25 )
| ~ ( X28 @ X13 @ X25 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X25: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X12: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X11 @ X27 ) ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X29 @ X14 @ X15 ) )
| ( X7 = X11 )
| ~ ( X4 @ X6 @ X7 )
| ( X29 @ X11 @ X7 )
| ~ ! [X14: $i,X15: $i] :
( ( X28 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ( X29 @ X12 @ X26 )
| ~ ( X29 @ X13 @ X26 )
| ~ ( X29 @ X12 @ X13 ) )
| ( X28 @ X7 @ X11 )
| ~ ( X4 @ X6 @ X11 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X36: $i > $i > $o,X37: $i > $i > $o,X7: $i] :
( ~ ! [X13: $i,X12: $i,X26: $i] :
( ~ ( X37 @ X12 @ X13 )
| ( X37 @ X12 @ X26 )
| ~ ( X37 @ X13 @ X26 ) )
| ~ ! [X25: $i,X12: $i,X13: $i] :
( ~ ( X36 @ X13 @ X25 )
| ( X36 @ X12 @ X25 )
| ~ ( X36 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X37 @ X14 @ X15 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X7 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X11: $i,X12: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) ) )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X11: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 ) )
| ( X5 @ X7 @ X6 ) )
& ( X6 != X7 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X25: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X6 @ X27 ) ) )
| ( X37 @ X6 @ X7 )
| ( X6 = X7 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X36 @ X14 @ X15 ) )
| ( X36 @ X7 @ X6 ) ) )
= cr )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i] : ( X4 @ X6 @ X6 ) )
= refl )
& ( infl
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o,X7: $i,X6: $i] :
( ( X8 @ X4 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( po
= ( ^ [X4: $i > $i > $o] :
( ! [X6: $i] : ( X4 @ X6 @ X6 )
& ! [X6: $i,X7: $i] :
( ( X6 = X7 )
| ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) )
& ! [X7: $i,X11: $i,X6: $i] :
( ~ ( X4 @ X7 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ( X4 @ X6 @ X11 ) ) ) ) )
& ( 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 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) ) ) ) )
& ( ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X10: $i,X4: $i > $i > $o,X9: $i,X5: $i > $i > $o] :
( ( X8 @ X5 @ X9 @ X10 )
| ~ ! [X6: $i,X7: $i] :
( ( X5 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) )
| ~ ( X8 @ X4 @ X9 @ X10 ) ) )
= mono )
& ( norm
= ( ^ [X4: $i > $i > $o] :
! [X23: $i,X6: $i] :
( ~ ! [X24: $i] :
( ~ ! [X22: $i] :
~ ( X4 @ X24 @ X22 )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X6 @ X24 ) ) )
| ~ ( X4 @ X6 @ X23 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) ) )
= asymm )
& ( ( ^ [X4: $i > $i > $o,X6: $i] :
! [X7: $i] :
~ ( X4 @ X6 @ X7 ) )
= innf )
& ( sconfl
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X31: $i > $i > $o,X6: $i,X30: $i > $i > $o,X11: $i] :
( ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X31 @ X12 @ X13 )
| ~ ( X31 @ X13 @ X26 )
| ( X31 @ X12 @ X26 ) )
| ( X31 @ X11 @ X7 )
| ( X30 @ X7 @ X11 )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X30 @ X13 @ X25 )
| ( X30 @ X12 @ X25 )
| ~ ( X30 @ X12 @ X13 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X12: $i,X25: $i,X13: $i] :
( ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ( X5 @ X11 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X26: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 ) ) ) )
| ~ ( X4 @ X6 @ X11 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X31 @ X14 @ X15 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X30 @ X14 @ X15 ) )
| ( ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X32: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X32 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X32 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) )
| ( X7 = X11 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i] :
~ ( X4 @ X6 @ X6 ) )
= irrefl )
& ( symm
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( rc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X6 = X7 )
| ( X4 @ X6 @ X7 ) ) ) )
& ( idem
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o] :
( ( X8 @ X4 )
= ( X8 @ ( X8 @ X4 ) ) ) ) )
& ( antisymm
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ( X6 = X7 )
| ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X19: $i,X18: $i > $o] :
( ~ ( X18 @ X19 )
| ~ ! [X6: $i] :
( ~ ! [X7: $i] :
( ~ ( X18 @ X7 )
| ~ ( X4 @ X6 @ X7 ) )
| ~ ( X18 @ X6 ) ) ) )
= term )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oJoehLhDex/DTF2THF_6848.p',sev441_1) ).
thf(f139,plain,
! [X1: $i] :
( ( ( d2unsorted @ ( sK3 @ X1 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f138]) ).
thf(f138,plain,
! [X1: $i] :
( ( ^ [Y0: d_unsorted] :
( ( d2unsorted @ Y0 )
= X1 )
@ ( sK3 @ X1 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X1: $i] :
( ( ?? @ d_unsorted
@ ^ [Y0: d_unsorted] :
( ( d2unsorted @ Y0 )
= X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= trans ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) ) ) )
| ~ ( Y1 @ Y2 ) ) ) ) )
= term )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( symm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
= irrefl )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y5 != Y3 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y4 @ Y8 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y0 @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= mono )
& ( 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 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ( po
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
& ( 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 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y3 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 = Y1 )
| ( Y2 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) ) ) )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y4 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y2 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ( Y2 @ Y6 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= cr )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( Y0 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y2 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y7 @ Y8 )
| ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
= so )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
& ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( Y2 @ Y4 ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y0 )
= ( d2unsorted @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y2 = Y1 ) ) ) ) ) )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= trans )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f5752,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( X2 != X3 )
| ( ( join @ X1 @ X2 @ X3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f5751]) ).
thf(f5751,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( $false
= ( X2 = X3 ) )
| ( ( join @ X1 @ X2 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f5749]) ).
thf(f5749,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( X2 != X3 )
= $true )
| ( ( join @ X1 @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f5747]) ).
thf(f5747,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ X3 @ X2 ) ) ) )
= $true )
| ( ( join @ X1 @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f5745]) ).
thf(f5745,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ X3 @ X2 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X2 @ X3 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( ( join @ X1 @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f5743]) ).
thf(f5743,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( join @ X1 @ X2 @ X3 )
= $true )
| ( ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ X3 @ X2 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X2 @ X3 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y2 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f5742]) ).
thf(f5742,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( join @ X1 @ X2 @ X3 )
= $true )
| ( $false
= ( ~ ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ X3 @ X2 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X2 @ X3 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y2 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f5740]) ).
thf(f5740,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ~ ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ X3 @ X2 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X2 @ X3 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y3 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y2 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= ( join @ X1 @ X2 @ X3 ) ),
inference(beta_eta_normalization,[status(thm)],[f5739]) ).
thf(f5739,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i] :
~ ( ( X2 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) )
| ( Y1 @ Y0 @ X2 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
@ X3 )
= ( join @ X1 @ X2 @ X3 ) ),
inference(argument_congruence,[status(thm)],[f4629]) ).
thf(f4629,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i] :
~ ( ( X2 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) )
| ( Y1 @ Y0 @ X2 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 )
| ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
= ( join @ X1 @ X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f4628]) ).
thf(f4628,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i,Y1: $i] :
~ ( ( Y0 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) )
| ( Y2 @ Y1 @ Y0 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
@ X2 )
= ( join @ X1 @ X2 ) ),
inference(argument_congruence,[status(thm)],[f4226]) ).
thf(f4226,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i,Y1: $i] :
~ ( ( Y0 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) )
| ( Y2 @ Y1 @ Y0 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
= ( join @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f4225]) ).
thf(f4225,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
@ X1 )
= ( join @ X1 ) ),
inference(argument_congruence,[status(thm)],[f38]) ).
thf(f38,plain,
( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( Y1 != Y2 )
& ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
= join )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f4848,plain,
( ! [X0: $i] :
( $false
= ( join @ sK2 @ sK13 @ X0 ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f4843,f152]) ).
thf(f4843,plain,
( ( $false
= ( join @ sK2 @ sK13 @ sK12 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f4838]) ).
thf(f4838,plain,
( ( ( ( ( trc @ sK2 @ sK11 @ sK12 )
& ( trc @ sK2 @ sK11 @ sK13 ) )
=> ( join @ sK2 @ sK13 @ sK12 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f4837]) ).
thf(f4837,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( trc @ sK2 @ sK11 @ sK12 )
& ( trc @ sK2 @ sK11 @ Y0 ) )
=> ( join @ sK2 @ Y0 @ sK12 ) )
@ sK13 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f4836]) ).
thf(f4836,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( trc @ sK2 @ sK11 @ sK12 )
& ( trc @ sK2 @ sK11 @ Y0 ) )
=> ( join @ sK2 @ Y0 @ sK12 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f4835]) ).
thf(f4835,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( trc @ sK2 @ sK11 @ Y0 )
& ( trc @ sK2 @ sK11 @ Y1 ) )
=> ( join @ sK2 @ Y1 @ Y0 ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f4834]) ).
thf(f4834,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( trc @ sK2 @ sK11 @ Y0 )
& ( trc @ sK2 @ sK11 @ Y1 ) )
=> ( join @ sK2 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f4827]) ).
thf(f4827,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK2 @ Y0 @ Y1 )
& ( trc @ sK2 @ Y0 @ Y2 ) )
=> ( join @ sK2 @ Y2 @ Y1 ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK2 @ Y0 @ Y1 )
& ( trc @ sK2 @ Y0 @ Y2 ) )
=> ( join @ sK2 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f146]) ).
thf(f146,definition,
( spl0_4
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK2 @ Y0 @ Y1 )
& ( trc @ sK2 @ Y0 @ Y2 ) )
=> ( join @ sK2 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f4823,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[status(thm)],[f4822]) ).
thf(f4822,plain,
( $false
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f4821]) ).
thf(f4821,plain,
( ( $false = $true )
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f4820]) ).
thf(f4820,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] : $true
@ sK25 ) )
| ~ spl0_17 ),
inference(sigma_clausification,[status(thm)],[f4809]) ).
thf(f4809,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : $true )
= $false )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f4808]) ).
thf(f4808,definition,
( spl0_17
<=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f4819,plain,
( ~ spl0_3
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[status(thm)],[f4818]) ).
thf(f4818,plain,
( $false
| ~ spl0_3
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f4813]) ).
thf(f4813,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[status(thm)],[f144,f4806]) ).
thf(f4806,plain,
( ! [X1: $i > $i > $o] :
( ( confl @ X1 )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f4805]) ).
thf(f4805,definition,
( spl0_16
<=> ! [X1: $i > $i > $o] :
( ( confl @ X1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f144,plain,
( ( ( confl @ sK2 )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f143]) ).
thf(f143,definition,
( spl0_3
<=> ( ( confl @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f4810,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f4803,f4808,f4805]) ).
thf(f4803,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : $true )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f4802]) ).
thf(f4802,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( $true
| ( sK23 @ X1 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f4801]) ).
thf(f4801,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( $true
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK23 @ X1 @ Y2 @ Y1 ) ) ) )
| ( sK23 @ X1 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f4800]) ).
thf(f4800,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( $true
| ( ( ( d2unsorted @ d_unsorted_0 )
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK23 @ X1 @ Y2 @ Y1 ) ) ) )
| ( sK23 @ X1 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f4799]) ).
thf(f4799,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ ( d2unsorted @ d_unsorted_0 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ ( d2unsorted @ d_unsorted_0 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( Y0 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( ( d2unsorted @ d_unsorted_0 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ( sK23 @ X1 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) )
| $true
| ( ( ( d2unsorted @ d_unsorted_0 )
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK23 @ X1 @ Y2 @ Y1 ) ) ) )
| ( sK23 @ X1 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f4798]) ).
thf(f4798,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ ( d2unsorted @ d_unsorted_0 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ ( d2unsorted @ d_unsorted_0 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( Y0 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( ( d2unsorted @ d_unsorted_0 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ( sK23 @ X1 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ( ( d2unsorted @ d_unsorted_0 )
= ( d2unsorted @ d_unsorted_0 ) )
| ( ( ( d2unsorted @ d_unsorted_0 )
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK23 @ X1 @ Y2 @ Y1 ) ) ) )
| ( sK23 @ X1 @ ( d2unsorted @ d_unsorted_0 ) @ ( d2unsorted @ d_unsorted_0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4797,f141]) ).
thf(f4797,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ ( d2unsorted @ d_unsorted_0 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( Y0 @ ( sK22 @ X1 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( ( sK22 @ X1 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ( sK23 @ X1 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ( ( d2unsorted @ d_unsorted_0 )
= ( sK22 @ X1 ) )
| ( ( ( d2unsorted @ d_unsorted_0 )
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( d2unsorted @ d_unsorted_0 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK23 @ X1 @ Y2 @ Y1 ) ) ) )
| ( sK23 @ X1 @ ( d2unsorted @ d_unsorted_0 ) @ ( sK22 @ X1 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f4796,f141]) ).
thf(f4796,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ ( sK24 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ( Y0 @ ( sK22 @ X1 ) @ ( sK24 @ X1 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y3 @ Y4 )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( ( sK22 @ X1 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ( sK23 @ X1 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ( ( ( sK24 @ X1 )
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK21 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK23 @ X1 @ Y2 @ Y1 ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4791]) ).
thf(f4791,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ ( sK22 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( Y1 @ ( sK22 @ X1 ) @ Y0 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ ( sK21 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y4 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( ( sK22 @ X1 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ~ ( sK23 @ X1 @ Y3 @ Y4 )
| ( sK23 @ X1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 )
| ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ( Y0
= ( sK22 @ X1 ) )
| ( ( Y0
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ ( sK21 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( sK23 @ X1 @ Y3 @ Y2 ) ) ) )
| ( sK23 @ X1 @ Y0 @ ( sK22 @ X1 ) ) ) )
@ ( sK24 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f4789]) ).
thf(f4789,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ( Y3 @ ( sK22 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ( Y1 @ ( sK22 @ X1 ) @ Y0 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ ( sK21 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y4 @ Y5 )
| ( Y2 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( ( sK22 @ X1 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ~ ( sK23 @ X1 @ Y3 @ Y4 )
| ( sK23 @ X1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 )
| ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ( Y0
= ( sK22 @ X1 ) )
| ( ( Y0
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ ( sK21 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( sK23 @ X1 @ Y3 @ Y2 ) ) ) )
| ( sK23 @ X1 @ Y0 @ ( sK22 @ X1 ) ) ) ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4785]) ).
thf(f4785,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ( Y4 @ ( sK22 @ X1 ) @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ ( sK21 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( ( sK22 @ X1 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y4 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ( Y1
= ( sK22 @ X1 ) )
| ( ( Y1
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ ( sK21 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) ) )
| ( Y0 @ Y1 @ ( sK22 @ X1 ) ) ) ) )
@ ( sK23 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f4782]) ).
thf(f4782,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ( Y4 @ ( sK22 @ X1 ) @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ ( sK21 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( ( sK22 @ X1 )
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y0 @ Y4 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ( Y1
= ( sK22 @ X1 ) )
| ( ( Y1
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ ( sK21 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) ) )
| ( Y0 @ Y1 @ ( sK22 @ X1 ) ) ) ) ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4779]) ).
thf(f4779,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ( Y3 @ Y0 @ Y2 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ ( sK21 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
& ( Y0
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y1 @ Y4 @ Y5 )
| ~ ( Y1 @ Y5 @ Y6 )
| ( Y1 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y2 = Y0 )
| ( ( Y2
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( X1 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ ( sK21 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) ) )
| ( Y1 @ Y2 @ Y0 ) ) ) ) )
@ ( sK22 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f4644]) ).
thf(f4644,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ( Y5 @ Y0 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ( Y3 @ Y0 @ Y2 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ ( sK21 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) ) ) )
& ( Y0
!= ( sK21 @ X1 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y1 @ Y4 @ Y5 )
| ~ ( Y1 @ Y5 @ Y6 )
| ( Y1 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y2 = Y0 )
| ( ( Y2
!= ( sK21 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( X1 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ ( sK21 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) ) )
| ( Y1 @ Y2 @ Y0 ) ) ) ) ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4643]) ).
thf(f4643,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( X1 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) )
& ( Y1 != Y0 ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y5 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 ) ) ) ) )
| ( Y3 = Y1 )
| ( ( Y3 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( X1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y3 @ Y1 ) ) ) ) ) )
@ ( sK21 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f4040]) ).
thf(f4040,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( X1 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) )
& ( Y1 != Y0 ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y5 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 ) ) ) ) )
| ( Y3 = Y1 )
| ( ( Y3 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( X1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y3 @ Y1 ) ) ) ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f4039]) ).
thf(f4039,plain,
! [X1: $i > $i > $o] :
( ( confl @ X1 )
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( X1 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) )
& ( Y1 != Y0 ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y5 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y7 @ Y6 ) ) ) ) )
| ( Y3 = Y1 )
| ( ( Y3 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( X1 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4038]) ).
thf(f4038,plain,
! [X1: $i > $i > $o] :
( ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) )
@ X1 )
= ( confl @ X1 ) ),
inference(argument_congruence,[status(thm)],[f99]) ).
thf(f99,plain,
( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( confl
= ( ^ [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] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) )
| ( Y5 @ Y2 @ Y4 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y0 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y7 @ Y9 ) ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y6 @ Y7 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) )
| ( Y4 = Y2 )
| ( ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y9 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y3 @ Y7 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f148,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f108,f146,f143]) ).
thf(f108,plain,
( ( ( confl @ sK2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK2 @ Y0 @ Y1 )
& ( trc @ sK2 @ Y0 @ Y2 ) )
=> ( join @ sK2 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( confl @ sK2 )
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK2 @ Y0 @ Y1 )
& ( trc @ sK2 @ Y0 @ Y2 ) )
=> ( join @ sK2 @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
( ( confl @ sK2 )
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f104]) ).
thf(f104,plain,
( confl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
= ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( confl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( confl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( confl
!= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( trc @ X0 @ X3 @ X1 )
& ( trc @ X0 @ X3 @ X2 ) )
=> ( join @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( confl
!= ( ^ [X4: $i > $i > $o] :
! [X11: $i,X7: $i,X6: $i] :
( ( ( trc @ X4 @ X6 @ X11 )
& ( trc @ X4 @ X6 @ X7 ) )
=> ( join @ X4 @ X11 @ X7 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( confl
= ( ^ [X4: $i > $i > $o] :
! [X11: $i,X7: $i,X6: $i] :
( ( ( trc @ X4 @ X6 @ X11 )
& ( trc @ X4 @ X6 @ X7 ) )
=> ( join @ X4 @ X11 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oJoehLhDex/DTF2THF_6848.p',confluent) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 09:32:04 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.21/0.46 % Domain : Software Verification
% 0.21/0.46 % Problem : Benchmark: SEV441^1, Active target: confluent
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English :
% 0.21/0.46
% 0.21/0.46 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Kon26]
% 0.21/0.46 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : ? v9.3.0
% 0.21/0.46 % Syntax : Number of formulae : 35 ( 1 unt; 33 typ; 0 def)
% 0.21/0.46 % Number of atoms : 84 ( 51 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 33 ( 42 avg)
% 0.21/0.46 % Number of connectives : 987 ( 227 ~; 218 |; 44 &; 496 @)
% 0.21/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 32 ( 17 avg)
% 0.21/0.46 % Number of types : 4 ( 2 usr)
% 0.21/0.46 % Number of type conns : 262 ( 262 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 32 ( 31 usr; 1 con; 0-3 aty)
% 0.21/0.46 % Number of variables : 314 ( 48 ^; 265 !; 1 ?; 314 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments :
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(unsorted_type,type,
% 0.21/0.46 unsorted: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(subrel_decl,type,
% 0.21/0.46 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(inv_decl,type,
% 0.21/0.46 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(idem_decl,type,
% 0.21/0.46 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(infl_decl,type,
% 0.21/0.46 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(mono_decl,type,
% 0.21/0.46 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(refl_decl,type,
% 0.21/0.46 refl: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(irrefl_decl,type,
% 0.21/0.46 irrefl: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(rc_decl,type,
% 0.21/0.46 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(symm_decl,type,
% 0.21/0.46 symm: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(antisymm_decl,type,
% 0.21/0.46 antisymm: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(asymm_decl,type,
% 0.21/0.46 asymm: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sc_decl,type,
% 0.21/0.46 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(trans_decl,type,
% 0.21/0.46 trans: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(tc_decl,type,
% 0.21/0.46 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(trc_decl,type,
% 0.21/0.46 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(trsc_decl,type,
% 0.21/0.46 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(po_decl,type,
% 0.21/0.46 po: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(so_decl,type,
% 0.21/0.46 so: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(total_decl,type,
% 0.21/0.46 total: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(term_decl,type,
% 0.21/0.46 term: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(ind_decl,type,
% 0.21/0.46 ind: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(innf_decl,type,
% 0.21/0.46 innf: ( $i > $i > $o ) > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(nfof_decl,type,
% 0.21/0.46 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(norm_decl,type,
% 0.21/0.46 norm: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(join_decl,type,
% 0.21/0.46 join: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(lconfl_decl,type,
% 0.21/0.46 lconfl: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sconfl_decl,type,
% 0.21/0.46 sconfl: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(confl_decl,type,
% 0.21/0.46 confl: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(cr_decl,type,
% 0.21/0.46 cr: ( $i > $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 %----Types of the domains
% 0.21/0.46 thf(d_unsorted_type,type,
% 0.21/0.46 d_unsorted: $tType ).
% 0.21/0.46
% 0.21/0.46 %----Types of the promotion functions
% 0.21/0.46 thf(d2unsorted_decl,type,
% 0.21/0.46 d2unsorted: d_unsorted > $i ).
% 0.21/0.46
% 0.21/0.46 %----Types of the domain elements
% 0.21/0.46 thf(d_unsorted_0_decl,type,
% 0.21/0.46 d_unsorted_0: d_unsorted ).
% 0.21/0.46
% 0.21/0.46 thf(sev441_1,axiom,
% 0.21/0.46 ( ! [U: $i] :
% 0.21/0.46 ? [DU: d_unsorted] :
% 0.21/0.46 ( U
% 0.21/0.46 = ( d2unsorted @ DU ) )
% 0.21/0.46 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.21/0.46 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.21/0.46 ( ( ( d2unsorted @ DU1 )
% 0.21/0.46 = ( d2unsorted @ DU2 ) )
% 0.21/0.46 => ( DU1 = DU2 ) )
% 0.21/0.46 & ( subrel
% 0.21/0.46 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ( S @ X @ Y ) ) ) )
% 0.21/0.46 & ( inv
% 0.21/0.46 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 0.21/0.46 & ( idem
% 0.21/0.46 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.21/0.46 ! [R: $i > $i > $o] :
% 0.21/0.46 ( ( F @ R )
% 0.21/0.46 = ( F @ ( F @ R ) ) ) ) )
% 0.21/0.46 & ( infl
% 0.21/0.46 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.21/0.46 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ( F @ R @ X @ Y ) ) ) )
% 0.21/0.46 & ( mono
% 0.21/0.46 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.21/0.46 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 0.21/0.46 ( ~ ! [X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ( S @ X @ Y ) )
% 0.21/0.46 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 0.21/0.46 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 0.21/0.46 & ( refl
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i] : ( R @ X @ X ) ) )
% 0.21/0.46 & ( irrefl
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i] :
% 0.21/0.46 ~ ( R @ X @ X ) ) )
% 0.21/0.46 & ( rc
% 0.21/0.46 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.21/0.46 ( ( X = Y )
% 0.21/0.46 | ( R @ X @ Y ) ) ) )
% 0.21/0.46 & ( symm
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ( R @ Y @ X ) ) ) )
% 0.21/0.46 & ( antisymm
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ~ ( R @ Y @ X )
% 0.21/0.46 | ( X = Y ) ) ) )
% 0.21/0.46 & ( asymm
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ~ ( R @ Y @ X ) ) ) )
% 0.21/0.46 & ( sc
% 0.21/0.46 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.21/0.46 ( ( R @ Y @ X )
% 0.21/0.46 | ( R @ X @ Y ) ) ) )
% 0.21/0.46 & ( trans
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i,Z: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ~ ( R @ Y @ Z )
% 0.21/0.46 | ( R @ X @ Z ) ) ) )
% 0.21/0.46 & ( tc
% 0.21/0.46 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.21/0.46 ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Y ) ) ) )
% 0.21/0.46 & ( trc
% 0.21/0.46 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.21/0.46 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.21/0.46 | ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.21/0.46 & ( trsc
% 0.21/0.46 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.21/0.46 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.21/0.46 | ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 0.21/0.46 | ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.21/0.46 & ( po
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ( ! [X: $i] : ( R @ X @ X )
% 0.21/0.46 & ! [X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ~ ( R @ Y @ X )
% 0.21/0.46 | ( X = Y ) )
% 0.21/0.46 & ! [X: $i,Y: $i,Z: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ~ ( R @ Y @ Z )
% 0.21/0.46 | ( R @ X @ Z ) ) ) ) )
% 0.21/0.46 & ( so
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ( ! [X: $i,Y: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ~ ( R @ Y @ X ) )
% 0.21/0.46 & ! [X: $i,Y: $i,Z: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Y )
% 0.21/0.46 | ~ ( R @ Y @ Z )
% 0.21/0.46 | ( R @ X @ Z ) ) ) ) )
% 0.21/0.46 & ( total
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i] :
% 0.21/0.46 ( ( X = Y )
% 0.21/0.46 | ( R @ X @ Y )
% 0.21/0.46 | ( R @ Y @ X ) ) ) )
% 0.21/0.46 & ( term
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [A: $i > $o,Bound_variable_862: $i] :
% 0.21/0.46 ( ~ ( A @ Bound_variable_862 )
% 0.21/0.46 | ~ ! [X: $i] :
% 0.21/0.46 ( ~ ( A @ X )
% 0.21/0.46 | ~ ! [Y: $i] :
% 0.21/0.46 ( ~ ( A @ Y )
% 0.21/0.46 | ~ ( R @ X @ Y ) ) ) ) ) )
% 0.21/0.46 & ( ind
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [P: $i > $o,Bound_variable_917: $i] :
% 0.21/0.46 ( ~ ! [X: $i] :
% 0.21/0.46 ( ~ ! [Y: $i] :
% 0.21/0.46 ( ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Y ) )
% 0.21/0.46 | ( P @ Y ) )
% 0.21/0.46 | ( P @ X ) )
% 0.21/0.46 | ( P @ Bound_variable_917 ) ) ) )
% 0.21/0.46 & ( innf
% 0.21/0.46 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.21/0.46 ! [Y: $i] :
% 0.21/0.46 ~ ( R @ X @ Y ) ) )
% 0.21/0.46 & ( nfof
% 0.21/0.46 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.21/0.46 ( ( ( X = Y )
% 0.21/0.46 | ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ X ) ) )
% 0.21/0.46 & ! [Bound_variable_985: $i] :
% 0.21/0.46 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 0.21/0.46 & ( norm
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Bound_variable_1075: $i] :
% 0.21/0.46 ( ~ ( R @ X @ Bound_variable_1075 )
% 0.21/0.46 | ~ ! [Bound_variable_1049: $i] :
% 0.21/0.46 ( ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Bound_variable_1049 ) )
% 0.21/0.46 | ~ ! [Bound_variable_985: $i] :
% 0.21/0.46 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 0.21/0.46 & ( join
% 0.21/0.46 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.21/0.46 ~ ( ( X != Y )
% 0.21/0.46 & ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ X ) )
% 0.21/0.46 & ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Y ) )
% 0.21/0.46 & ! [Bound_variable_1218: $i] :
% 0.21/0.46 ( ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ Bound_variable_1218 ) )
% 0.21/0.46 | ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 0.21/0.46 & ( lconfl
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 0.21/0.46 ( ~ ( R @ X @ Z )
% 0.21/0.46 | ~ ( R @ X @ Y )
% 0.21/0.46 | ( Y = Z )
% 0.21/0.46 | ~ ! [Bound_variable_1218: $i] :
% 0.21/0.46 ( ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ Bound_variable_1218 ) )
% 0.21/0.46 | ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1293 @ Y @ Z )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 0.21/0.46 & ( sconfl
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 0.21/0.46 ( ~ ( R @ X @ Z )
% 0.21/0.46 | ( ( X != Y )
% 0.21/0.46 & ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Y ) ) )
% 0.21/0.46 | ( Y = Z )
% 0.21/0.46 | ~ ! [Bound_variable_1218: $i] :
% 0.21/0.46 ( ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ Bound_variable_1218 ) )
% 0.21/0.46 | ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1371 @ Y @ Z )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 0.21/0.46 & ( confl
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 0.21/0.46 ( ( ( X != Z )
% 0.21/0.46 & ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Z ) ) )
% 0.21/0.46 | ( ( X != Y )
% 0.21/0.46 & ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Y ) ) )
% 0.21/0.46 | ( Y = Z )
% 0.21/0.46 | ~ ! [Bound_variable_1218: $i] :
% 0.21/0.46 ( ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ Bound_variable_1218 ) )
% 0.21/0.46 | ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1444 @ Y @ Z )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 0.21/0.46 & ( cr
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 0.21/0.46 ( ( ( X != Y )
% 0.21/0.46 & ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ X ) )
% 0.21/0.46 & ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Z )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Z ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Y ) ) )
% 0.21/0.46 | ( X = Y )
% 0.21/0.46 | ~ ! [Bound_variable_1218: $i] :
% 0.21/0.46 ( ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ Y @ Bound_variable_1218 ) )
% 0.21/0.46 | ~ ! [S: $i > $i > $o] :
% 0.21/0.46 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( S @ X @ Bound_variable_1218 ) ) )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.21/0.46 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1522 @ Y @ X )
% 0.21/0.46 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.21/0.46 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 0.21/0.46 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.21/0.46 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.21/0.46 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.21/0.46 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.21/0.46 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.21/0.46 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(confluent,conjecture,
% 0.21/0.46 ( confl
% 0.21/0.46 = ( ^ [R: $i > $i > $o] :
% 0.21/0.46 ! [X: $i,Y: $i,Z: $i] :
% 0.21/0.46 ( ( ( trc @ R @ X @ Z )
% 0.21/0.46 & ( trc @ R @ X @ Y ) )
% 0.21/0.46 => ( join @ R @ Z @ Y ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 ------------------------
% 1.92/1.39 ---- Embedded in THF ---
% 1.92/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.92/1.39 %%% Generated on Tue May 05 09:32:05 EDT 2026
% 1.92/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.92/1.39 %%% Logic specification used:
% 1.92/1.39 %%% thf(spec, logic, $$dhol).
% 1.92/1.39
% 1.92/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oJoehLhDex/DTF2DTF6848.p
% See solution above
% 1.92/1.39 ------------------------
% 2.14/1.41 ---- Cleaned THF ---
% 2.14/1.41 thf(unsorted_type,type,
% 2.14/1.41 unsorted: $tType ).
% 2.14/1.41
% 2.14/1.41 thf(subrel_decl,type,
% 2.14/1.41 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(inv_decl,type,
% 2.14/1.41 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(idem_decl,type,
% 2.14/1.41 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(infl_decl,type,
% 2.14/1.41 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(mono_decl,type,
% 2.14/1.41 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(refl_decl,type,
% 2.14/1.41 refl: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(irrefl_decl,type,
% 2.14/1.41 irrefl: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(rc_decl,type,
% 2.14/1.41 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(symm_decl,type,
% 2.14/1.41 symm: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(antisymm_decl,type,
% 2.14/1.41 antisymm: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(asymm_decl,type,
% 2.14/1.41 asymm: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(sc_decl,type,
% 2.14/1.41 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(trans_decl,type,
% 2.14/1.41 trans: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(tc_decl,type,
% 2.14/1.41 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(trc_decl,type,
% 2.14/1.41 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(trsc_decl,type,
% 2.14/1.41 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(po_decl,type,
% 2.14/1.41 po: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(so_decl,type,
% 2.14/1.41 so: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(total_decl,type,
% 2.14/1.41 total: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(term_decl,type,
% 2.14/1.41 term: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(ind_decl,type,
% 2.14/1.41 ind: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(innf_decl,type,
% 2.14/1.41 innf: ( $i > $i > $o ) > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(nfof_decl,type,
% 2.14/1.41 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(norm_decl,type,
% 2.14/1.41 norm: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(join_decl,type,
% 2.14/1.41 join: ( $i > $i > $o ) > $i > $i > $o ).
% 2.14/1.41
% 2.14/1.41 thf(lconfl_decl,type,
% 2.14/1.41 lconfl: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(sconfl_decl,type,
% 2.14/1.41 sconfl: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(confl_decl,type,
% 2.14/1.41 confl: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(cr_decl,type,
% 2.14/1.41 cr: ( $i > $i > $o ) > $o ).
% 2.14/1.41
% 2.14/1.41 thf(d_unsorted_type,type,
% 2.14/1.41 d_unsorted: $tType ).
% 2.14/1.41
% 2.14/1.41 thf(d2unsorted_decl,type,
% 2.14/1.41 d2unsorted: d_unsorted > $i ).
% 2.14/1.41
% 2.14/1.41 thf(d_unsorted_0_decl,type,
% 2.14/1.41 d_unsorted_0: d_unsorted ).
% 2.14/1.41
% 2.14/1.41 thf(sev441_1,axiom,
% 2.14/1.41 ( ! [U: $i] :
% 2.14/1.41 ? [DU: d_unsorted] :
% 2.14/1.41 ( U
% 2.14/1.41 = ( d2unsorted @ DU ) )
% 2.14/1.41 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 2.14/1.41 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 2.14/1.41 ( ( ( d2unsorted @ DU1 )
% 2.14/1.41 = ( d2unsorted @ DU2 ) )
% 2.14/1.41 => ( DU1 = DU2 ) )
% 2.14/1.41 & ( subrel
% 2.14/1.41 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ( S @ X @ Y ) ) ) )
% 2.14/1.41 & ( inv
% 2.14/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 2.14/1.41 & ( idem
% 2.14/1.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 2.14/1.41 ! [R: $i > $i > $o] :
% 2.14/1.41 ( ( F @ R )
% 2.14/1.41 = ( F @ ( F @ R ) ) ) ) )
% 2.14/1.41 & ( infl
% 2.14/1.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 2.14/1.41 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ( F @ R @ X @ Y ) ) ) )
% 2.14/1.41 & ( mono
% 2.14/1.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 2.14/1.41 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 2.14/1.41 ( ~ ! [X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ( S @ X @ Y ) )
% 2.14/1.41 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 2.14/1.41 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 2.14/1.41 & ( refl
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i] : ( R @ X @ X ) ) )
% 2.14/1.41 & ( irrefl
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i] :
% 2.14/1.41 ~ ( R @ X @ X ) ) )
% 2.14/1.41 & ( rc
% 2.14/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.14/1.41 ( ( X = Y )
% 2.14/1.41 | ( R @ X @ Y ) ) ) )
% 2.14/1.41 & ( symm
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ( R @ Y @ X ) ) ) )
% 2.14/1.41 & ( antisymm
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ~ ( R @ Y @ X )
% 2.14/1.41 | ( X = Y ) ) ) )
% 2.14/1.41 & ( asymm
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ~ ( R @ Y @ X ) ) ) )
% 2.14/1.41 & ( sc
% 2.14/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.14/1.41 ( ( R @ Y @ X )
% 2.14/1.41 | ( R @ X @ Y ) ) ) )
% 2.14/1.41 & ( trans
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i,Z: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ~ ( R @ Y @ Z )
% 2.14/1.41 | ( R @ X @ Z ) ) ) )
% 2.14/1.41 & ( tc
% 2.14/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.14/1.41 ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Y ) ) ) )
% 2.14/1.41 & ( trc
% 2.14/1.41 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 2.14/1.41 ( ( Flatten_var_0 = Flatten_var_1 )
% 2.14/1.41 | ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 2.14/1.41 & ( trsc
% 2.14/1.41 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 2.14/1.41 ( ( Flatten_var_0 = Flatten_var_1 )
% 2.14/1.41 | ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 2.14/1.41 | ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 2.14/1.41 & ( po
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ( ! [X: $i] : ( R @ X @ X )
% 2.14/1.41 & ! [X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ~ ( R @ Y @ X )
% 2.14/1.41 | ( X = Y ) )
% 2.14/1.41 & ! [X: $i,Y: $i,Z: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ~ ( R @ Y @ Z )
% 2.14/1.41 | ( R @ X @ Z ) ) ) ) )
% 2.14/1.41 & ( so
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ( ! [X: $i,Y: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ~ ( R @ Y @ X ) )
% 2.14/1.41 & ! [X: $i,Y: $i,Z: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Y )
% 2.14/1.41 | ~ ( R @ Y @ Z )
% 2.14/1.41 | ( R @ X @ Z ) ) ) ) )
% 2.14/1.41 & ( total
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i] :
% 2.14/1.41 ( ( X = Y )
% 2.14/1.41 | ( R @ X @ Y )
% 2.14/1.41 | ( R @ Y @ X ) ) ) )
% 2.14/1.41 & ( term
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [A: $i > $o,Bound_variable_862: $i] :
% 2.14/1.41 ( ~ ( A @ Bound_variable_862 )
% 2.14/1.41 | ~ ! [X: $i] :
% 2.14/1.41 ( ~ ( A @ X )
% 2.14/1.41 | ~ ! [Y: $i] :
% 2.14/1.41 ( ~ ( A @ Y )
% 2.14/1.41 | ~ ( R @ X @ Y ) ) ) ) ) )
% 2.14/1.41 & ( ind
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [P: $i > $o,Bound_variable_917: $i] :
% 2.14/1.41 ( ~ ! [X: $i] :
% 2.14/1.41 ( ~ ! [Y: $i] :
% 2.14/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Y ) )
% 2.14/1.41 | ( P @ Y ) )
% 2.14/1.41 | ( P @ X ) )
% 2.14/1.41 | ( P @ Bound_variable_917 ) ) ) )
% 2.14/1.41 & ( innf
% 2.14/1.41 = ( ^ [R: $i > $i > $o,X: $i] :
% 2.14/1.41 ! [Y: $i] :
% 2.14/1.41 ~ ( R @ X @ Y ) ) )
% 2.14/1.41 & ( nfof
% 2.14/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.14/1.41 ( ( ( X = Y )
% 2.14/1.41 | ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ X ) ) )
% 2.14/1.41 & ! [Bound_variable_985: $i] :
% 2.14/1.41 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 2.14/1.41 & ( norm
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Bound_variable_1075: $i] :
% 2.14/1.41 ( ~ ( R @ X @ Bound_variable_1075 )
% 2.14/1.41 | ~ ! [Bound_variable_1049: $i] :
% 2.14/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Bound_variable_1049 ) )
% 2.14/1.41 | ~ ! [Bound_variable_985: $i] :
% 2.14/1.41 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 2.14/1.41 & ( join
% 2.14/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.14/1.41 ~ ( ( X != Y )
% 2.14/1.41 & ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ X ) )
% 2.14/1.41 & ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Y ) )
% 2.14/1.41 & ! [Bound_variable_1218: $i] :
% 2.14/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.14/1.41 | ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 2.14/1.41 & ( lconfl
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 2.14/1.41 ( ~ ( R @ X @ Z )
% 2.14/1.41 | ~ ( R @ X @ Y )
% 2.14/1.41 | ( Y = Z )
% 2.14/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.14/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.14/1.41 | ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Z @ Bound_variable_1218 ) ) )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1293 @ Y @ Z )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 2.14/1.41 & ( sconfl
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 2.14/1.41 ( ~ ( R @ X @ Z )
% 2.14/1.41 | ( ( X != Y )
% 2.14/1.41 & ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Y ) ) )
% 2.14/1.41 | ( Y = Z )
% 2.14/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.14/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.14/1.41 | ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Z @ Bound_variable_1218 ) ) )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1371 @ Y @ Z )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 2.14/1.41 & ( confl
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 2.14/1.41 ( ( ( X != Z )
% 2.14/1.41 & ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Z ) ) )
% 2.14/1.41 | ( ( X != Y )
% 2.14/1.41 & ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Y ) ) )
% 2.14/1.41 | ( Y = Z )
% 2.14/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.14/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.14/1.41 | ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Z @ Bound_variable_1218 ) ) )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1444 @ Y @ Z )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 2.14/1.41 & ( cr
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 2.14/1.41 ( ( ( X != Y )
% 2.14/1.41 & ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ X ) )
% 2.14/1.41 & ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Y ) ) )
% 2.14/1.41 | ( X = Y )
% 2.14/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.14/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.14/1.41 | ~ ! [S: $i > $i > $o] :
% 2.14/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( S @ X @ Bound_variable_1218 ) ) )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.14/1.41 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1522 @ Y @ X )
% 2.14/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.14/1.41 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 2.14/1.41 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.14/1.41 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.14/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.14/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.14/1.41 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.14/1.41 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 2.14/1.41
% 2.14/1.41 thf(confluent,conjecture,
% 2.14/1.41 ( confl
% 2.14/1.41 = ( ^ [R: $i > $i > $o] :
% 2.14/1.41 ! [X: $i,Y: $i,Z: $i] :
% 2.14/1.41 ( ( ( trc @ R @ X @ Z )
% 2.14/1.41 & ( trc @ R @ X @ Y ) )
% 2.14/1.41 => ( join @ R @ Z @ Y ) ) ) ) ).
% 2.14/1.41 ------------------------
% 2.14/1.43 % (7221)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/183Mi)
% 2.14/1.44 % (7222)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_6848 for (2999ds/4Mi)
% 2.14/1.44 % (7223)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_6848 for (2999ds/27Mi)
% 2.14/1.44 % (7224)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/2Mi)
% 2.14/1.44 % (7225)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_6848 for (2999ds/2Mi)
% 2.14/1.44 % (7226)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_6848 for (2999ds/275Mi)
% 2.14/1.44 % (7227)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/18Mi)
% 2.14/1.44 % (7225)Instruction limit reached!
% 2.14/1.44 % (7225)------------------------------
% 2.14/1.44 % (7225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.44 % (7225)Termination reason: Unknown
% 2.14/1.44 % (7225)Termination phase: shuffling
% 2.14/1.44
% 2.14/1.44 % (7225)Memory used [KB]: 1023
% 2.14/1.44 % (7225)Time elapsed: 0.003 s
% 2.14/1.44 % (7225)Instructions burned: 2 (million)
% 2.14/1.44 % (7225)------------------------------
% 2.14/1.44 % (7225)------------------------------
% 2.14/1.44 % (7222)Instruction limit reached!
% 2.14/1.44 % (7222)------------------------------
% 2.14/1.44 % (7222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.44 % (7222)Termination reason: Unknown
% 2.14/1.44 % (7222)Termination phase: shuffling
% 2.14/1.44
% 2.14/1.44 % (7222)Memory used [KB]: 1151
% 2.14/1.44 % (7222)Time elapsed: 0.004 s
% 2.14/1.44 % (7222)Instructions burned: 4 (million)
% 2.14/1.44 % (7222)------------------------------
% 2.14/1.44 % (7222)------------------------------
% 2.14/1.44 % (7224)Instruction limit reached!
% 2.14/1.44 % (7224)------------------------------
% 2.14/1.44 % (7224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.44 % (7224)Termination reason: Unknown
% 2.14/1.44 % (7224)Termination phase: shuffling
% 2.14/1.44
% 2.14/1.44 % (7224)Memory used [KB]: 1151
% 2.14/1.44 % (7224)Time elapsed: 0.004 s
% 2.14/1.44 % (7224)Instructions burned: 3 (million)
% 2.14/1.44 % (7224)------------------------------
% 2.14/1.44 % (7224)------------------------------
% 2.14/1.45 % (7227)Instruction limit reached!
% 2.14/1.45 % (7227)------------------------------
% 2.14/1.45 % (7227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.45 % (7227)Termination reason: Unknown
% 2.14/1.45 % (7227)Termination phase: Property scanning
% 2.14/1.45
% 2.14/1.45 % (7227)Memory used [KB]: 1407
% 2.14/1.45 % (7227)Time elapsed: 0.012 s
% 2.14/1.45 % (7227)Instructions burned: 19 (million)
% 2.14/1.45 % (7227)------------------------------
% 2.14/1.45 % (7227)------------------------------
% 2.14/1.45 % (7223)Instruction limit reached!
% 2.14/1.45 % (7223)------------------------------
% 2.14/1.45 % (7223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.45 % (7223)Termination reason: Unknown
% 2.14/1.45 % (7223)Termination phase: Preprocessing 3
% 2.14/1.45
% 2.14/1.45 % (7223)Memory used [KB]: 1535
% 2.14/1.45 % (7223)Time elapsed: 0.016 s
% 2.14/1.45 % (7223)Instructions burned: 28 (million)
% 2.14/1.45 % (7223)------------------------------
% 2.14/1.45 % (7223)------------------------------
% 2.14/1.45 % (7226)Refutation not found, incomplete strategy
% 2.14/1.45 % (7226)------------------------------
% 2.14/1.45 % (7226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.45 % (7226)Termination reason: Refutation not found, incomplete strategy
% 2.14/1.45
% 2.14/1.45
% 2.14/1.45 % (7226)Memory used [KB]: 6012
% 2.14/1.45 % (7226)Time elapsed: 0.017 s
% 2.14/1.45 % (7226)Instructions burned: 30 (million)
% 2.14/1.45 % (7226)------------------------------
% 2.14/1.45 % (7226)------------------------------
% 2.14/1.46 % (7228)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/3Mi)
% 2.14/1.46 % (7229)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_6848 for (2999ds/37Mi)
% 2.14/1.46 % (7230)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_6848 for (2999ds/15Mi)
% 2.14/1.46 % (7228)Instruction limit reached!
% 2.14/1.46 % (7228)------------------------------
% 2.14/1.46 % (7228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.46 % (7228)Termination reason: Unknown
% 2.14/1.46 % (7228)Termination phase: shuffling
% 2.14/1.46
% 2.14/1.46 % (7228)Memory used [KB]: 1151
% 2.14/1.46 % (7228)Time elapsed: 0.004 s
% 2.14/1.46 % (7228)Instructions burned: 4 (million)
% 2.14/1.46 % (7228)------------------------------
% 2.14/1.46 % (7228)------------------------------
% 2.14/1.47 % (7230)Instruction limit reached!
% 2.14/1.47 % (7230)------------------------------
% 2.14/1.47 % (7230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.47 % (7230)Termination reason: Unknown
% 2.14/1.47 % (7230)Termination phase: shuffling
% 2.14/1.47
% 2.14/1.47 % (7230)Memory used [KB]: 1407
% 2.14/1.47 % (7230)Time elapsed: 0.010 s
% 2.14/1.47 % (7230)Instructions burned: 16 (million)
% 2.14/1.47 % (7230)------------------------------
% 2.14/1.47 % (7230)------------------------------
% 2.14/1.47 % (7231)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_6848 for (2999ds/3Mi)
% 2.14/1.47 % (7231)Instruction limit reached!
% 2.14/1.47 % (7231)------------------------------
% 2.14/1.47 % (7231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.47 % (7231)Termination reason: Unknown
% 2.14/1.47 % (7231)Termination phase: shuffling
% 2.14/1.47
% 2.14/1.47 % (7231)Memory used [KB]: 1151
% 2.14/1.47 % (7231)Time elapsed: 0.004 s
% 2.14/1.47 % (7231)Instructions burned: 4 (million)
% 2.14/1.47 % (7231)------------------------------
% 2.14/1.47 % (7231)------------------------------
% 2.14/1.47 % (7233)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/7Mi)
% 2.14/1.47 % (7232)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_6848 for (2999ds/1041Mi)
% 2.14/1.47 % (7233)Instruction limit reached!
% 2.14/1.47 % (7233)------------------------------
% 2.14/1.47 % (7233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.47 % (7233)Termination reason: Unknown
% 2.14/1.47 % (7233)Termination phase: shuffling
% 2.14/1.47
% 2.14/1.47 % (7233)Memory used [KB]: 1279
% 2.14/1.47 % (7233)Time elapsed: 0.004 s
% 2.14/1.47 % (7233)Instructions burned: 9 (million)
% 2.14/1.47 % (7233)------------------------------
% 2.14/1.47 % (7233)------------------------------
% 2.14/1.48 % (7234)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/16Mi)
% 2.14/1.48 % (7229)Instruction limit reached!
% 2.14/1.48 % (7229)------------------------------
% 2.14/1.48 % (7229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (7229)Termination reason: Unknown
% 2.14/1.48 % (7229)Termination phase: Saturation
% 2.14/1.48
% 2.14/1.48 % (7229)Memory used [KB]: 6012
% 2.14/1.48 % (7229)Time elapsed: 0.020 s
% 2.14/1.48 % (7229)Instructions burned: 38 (million)
% 2.14/1.48 % (7229)------------------------------
% 2.14/1.48 % (7229)------------------------------
% 2.14/1.48 % (7237)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/7Mi)
% 2.14/1.48 % (7234)Instruction limit reached!
% 2.14/1.48 % (7234)------------------------------
% 2.14/1.48 % (7234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (7234)Termination reason: Unknown
% 2.14/1.48 % (7234)Termination phase: Property scanning
% 2.14/1.48
% 2.14/1.48 % (7234)Memory used [KB]: 1407
% 2.14/1.48 % (7234)Time elapsed: 0.008 s
% 2.14/1.48 % (7234)Instructions burned: 17 (million)
% 2.14/1.48 % (7234)------------------------------
% 2.14/1.48 % (7234)------------------------------
% 2.14/1.48 % (7237)Instruction limit reached!
% 2.14/1.48 % (7237)------------------------------
% 2.14/1.48 % (7237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (7237)Termination reason: Unknown
% 2.14/1.48 % (7237)Termination phase: shuffling
% 2.14/1.48
% 2.14/1.48 % (7237)Memory used [KB]: 1279
% 2.14/1.48 % (7237)Time elapsed: 0.003 s
% 2.14/1.48 % (7237)Instructions burned: 7 (million)
% 2.14/1.48 % (7237)------------------------------
% 2.14/1.48 % (7237)------------------------------
% 2.14/1.48 % (7221)Instruction limit reached!
% 2.14/1.48 % (7221)------------------------------
% 2.14/1.48 % (7221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.48 % (7221)Termination reason: Unknown
% 2.14/1.48 % (7221)Termination phase: Saturation
% 2.14/1.48
% 2.14/1.48 % (7221)Memory used [KB]: 6524
% 2.14/1.48 % (7221)Time elapsed: 0.053 s
% 2.14/1.48 % (7221)Instructions burned: 183 (million)
% 2.14/1.48 % (7221)------------------------------
% 2.14/1.48 % (7221)------------------------------
% 2.14/1.48 % (7235)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_6848 for (2999ds/3Mi)
% 2.14/1.49 % (7235)Instruction limit reached!
% 2.14/1.49 % (7235)------------------------------
% 2.14/1.49 % (7235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.49 % (7235)Termination reason: Unknown
% 2.14/1.49 % (7235)Termination phase: shuffling
% 2.14/1.49
% 2.14/1.49 % (7235)Memory used [KB]: 1151
% 2.14/1.49 % (7235)Time elapsed: 0.004 s
% 2.14/1.49 % (7235)Instructions burned: 4 (million)
% 2.14/1.49 % (7235)------------------------------
% 2.14/1.49 % (7235)------------------------------
% 2.14/1.49 % (7236)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_6848 for (2999ds/3Mi)
% 2.14/1.49 % (7236)Instruction limit reached!
% 2.14/1.49 % (7236)------------------------------
% 2.14/1.49 % (7236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.49 % (7236)Termination reason: Unknown
% 2.14/1.49 % (7236)Termination phase: shuffling
% 2.14/1.49
% 2.14/1.49 % (7236)Memory used [KB]: 1151
% 2.14/1.49 % (7236)Time elapsed: 0.004 s
% 2.14/1.49 % (7236)Instructions burned: 4 (million)
% 2.14/1.49 % (7236)------------------------------
% 2.14/1.49 % (7236)------------------------------
% 2.14/1.49 % (7239)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/4Mi)
% 2.14/1.49 % (7240)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/18Mi)
% 2.14/1.49 % (7238)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/3Mi)
% 2.14/1.49 % (7239)Instruction limit reached!
% 2.14/1.49 % (7239)------------------------------
% 2.14/1.49 % (7239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.49 % (7239)Termination reason: Unknown
% 2.14/1.49 % (7239)Termination phase: shuffling
% 2.14/1.49
% 2.14/1.49 % (7239)Memory used [KB]: 1151
% 2.14/1.49 % (7239)Time elapsed: 0.003 s
% 2.14/1.49 % (7239)Instructions burned: 4 (million)
% 2.14/1.49 % (7239)------------------------------
% 2.14/1.49 % (7239)------------------------------
% 2.14/1.49 % (7241)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/710Mi)
% 2.14/1.49 % (7238)Instruction limit reached!
% 2.14/1.49 % (7238)------------------------------
% 2.14/1.49 % (7238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.14/1.49 % (7238)Termination reason: Unknown
% 2.14/1.49 % (7238)Termination phase: shuffling
% 2.14/1.49
% 2.14/1.49 % (7238)Memory used [KB]: 1151
% 2.14/1.49 % (7238)Time elapsed: 0.004 s
% 2.14/1.49 % (7238)Instructions burned: 4 (million)
% 2.14/1.49 % (7238)------------------------------
% 2.14/1.49 % (7238)------------------------------
% 2.15/1.50 % (7240)Instruction limit reached!
% 2.15/1.50 % (7240)------------------------------
% 2.15/1.50 % (7240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.50 % (7240)Termination reason: Unknown
% 2.15/1.50 % (7240)Termination phase: Property scanning
% 2.15/1.50
% 2.15/1.50 % (7240)Memory used [KB]: 1535
% 2.15/1.50 % (7240)Time elapsed: 0.006 s
% 2.15/1.50 % (7240)Instructions burned: 19 (million)
% 2.15/1.50 % (7240)------------------------------
% 2.15/1.50 % (7240)------------------------------
% 2.15/1.50 % (7242)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/6Mi)
% 2.15/1.50 % (7244)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_6848 for (2999ds/21Mi)
% 2.15/1.51 % (7243)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_6848 for (2999ds/902Mi)
% 2.15/1.51 % (7242)Instruction limit reached!
% 2.15/1.51 % (7242)------------------------------
% 2.15/1.51 % (7242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.51 % (7242)Termination reason: Unknown
% 2.15/1.51 % (7242)Termination phase: shuffling
% 2.15/1.51
% 2.15/1.51 % (7242)Memory used [KB]: 1279
% 2.15/1.51 % (7242)Time elapsed: 0.005 s
% 2.15/1.51 % (7242)Instructions burned: 8 (million)
% 2.15/1.51 % (7242)------------------------------
% 2.15/1.51 % (7242)------------------------------
% 2.15/1.51 % (7246)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_6848 for (2999ds/6Mi)
% 2.15/1.51 % (7245)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/5Mi)
% 2.15/1.51 % (7246)Instruction limit reached!
% 2.15/1.51 % (7246)------------------------------
% 2.15/1.51 % (7246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.51 % (7246)Termination reason: Unknown
% 2.15/1.51 % (7246)Termination phase: shuffling
% 2.15/1.51
% 2.15/1.51 % (7246)Memory used [KB]: 1279
% 2.15/1.51 % (7246)Time elapsed: 0.003 s
% 2.15/1.51 % (7246)Instructions burned: 7 (million)
% 2.15/1.51 % (7246)------------------------------
% 2.15/1.51 % (7246)------------------------------
% 2.15/1.51 % (7245)Instruction limit reached!
% 2.15/1.51 % (7245)------------------------------
% 2.15/1.51 % (7245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.51 % (7245)Termination reason: Unknown
% 2.15/1.51 % (7245)Termination phase: shuffling
% 2.15/1.51
% 2.15/1.51 % (7245)Memory used [KB]: 1279
% 2.15/1.51 % (7245)Time elapsed: 0.003 s
% 2.15/1.51 % (7245)Instructions burned: 6 (million)
% 2.15/1.51 % (7245)------------------------------
% 2.15/1.51 % (7245)------------------------------
% 2.15/1.51 % (7244)Instruction limit reached!
% 2.15/1.51 % (7244)------------------------------
% 2.15/1.51 % (7244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.51 % (7244)Termination reason: Unknown
% 2.15/1.51 % (7244)Termination phase: Property scanning
% 2.15/1.51
% 2.15/1.51 % (7244)Memory used [KB]: 1535
% 2.15/1.51 % (7244)Time elapsed: 0.007 s
% 2.15/1.51 % (7244)Instructions burned: 21 (million)
% 2.15/1.51 % (7244)------------------------------
% 2.15/1.51 % (7244)------------------------------
% 2.15/1.52 % (7248)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_6848 for (2999ds/779Mi)
% 2.15/1.52 % (7249)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_6848 for (2999ds/19Mi)
% 2.15/1.52 % (7250)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/879Mi)
% 2.15/1.52 % (7247)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/377Mi)
% 2.15/1.52 % (7249)Instruction limit reached!
% 2.15/1.52 % (7249)------------------------------
% 2.15/1.52 % (7249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.52 % (7249)Termination reason: Unknown
% 2.15/1.52 % (7249)Termination phase: Property scanning
% 2.15/1.52
% 2.15/1.52 % (7249)Memory used [KB]: 1407
% 2.15/1.52 % (7249)Time elapsed: 0.007 s
% 2.15/1.52 % (7249)Instructions burned: 19 (million)
% 2.15/1.52 % (7249)------------------------------
% 2.15/1.52 % (7249)------------------------------
% 2.15/1.53 % (7243)Refutation not found, incomplete strategy
% 2.15/1.53 % (7243)------------------------------
% 2.15/1.53 % (7243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.53 % (7243)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.53
% 2.15/1.53
% 2.15/1.53 % (7243)Memory used [KB]: 6012
% 2.15/1.53 % (7243)Time elapsed: 0.026 s
% 2.15/1.53 % (7243)Instructions burned: 49 (million)
% 2.15/1.53 % (7243)------------------------------
% 2.15/1.53 % (7243)------------------------------
% 2.15/1.53 % (7251)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6848 for (2999ds/17Mi)
% 2.15/1.54 % (7251)Instruction limit reached!
% 2.15/1.54 % (7251)------------------------------
% 2.15/1.54 % (7251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.54 % (7251)Termination reason: Unknown
% 2.15/1.54 % (7251)Termination phase: Property scanning
% 2.15/1.54
% 2.15/1.54 % (7251)Memory used [KB]: 1535
% 2.15/1.54 % (7251)Time elapsed: 0.007 s
% 2.15/1.54 % (7251)Instructions burned: 19 (million)
% 2.15/1.54 % (7251)------------------------------
% 2.15/1.54 % (7251)------------------------------
% 2.15/1.55 % (7252)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6848 for (2998ds/3Mi)
% 2.15/1.55 % (7253)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6848 for (2998ds/30Mi)
% 2.15/1.55 % (7252)Instruction limit reached!
% 2.15/1.55 % (7252)------------------------------
% 2.15/1.55 % (7252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.55 % (7252)Termination reason: Unknown
% 2.15/1.55 % (7252)Termination phase: shuffling
% 2.15/1.55
% 2.15/1.55 % (7252)Memory used [KB]: 1151
% 2.15/1.55 % (7252)Time elapsed: 0.004 s
% 2.15/1.55 % (7252)Instructions burned: 4 (million)
% 2.15/1.55 % (7252)------------------------------
% 2.15/1.55 % (7252)------------------------------
% 2.15/1.56 % (7253)Instruction limit reached!
% 2.15/1.56 % (7253)------------------------------
% 2.15/1.56 % (7253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.56 % (7253)Termination reason: Unknown
% 2.15/1.56 % (7253)Termination phase: Property scanning
% 2.15/1.56
% 2.15/1.56 % (7253)Memory used [KB]: 1535
% 2.15/1.56 % (7253)Time elapsed: 0.010 s
% 2.15/1.56 % (7253)Instructions burned: 30 (million)
% 2.15/1.56 % (7253)------------------------------
% 2.15/1.56 % (7253)------------------------------
% 2.15/1.56 % (7254)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6848 for (2998ds/127Mi)
% 2.15/1.57 % (7255)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6848 for (2998ds/100Mi)
% 2.15/1.59 % (7255)Instruction limit reached!
% 2.15/1.59 % (7255)------------------------------
% 2.15/1.59 % (7255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.59 % (7255)Termination reason: Unknown
% 2.15/1.59 % (7255)Termination phase: Saturation
% 2.15/1.59
% 2.15/1.59 % (7255)Memory used [KB]: 6012
% 2.15/1.59 % (7255)Time elapsed: 0.028 s
% 2.15/1.59 % (7255)Instructions burned: 100 (million)
% 2.15/1.59 % (7255)------------------------------
% 2.15/1.59 % (7255)------------------------------
% 2.15/1.60 % (7254)Instruction limit reached!
% 2.15/1.60 % (7254)------------------------------
% 2.15/1.60 % (7254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.60 % (7254)Termination reason: Unknown
% 2.15/1.60 % (7254)Termination phase: Saturation
% 2.15/1.60
% 2.15/1.60 % (7254)Memory used [KB]: 6140
% 2.15/1.60 % (7254)Time elapsed: 0.039 s
% 2.15/1.60 % (7254)Instructions burned: 130 (million)
% 2.15/1.60 % (7254)------------------------------
% 2.15/1.60 % (7254)------------------------------
% 2.15/1.60 % (7256)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_6848 for (2998ds/3Mi)
% 2.15/1.61 % (7256)Instruction limit reached!
% 2.15/1.61 % (7256)------------------------------
% 2.15/1.61 % (7256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.61 % (7256)Termination reason: Unknown
% 2.15/1.61 % (7256)Termination phase: shuffling
% 2.15/1.61
% 2.15/1.61 % (7256)Memory used [KB]: 1151
% 2.15/1.61 % (7256)Time elapsed: 0.003 s
% 2.15/1.61 % (7256)Instructions burned: 5 (million)
% 2.15/1.61 % (7256)------------------------------
% 2.15/1.61 % (7256)------------------------------
% 2.15/1.61 % (7257)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_6848 for (2998ds/20Mi)
% 2.15/1.62 % (7258)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_6848 for (2998ds/86Mi)
% 2.15/1.62 % (7257)Instruction limit reached!
% 2.15/1.62 % (7257)------------------------------
% 2.15/1.62 % (7257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.62 % (7257)Termination reason: Unknown
% 2.15/1.62 % (7257)Termination phase: Property scanning
% 2.15/1.62
% 2.15/1.62 % (7257)Memory used [KB]: 1535
% 2.15/1.62 % (7257)Time elapsed: 0.008 s
% 2.15/1.62 % (7257)Instructions burned: 22 (million)
% 2.15/1.62 % (7257)------------------------------
% 2.15/1.62 % (7257)------------------------------
% 2.15/1.63 % (7259)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_6848 for (2998ds/107Mi)
% 2.15/1.64 % (7258)Instruction limit reached!
% 2.15/1.64 % (7258)------------------------------
% 2.15/1.64 % (7258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.64 % (7258)Termination reason: Unknown
% 2.15/1.64 % (7258)Termination phase: Saturation
% 2.15/1.64
% 2.15/1.64 % (7258)Memory used [KB]: 6012
% 2.15/1.64 % (7258)Time elapsed: 0.025 s
% 2.15/1.64 % (7258)Instructions burned: 86 (million)
% 2.15/1.64 % (7258)------------------------------
% 2.15/1.64 % (7258)------------------------------
% 2.15/1.65 % (7260)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_6848 for (2997ds/39Mi)
% 2.15/1.66 % (7259)Instruction limit reached!
% 2.15/1.66 % (7259)------------------------------
% 2.15/1.66 % (7259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.66 % (7259)Termination reason: Unknown
% 2.15/1.66 % (7259)Termination phase: Saturation
% 2.15/1.66
% 2.15/1.66 % (7259)Memory used [KB]: 6140
% 2.15/1.66 % (7259)Time elapsed: 0.031 s
% 2.15/1.66 % (7259)Instructions burned: 108 (million)
% 2.15/1.66 % (7259)------------------------------
% 2.15/1.66 % (7259)------------------------------
% 2.15/1.66 % (7260)Instruction limit reached!
% 2.15/1.66 % (7260)------------------------------
% 2.15/1.66 % (7260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.66 % (7260)Termination reason: Unknown
% 2.15/1.66 % (7260)Termination phase: Saturation
% 2.15/1.66
% 2.15/1.66 % (7260)Memory used [KB]: 6012
% 2.15/1.66 % (7260)Time elapsed: 0.013 s
% 2.15/1.66 % (7260)Instructions burned: 41 (million)
% 2.15/1.66 % (7260)------------------------------
% 2.15/1.66 % (7260)------------------------------
% 2.15/1.67 % (7247)Instruction limit reached!
% 2.15/1.67 % (7247)------------------------------
% 2.15/1.67 % (7247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.67 % (7247)Termination reason: Unknown
% 2.15/1.67 % (7247)Termination phase: Saturation
% 2.15/1.67
% 2.15/1.67 % (7247)Memory used [KB]: 7419
% 2.15/1.67 % (7247)Time elapsed: 0.144 s
% 2.15/1.67 % (7247)Instructions burned: 380 (million)
% 2.15/1.67 % (7247)------------------------------
% 2.15/1.67 % (7247)------------------------------
% 2.15/1.67 % (7261)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_6848 for (2997ds/448Mi)
% 2.15/1.67 % (7262)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_6848 for (2997ds/46Mi)
% 2.15/1.68 % (7263)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_6848 for (2997ds/98Mi)
% 2.15/1.68 % (7261)Refutation not found, incomplete strategy
% 2.15/1.68 % (7261)------------------------------
% 2.15/1.68 % (7261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.68 % (7261)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.68
% 2.15/1.68
% 2.15/1.68 % (7261)Memory used [KB]: 6012
% 2.15/1.68 % (7261)Time elapsed: 0.012 s
% 2.15/1.68 % (7261)Instructions burned: 37 (million)
% 2.15/1.68 % (7261)------------------------------
% 2.15/1.68 % (7261)------------------------------
% 2.15/1.68 % (7262)Instruction limit reached!
% 2.15/1.68 % (7262)------------------------------
% 2.15/1.68 % (7262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.68 % (7262)Termination reason: Unknown
% 2.15/1.68 % (7262)Termination phase: Property scanning
% 2.15/1.68
% 2.15/1.68 % (7262)Memory used [KB]: 1535
% 2.15/1.68 % (7262)Time elapsed: 0.014 s
% 2.15/1.68 % (7262)Instructions burned: 47 (million)
% 2.15/1.68 % (7262)------------------------------
% 2.15/1.68 % (7262)------------------------------
% 2.15/1.68 % (7241)Instruction limit reached!
% 2.15/1.68 % (7241)------------------------------
% 2.15/1.68 % (7241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.68 % (7241)Termination reason: Unknown
% 2.15/1.68 % (7241)Termination phase: Saturation
% 2.15/1.68
% 2.15/1.68 % (7241)Memory used [KB]: 9083
% 2.15/1.68 % (7241)Time elapsed: 0.192 s
% 2.15/1.68 % (7241)Instructions burned: 711 (million)
% 2.15/1.68 % (7241)------------------------------
% 2.15/1.68 % (7241)------------------------------
% 2.15/1.69 % (7264)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_6848 for (2997ds/507Mi)
% 2.15/1.69 % (7265)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_6848 for (2997ds/149Mi)
% 2.15/1.69 % (7266)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_6848 for (2997ds/39Mi)
% 2.15/1.70 % (7263)Instruction limit reached!
% 2.15/1.70 % (7263)------------------------------
% 2.15/1.70 % (7263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.70 % (7263)Termination reason: Unknown
% 2.15/1.70 % (7263)Termination phase: Saturation
% 2.15/1.70
% 2.15/1.70 % (7263)Memory used [KB]: 1535
% 2.15/1.70 % (7263)Time elapsed: 0.028 s
% 2.15/1.70 % (7263)Instructions burned: 100 (million)
% 2.15/1.70 % (7263)------------------------------
% 2.15/1.70 % (7263)------------------------------
% 2.15/1.70 % (7266)Instruction limit reached!
% 2.15/1.70 % (7266)------------------------------
% 2.15/1.70 % (7266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.70 % (7266)Termination reason: Unknown
% 2.15/1.70 % (7266)Termination phase: Property scanning
% 2.15/1.70
% 2.15/1.70 % (7266)Memory used [KB]: 1535
% 2.15/1.70 % (7266)Time elapsed: 0.011 s
% 2.15/1.70 % (7266)Instructions burned: 41 (million)
% 2.15/1.70 % (7266)------------------------------
% 2.15/1.70 % (7266)------------------------------
% 2.15/1.71 % (7267)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_6848 for (2997ds/6Mi)
% 2.15/1.71 % (7268)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_6848 for (2997ds/1087Mi)
% 2.15/1.71 % (7267)Instruction limit reached!
% 2.15/1.71 % (7267)------------------------------
% 2.15/1.71 % (7267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.71 % (7267)Termination reason: Unknown
% 2.15/1.71 % (7267)Termination phase: shuffling
% 2.15/1.71
% 2.15/1.71 % (7267)Memory used [KB]: 1279
% 2.15/1.71 % (7267)Time elapsed: 0.004 s
% 2.15/1.71 % (7267)Instructions burned: 8 (million)
% 2.15/1.71 % (7267)------------------------------
% 2.15/1.71 % (7267)------------------------------
% 2.15/1.72 % (7269)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_6848 for (2997ds/47Mi)
% 2.15/1.74 % (7265)Instruction limit reached!
% 2.15/1.74 % (7265)------------------------------
% 2.15/1.74 % (7265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.74 % (7265)Termination reason: Unknown
% 2.15/1.74 % (7265)Termination phase: Saturation
% 2.15/1.74
% 2.15/1.74 % (7265)Memory used [KB]: 6396
% 2.15/1.74 % (7265)Time elapsed: 0.067 s
% 2.15/1.74 % (7265)Instructions burned: 150 (million)
% 2.15/1.74 % (7265)------------------------------
% 2.15/1.74 % (7265)------------------------------
% 2.15/1.74 % (7269)Instruction limit reached!
% 2.15/1.74 % (7269)------------------------------
% 2.15/1.74 % (7269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.74 % (7269)Termination reason: Unknown
% 2.15/1.74 % (7269)Termination phase: Saturation
% 2.15/1.74
% 2.15/1.74 % (7269)Memory used [KB]: 6012
% 2.15/1.74 % (7269)Time elapsed: 0.015 s
% 2.15/1.74 % (7269)Instructions burned: 49 (million)
% 2.15/1.74 % (7269)------------------------------
% 2.15/1.74 % (7269)------------------------------
% 2.15/1.74 % (7248)Instruction limit reached!
% 2.15/1.74 % (7248)------------------------------
% 2.15/1.74 % (7248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.74 % (7248)Termination reason: Unknown
% 2.15/1.74 % (7248)Termination phase: Saturation
% 2.15/1.74
% 2.15/1.74 % (7248)Memory used [KB]: 7164
% 2.15/1.74 % (7248)Time elapsed: 0.222 s
% 2.15/1.74 % (7248)Instructions burned: 782 (million)
% 2.15/1.74 % (7248)------------------------------
% 2.15/1.74 % (7248)------------------------------
% 2.15/1.75 % (7270)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_6848 for (2996ds/44Mi)
% 2.15/1.75 % (7271)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_6848 for (2996ds/432Mi)
% 2.15/1.75 % (7272)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/62Mi)
% 2.15/1.76 % (7270)Refutation not found, incomplete strategy
% 2.15/1.76 % (7270)------------------------------
% 2.15/1.76 % (7270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.76 % (7270)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.76
% 2.15/1.76
% 2.15/1.76 % (7270)Memory used [KB]: 1535
% 2.15/1.76 % (7270)Time elapsed: 0.011 s
% 2.15/1.76 % (7270)Instructions burned: 33 (million)
% 2.15/1.76 % (7270)------------------------------
% 2.15/1.76 % (7270)------------------------------
% 2.15/1.76 % (7272)Instruction limit reached!
% 2.15/1.76 % (7272)------------------------------
% 2.15/1.76 % (7272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.76 % (7272)Termination reason: Unknown
% 2.15/1.76 % (7272)Termination phase: Saturation
% 2.15/1.76
% 2.15/1.76 % (7272)Memory used [KB]: 6268
% 2.15/1.76 % (7272)Time elapsed: 0.017 s
% 2.15/1.76 % (7272)Instructions burned: 63 (million)
% 2.15/1.76 % (7272)------------------------------
% 2.15/1.76 % (7272)------------------------------
% 2.15/1.77 % (7273)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/31Mi)
% 2.15/1.77 % (7250)Instruction limit reached!
% 2.15/1.77 % (7250)------------------------------
% 2.15/1.77 % (7250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.77 % (7250)Termination reason: Unknown
% 2.15/1.77 % (7250)Termination phase: Saturation
% 2.15/1.77
% 2.15/1.77 % (7250)Memory used [KB]: 9210
% 2.15/1.77 % (7250)Time elapsed: 0.255 s
% 2.15/1.77 % (7250)Instructions burned: 879 (million)
% 2.15/1.77 % (7250)------------------------------
% 2.15/1.77 % (7250)------------------------------
% 2.15/1.77 % (7274)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/96Mi)
% 2.15/1.78 % (7273)Instruction limit reached!
% 2.15/1.78 % (7273)------------------------------
% 2.15/1.78 % (7273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.78 % (7273)Termination reason: Unknown
% 2.15/1.78 % (7273)Termination phase: Property scanning
% 2.15/1.78
% 2.15/1.78 % (7273)Memory used [KB]: 1535
% 2.15/1.78 % (7273)Time elapsed: 0.011 s
% 2.15/1.78 % (7273)Instructions burned: 34 (million)
% 2.15/1.78 % (7273)------------------------------
% 2.15/1.78 % (7273)------------------------------
% 2.15/1.78 % (7232)Instruction limit reached!
% 2.15/1.78 % (7232)------------------------------
% 2.15/1.78 % (7232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.78 % (7232)Termination reason: Unknown
% 2.15/1.78 % (7232)Termination phase: Saturation
% 2.15/1.78
% 2.15/1.78 % (7232)Memory used [KB]: 6780
% 2.15/1.78 % (7232)Time elapsed: 0.311 s
% 2.15/1.78 % (7232)Instructions burned: 1043 (million)
% 2.15/1.78 % (7232)------------------------------
% 2.15/1.78 % (7232)------------------------------
% 2.15/1.78 % (7275)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/453Mi)
% 2.15/1.79 % (7276)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/71Mi)
% 2.15/1.79 % (7277)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/83Mi)
% 2.15/1.80 % (7274)Instruction limit reached!
% 2.15/1.80 % (7274)------------------------------
% 2.15/1.80 % (7274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.80 % (7274)Termination reason: Unknown
% 2.15/1.80 % (7274)Termination phase: Saturation
% 2.15/1.80
% 2.15/1.80 % (7274)Memory used [KB]: 6012
% 2.15/1.80 % (7274)Time elapsed: 0.025 s
% 2.15/1.80 % (7274)Instructions burned: 98 (million)
% 2.15/1.80 % (7274)------------------------------
% 2.15/1.80 % (7274)------------------------------
% 2.15/1.80 % (7277)Refutation not found, incomplete strategy
% 2.15/1.80 % (7277)------------------------------
% 2.15/1.80 % (7277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.80 % (7277)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.80
% 2.15/1.80
% 2.15/1.80 % (7277)Memory used [KB]: 6012
% 2.15/1.80 % (7277)Time elapsed: 0.011 s
% 2.15/1.80 % (7277)Instructions burned: 33 (million)
% 2.15/1.80 % (7277)------------------------------
% 2.15/1.80 % (7277)------------------------------
% 2.15/1.81 % (7278)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/11Mi)
% 2.15/1.81 % (7276)Instruction limit reached!
% 2.15/1.81 % (7276)------------------------------
% 2.15/1.81 % (7276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.81 % (7276)Termination reason: Unknown
% 2.15/1.81 % (7276)Termination phase: Saturation
% 2.15/1.81
% 2.15/1.81 % (7276)Memory used [KB]: 6140
% 2.15/1.81 % (7276)Time elapsed: 0.023 s
% 2.15/1.81 % (7276)Instructions burned: 73 (million)
% 2.15/1.81 % (7276)------------------------------
% 2.15/1.81 % (7276)------------------------------
% 2.15/1.81 % (7279)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/41Mi)
% 2.15/1.81 % (7278)Instruction limit reached!
% 2.15/1.81 % (7278)------------------------------
% 2.15/1.81 % (7278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.81 % (7278)Termination reason: Unknown
% 2.15/1.81 % (7278)Termination phase: shuffling
% 2.15/1.81
% 2.15/1.81 % (7278)Memory used [KB]: 1279
% 2.15/1.81 % (7278)Time elapsed: 0.004 s
% 2.15/1.81 % (7278)Instructions burned: 12 (million)
% 2.15/1.81 % (7278)------------------------------
% 2.15/1.81 % (7278)------------------------------
% 2.15/1.82 % (7280)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/6Mi)
% 2.15/1.82 % (7281)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/150Mi)
% 2.15/1.82 % (7280)Instruction limit reached!
% 2.15/1.82 % (7280)------------------------------
% 2.15/1.82 % (7280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.82 % (7280)Termination reason: Unknown
% 2.15/1.82 % (7280)Termination phase: shuffling
% 2.15/1.82
% 2.15/1.82 % (7280)Memory used [KB]: 1279
% 2.15/1.82 % (7280)Time elapsed: 0.004 s
% 2.15/1.82 % (7280)Instructions burned: 8 (million)
% 2.15/1.82 % (7280)------------------------------
% 2.15/1.82 % (7280)------------------------------
% 2.15/1.82 % (7279)Instruction limit reached!
% 2.15/1.82 % (7279)------------------------------
% 2.15/1.82 % (7279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.82 % (7279)Termination reason: Unknown
% 2.15/1.82 % (7279)Termination phase: Saturation
% 2.15/1.82
% 2.15/1.82 % (7279)Memory used [KB]: 6012
% 2.15/1.82 % (7279)Time elapsed: 0.013 s
% 2.15/1.82 % (7279)Instructions burned: 42 (million)
% 2.15/1.82 % (7279)------------------------------
% 2.15/1.82 % (7279)------------------------------
% 2.15/1.83 % (7282)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/343Mi)
% 2.15/1.83 % (7283)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_6848 for (2996ds/109Mi)
% 2.15/1.83 % (7281)Refutation not found, incomplete strategy
% 2.15/1.83 % (7281)------------------------------
% 2.15/1.83 % (7281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.83 % (7281)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.83
% 2.15/1.83
% 2.15/1.83 % (7281)Memory used [KB]: 6012
% 2.15/1.83 % (7281)Time elapsed: 0.015 s
% 2.15/1.83 % (7281)Instructions burned: 54 (million)
% 2.15/1.83 % (7281)------------------------------
% 2.15/1.83 % (7281)------------------------------
% 2.15/1.83 % (7264)Instruction limit reached!
% 2.15/1.83 % (7264)------------------------------
% 2.15/1.83 % (7264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.83 % (7264)Termination reason: Unknown
% 2.15/1.83 % (7264)Termination phase: Saturation
% 2.15/1.83
% 2.15/1.83 % (7264)Memory used [KB]: 6524
% 2.15/1.83 % (7264)Time elapsed: 0.148 s
% 2.15/1.83 % (7264)Instructions burned: 510 (million)
% 2.15/1.83 % (7264)------------------------------
% 2.15/1.83 % (7264)------------------------------
% 2.15/1.84 % (7282)Refutation not found, incomplete strategy
% 2.15/1.84 % (7282)------------------------------
% 2.15/1.84 % (7282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.84 % (7282)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.84
% 2.15/1.84
% 2.15/1.84 % (7282)Memory used [KB]: 6012
% 2.15/1.84 % (7282)Time elapsed: 0.011 s
% 2.15/1.84 % (7282)Instructions burned: 34 (million)
% 2.15/1.84 % (7282)------------------------------
% 2.15/1.84 % (7282)------------------------------
% 2.15/1.84 % (7284)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/253Mi)
% 2.15/1.85 % (7285)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/140Mi)
% 2.15/1.85 % (7286)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/614Mi)
% 2.15/1.85 % (7284)Refutation not found, incomplete strategy
% 2.15/1.85 % (7284)------------------------------
% 2.15/1.85 % (7284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.85 % (7284)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.85
% 2.15/1.85
% 2.15/1.85 % (7284)Memory used [KB]: 6012
% 2.15/1.85 % (7284)Time elapsed: 0.010 s
% 2.15/1.85 % (7284)Instructions burned: 33 (million)
% 2.15/1.85 % (7284)------------------------------
% 2.15/1.85 % (7284)------------------------------
% 2.15/1.86 % (7283)Instruction limit reached!
% 2.15/1.86 % (7283)------------------------------
% 2.15/1.86 % (7283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.86 % (7283)Termination reason: Unknown
% 2.15/1.86 % (7283)Termination phase: Saturation
% 2.15/1.86
% 2.15/1.86 % (7283)Memory used [KB]: 6140
% 2.15/1.86 % (7283)Time elapsed: 0.031 s
% 2.15/1.86 % (7283)Instructions burned: 109 (million)
% 2.15/1.86 % (7283)------------------------------
% 2.15/1.86 % (7283)------------------------------
% 2.15/1.86 % (7285)Refutation not found, incomplete strategy
% 2.15/1.86 % (7285)------------------------------
% 2.15/1.86 % (7285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.86 % (7285)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.86
% 2.15/1.86
% 2.15/1.86 % (7285)Memory used [KB]: 6012
% 2.15/1.86 % (7285)Time elapsed: 0.018 s
% 2.15/1.86 % (7285)Instructions burned: 59 (million)
% 2.15/1.86 % (7285)------------------------------
% 2.15/1.86 % (7285)------------------------------
% 2.15/1.86 % (7287)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/202Mi)
% 2.15/1.87 % (7271)Instruction limit reached!
% 2.15/1.87 % (7271)------------------------------
% 2.15/1.87 % (7271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.87 % (7271)Termination reason: Unknown
% 2.15/1.87 % (7271)Termination phase: Saturation
% 2.15/1.87
% 2.15/1.87 % (7271)Memory used [KB]: 2430
% 2.15/1.87 % (7271)Time elapsed: 0.120 s
% 2.15/1.87 % (7271)Instructions burned: 434 (million)
% 2.15/1.87 % (7271)------------------------------
% 2.15/1.87 % (7271)------------------------------
% 2.15/1.87 % (7288)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/339Mi)
% 2.15/1.87 % (7289)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=283:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/283Mi)
% 2.15/1.88 % (7287)Refutation not found, incomplete strategy
% 2.15/1.88 % (7287)------------------------------
% 2.15/1.88 % (7287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.88 % (7287)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.88
% 2.15/1.88
% 2.15/1.88 % (7287)Memory used [KB]: 6012
% 2.15/1.88 % (7287)Time elapsed: 0.014 s
% 2.15/1.88 % (7287)Instructions burned: 51 (million)
% 2.15/1.88 % (7287)------------------------------
% 2.15/1.88 % (7287)------------------------------
% 2.15/1.88 % (7290)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/134Mi)
% 2.15/1.89 % (7291)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/298Mi)
% 2.15/1.89 % (7288)Refutation not found, incomplete strategy
% 2.15/1.89 % (7288)------------------------------
% 2.15/1.89 % (7288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.89 % (7288)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.89
% 2.15/1.89
% 2.15/1.89 % (7288)Memory used [KB]: 6012
% 2.15/1.89 % (7288)Time elapsed: 0.017 s
% 2.15/1.89 % (7288)Instructions burned: 57 (million)
% 2.15/1.89 % (7288)------------------------------
% 2.15/1.89 % (7288)------------------------------
% 2.15/1.90 % (7292)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/192Mi)
% 2.15/1.91 % (7275)Instruction limit reached!
% 2.15/1.91 % (7275)------------------------------
% 2.15/1.91 % (7275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.91 % (7275)Termination reason: Unknown
% 2.15/1.91 % (7275)Termination phase: Saturation
% 2.15/1.91
% 2.15/1.91 % (7275)Memory used [KB]: 6396
% 2.15/1.91 % (7275)Time elapsed: 0.128 s
% 2.15/1.91 % (7275)Instructions burned: 455 (million)
% 2.15/1.91 % (7275)------------------------------
% 2.15/1.91 % (7275)------------------------------
% 2.15/1.91 % (7290)Instruction limit reached!
% 2.15/1.91 % (7290)------------------------------
% 2.15/1.91 % (7290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.91 % (7290)Termination reason: Unknown
% 2.15/1.91 % (7290)Termination phase: Saturation
% 2.15/1.91
% 2.15/1.91 % (7290)Memory used [KB]: 6140
% 2.15/1.91 % (7290)Time elapsed: 0.039 s
% 2.15/1.91 % (7290)Instructions burned: 135 (million)
% 2.15/1.91 % (7290)------------------------------
% 2.15/1.91 % (7290)------------------------------
% 2.15/1.92 % (7293)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/258Mi)
% 2.15/1.92 % (7294)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_6848 for (2995ds/90Mi)
% 2.15/1.95 % (7289)Instruction limit reached!
% 2.15/1.95 % (7289)------------------------------
% 2.15/1.95 % (7289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.95 % (7289)Termination reason: Unknown
% 2.15/1.95 % (7289)Termination phase: Saturation
% 2.15/1.95
% 2.15/1.95 % (7289)Memory used [KB]: 6652
% 2.15/1.95 % (7289)Time elapsed: 0.076 s
% 2.15/1.95 % (7289)Instructions burned: 283 (million)
% 2.15/1.95 % (7289)------------------------------
% 2.15/1.95 % (7289)------------------------------
% 2.15/1.95 % (7292)Instruction limit reached!
% 2.15/1.95 % (7292)------------------------------
% 2.15/1.95 % (7292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.95 % (7292)Termination reason: Unknown
% 2.15/1.95 % (7292)Termination phase: Saturation
% 2.15/1.95
% 2.15/1.95 % (7292)Memory used [KB]: 6524
% 2.15/1.95 % (7292)Time elapsed: 0.052 s
% 2.15/1.95 % (7292)Instructions burned: 194 (million)
% 2.15/1.95 % (7292)------------------------------
% 2.15/1.95 % (7292)------------------------------
% 2.15/1.95 % (7294)Instruction limit reached!
% 2.15/1.95 % (7294)------------------------------
% 2.15/1.95 % (7294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.95 % (7294)Termination reason: Unknown
% 2.15/1.95 % (7294)Termination phase: Saturation
% 2.15/1.95
% 2.15/1.95 % (7294)Memory used [KB]: 6268
% 2.15/1.95 % (7294)Time elapsed: 0.030 s
% 2.15/1.95 % (7294)Instructions burned: 91 (million)
% 2.15/1.95 % (7294)------------------------------
% 2.15/1.95 % (7294)------------------------------
% 2.15/1.96 % (7295)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/231Mi)
% 2.15/1.96 % (7296)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/458Mi)
% 2.15/1.96 % (7297)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/31Mi)
% 2.15/1.97 % (7291)Instruction limit reached!
% 2.15/1.97 % (7291)------------------------------
% 2.15/1.97 % (7291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.97 % (7291)Termination reason: Unknown
% 2.15/1.97 % (7291)Termination phase: Saturation
% 2.15/1.97
% 2.15/1.97 % (7291)Memory used [KB]: 6396
% 2.15/1.97 % (7291)Time elapsed: 0.081 s
% 2.15/1.97 % (7291)Instructions burned: 300 (million)
% 2.15/1.97 % (7291)------------------------------
% 2.15/1.97 % (7291)------------------------------
% 2.15/1.97 % (7297)Instruction limit reached!
% 2.15/1.97 % (7297)------------------------------
% 2.15/1.97 % (7297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.97 % (7297)Termination reason: Unknown
% 2.15/1.97 % (7297)Termination phase: Property scanning
% 2.15/1.97
% 2.15/1.97 % (7297)Memory used [KB]: 1535
% 2.15/1.97 % (7297)Time elapsed: 0.009 s
% 2.15/1.97 % (7297)Instructions burned: 32 (million)
% 2.15/1.97 % (7297)------------------------------
% 2.15/1.97 % (7297)------------------------------
% 2.15/1.97 % (7298)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/297Mi)
% 2.15/1.98 % (7299)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/987Mi)
% 2.15/1.99 % (7298)Refutation not found, incomplete strategy
% 2.15/1.99 % (7298)------------------------------
% 2.15/1.99 % (7298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.99 % (7298)Termination reason: Refutation not found, incomplete strategy
% 2.15/1.99
% 2.15/1.99
% 2.15/1.99 % (7298)Memory used [KB]: 6012
% 2.15/1.99 % (7298)Time elapsed: 0.011 s
% 2.15/1.99 % (7298)Instructions burned: 38 (million)
% 2.15/1.99 % (7298)------------------------------
% 2.15/1.99 % (7298)------------------------------
% 2.15/1.99 % (7293)Instruction limit reached!
% 2.15/1.99 % (7293)------------------------------
% 2.15/1.99 % (7293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/1.99 % (7293)Termination reason: Unknown
% 2.15/1.99 % (7293)Termination phase: Saturation
% 2.15/1.99
% 2.15/1.99 % (7293)Memory used [KB]: 6652
% 2.15/1.99 % (7293)Time elapsed: 0.070 s
% 2.15/1.99 % (7293)Instructions burned: 261 (million)
% 2.15/1.99 % (7293)------------------------------
% 2.15/1.99 % (7293)------------------------------
% 2.15/2.00 % (7300)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/182Mi)
% 2.15/2.00 % (7301)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/182Mi)
% 2.15/2.00 % (7268)Instruction limit reached!
% 2.15/2.00 % (7268)------------------------------
% 2.15/2.00 % (7268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/2.00 % (7268)Termination reason: Unknown
% 2.15/2.00 % (7268)Termination phase: Saturation
% 2.15/2.00
% 2.15/2.00 % (7268)Memory used [KB]: 9978
% 2.15/2.00 % (7268)Time elapsed: 0.291 s
% 2.15/2.00 % (7268)Instructions burned: 1087 (million)
% 2.15/2.00 % (7268)------------------------------
% 2.15/2.00 % (7268)------------------------------
% 2.15/2.01 % (7295)Instruction limit reached!
% 2.15/2.01 % (7295)------------------------------
% 2.15/2.01 % (7295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.15/2.01 % (7295)Termination reason: Unknown
% 2.15/2.01 % (7295)Termination phase: Saturation
% 2.15/2.01
% 2.15/2.01 % (7295)Memory used [KB]: 6396
% 2.15/2.01 % (7295)Time elapsed: 0.055 s
% 2.15/2.01 % (7295)Instructions burned: 234 (million)
% 2.15/2.01 % (7295)------------------------------
% 2.15/2.01 % (7295)------------------------------
% 6.22/2.01 % (7302)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/154Mi)
% 6.22/2.01 % (7286)Instruction limit reached!
% 6.22/2.01 % (7286)------------------------------
% 6.22/2.01 % (7286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.01 % (7286)Termination reason: Unknown
% 6.22/2.01 % (7286)Termination phase: Saturation
% 6.22/2.01
% 6.22/2.01 % (7286)Memory used [KB]: 8699
% 6.22/2.01 % (7286)Time elapsed: 0.165 s
% 6.22/2.01 % (7286)Instructions burned: 614 (million)
% 6.22/2.01 % (7286)------------------------------
% 6.22/2.01 % (7286)------------------------------
% 6.22/2.02 % (7303)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/79Mi)
% 6.22/2.02 % (7304)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_6848 for (2994ds/216Mi)
% 6.22/2.03 % (7304)Refutation not found, incomplete strategy
% 6.22/2.03 % (7304)------------------------------
% 6.22/2.03 % (7304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.03 % (7304)Termination reason: Refutation not found, incomplete strategy
% 6.22/2.03
% 6.22/2.03
% 6.22/2.03 % (7304)Memory used [KB]: 6012
% 6.22/2.03 % (7304)Time elapsed: 0.010 s
% 6.22/2.03 % (7304)Instructions burned: 36 (million)
% 6.22/2.03 % (7304)------------------------------
% 6.22/2.03 % (7304)------------------------------
% 6.22/2.04 % (7303)Instruction limit reached!
% 6.22/2.04 % (7303)------------------------------
% 6.22/2.04 % (7303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.04 % (7303)Termination reason: Unknown
% 6.22/2.04 % (7303)Termination phase: Saturation
% 6.22/2.04
% 6.22/2.04 % (7303)Memory used [KB]: 6012
% 6.22/2.04 % (7303)Time elapsed: 0.021 s
% 6.22/2.04 % (7303)Instructions burned: 80 (million)
% 6.22/2.04 % (7303)------------------------------
% 6.22/2.04 % (7303)------------------------------
% 6.22/2.04 % (7305)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/114Mi)
% 6.22/2.04 % (7300)Instruction limit reached!
% 6.22/2.04 % (7300)------------------------------
% 6.22/2.04 % (7300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.04 % (7300)Termination reason: Unknown
% 6.22/2.04 % (7300)Termination phase: Saturation
% 6.22/2.04
% 6.22/2.04 % (7300)Memory used [KB]: 6524
% 6.22/2.04 % (7300)Time elapsed: 0.049 s
% 6.22/2.04 % (7300)Instructions burned: 184 (million)
% 6.22/2.04 % (7300)------------------------------
% 6.22/2.04 % (7300)------------------------------
% 6.22/2.05 % (7306)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/922Mi)
% 6.22/2.05 % (7307)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/182Mi)
% 6.22/2.06 % (7302)Instruction limit reached!
% 6.22/2.06 % (7302)------------------------------
% 6.22/2.06 % (7302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.06 % (7302)Termination reason: Unknown
% 6.22/2.06 % (7302)Termination phase: Saturation
% 6.22/2.06
% 6.22/2.06 % (7302)Memory used [KB]: 6780
% 6.22/2.06 % (7302)Time elapsed: 0.044 s
% 6.22/2.06 % (7302)Instructions burned: 155 (million)
% 6.22/2.06 % (7302)------------------------------
% 6.22/2.06 % (7302)------------------------------
% 6.22/2.06 % (7305)Refutation not found, incomplete strategy
% 6.22/2.06 % (7305)------------------------------
% 6.22/2.06 % (7305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.06 % (7305)Termination reason: Refutation not found, incomplete strategy
% 6.22/2.06
% 6.22/2.06
% 6.22/2.06 % (7305)Memory used [KB]: 6012
% 6.22/2.06 % (7305)Time elapsed: 0.015 s
% 6.22/2.06 % (7305)Instructions burned: 54 (million)
% 6.22/2.06 % (7305)------------------------------
% 6.22/2.06 % (7305)------------------------------
% 6.22/2.07 % (7308)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/164Mi)
% 6.22/2.07 % (7309)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/50Mi)
% 6.22/2.08 % (7308)Refutation not found, incomplete strategy
% 6.22/2.08 % (7308)------------------------------
% 6.22/2.08 % (7308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.08 % (7308)Termination reason: Refutation not found, incomplete strategy
% 6.22/2.08
% 6.22/2.08
% 6.22/2.08 % (7308)Memory used [KB]: 1535
% 6.22/2.08 % (7308)Time elapsed: 0.011 s
% 6.22/2.08 % (7308)Instructions burned: 38 (million)
% 6.22/2.08 % (7308)------------------------------
% 6.22/2.08 % (7308)------------------------------
% 6.22/2.08 % (7296)Instruction limit reached!
% 6.22/2.08 % (7296)------------------------------
% 6.22/2.08 % (7296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.08 % (7296)Termination reason: Unknown
% 6.22/2.08 % (7296)Termination phase: Saturation
% 6.22/2.08
% 6.22/2.08 % (7296)Memory used [KB]: 7547
% 6.22/2.08 % (7296)Time elapsed: 0.122 s
% 6.22/2.08 % (7296)Instructions burned: 458 (million)
% 6.22/2.08 % (7296)------------------------------
% 6.22/2.08 % (7296)------------------------------
% 6.22/2.08 % (7309)Instruction limit reached!
% 6.22/2.08 % (7309)------------------------------
% 6.22/2.08 % (7309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.08 % (7309)Termination reason: Unknown
% 6.22/2.08 % (7309)Termination phase: Saturation
% 6.22/2.08
% 6.22/2.08 % (7309)Memory used [KB]: 10490
% 6.22/2.08 % (7309)Time elapsed: 0.014 s
% 6.22/2.08 % (7309)Instructions burned: 51 (million)
% 6.22/2.08 % (7309)------------------------------
% 6.22/2.08 % (7309)------------------------------
% 6.22/2.09 % (7310)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/368Mi)
% 6.22/2.09 % (7311)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/1021Mi)
% 6.22/2.09 % (7312)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/267Mi)
% 6.22/2.10 % (7307)Instruction limit reached!
% 6.22/2.10 % (7307)------------------------------
% 6.22/2.10 % (7307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.10 % (7307)Termination reason: Unknown
% 6.22/2.10 % (7307)Termination phase: Saturation
% 6.22/2.10
% 6.22/2.10 % (7307)Memory used [KB]: 6012
% 6.22/2.10 % (7307)Time elapsed: 0.045 s
% 6.22/2.10 % (7307)Instructions burned: 182 (million)
% 6.22/2.10 % (7307)------------------------------
% 6.22/2.10 % (7307)------------------------------
% 6.22/2.10 % (7301)Instruction limit reached!
% 6.22/2.10 % (7301)------------------------------
% 6.22/2.10 % (7301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.10 % (7301)Termination reason: Unknown
% 6.22/2.10 % (7301)Termination phase: Saturation
% 6.22/2.10
% 6.22/2.10 % (7301)Memory used [KB]: 6524
% 6.22/2.10 % (7301)Time elapsed: 0.121 s
% 6.22/2.10 % (7301)Instructions burned: 182 (million)
% 6.22/2.10 % (7301)------------------------------
% 6.22/2.10 % (7301)------------------------------
% 6.22/2.11 % (7313)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/204Mi)
% 6.22/2.11 % (7314)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/26Mi)
% 6.79/2.12 % (7314)Instruction limit reached!
% 6.79/2.12 % (7314)------------------------------
% 6.79/2.12 % (7314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.12 % (7314)Termination reason: Unknown
% 6.79/2.12 % (7314)Termination phase: Property scanning
% 6.79/2.12
% 6.79/2.12 % (7314)Memory used [KB]: 1407
% 6.79/2.12 % (7314)Time elapsed: 0.008 s
% 6.79/2.12 % (7314)Instructions burned: 26 (million)
% 6.79/2.12 % (7314)------------------------------
% 6.79/2.12 % (7314)------------------------------
% 6.79/2.13 % (7315)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_6848 for (2993ds/53Mi)
% 6.79/2.14 % (7315)Instruction limit reached!
% 6.79/2.14 % (7315)------------------------------
% 6.79/2.14 % (7315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.14 % (7315)Termination reason: Unknown
% 6.79/2.14 % (7315)Termination phase: Saturation
% 6.79/2.14
% 6.79/2.14 % (7315)Memory used [KB]: 6012
% 6.79/2.14 % (7315)Time elapsed: 0.016 s
% 6.79/2.14 % (7315)Instructions burned: 54 (million)
% 6.79/2.14 % (7315)------------------------------
% 6.79/2.14 % (7315)------------------------------
% 6.79/2.15 % (7316)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_6848 for (2992ds/4436Mi)
% 6.79/2.16 % (7312)Instruction limit reached!
% 6.79/2.16 % (7312)------------------------------
% 6.79/2.16 % (7312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.16 % (7312)Termination reason: Unknown
% 6.79/2.16 % (7312)Termination phase: Saturation
% 6.79/2.16
% 6.79/2.16 % (7312)Memory used [KB]: 6524
% 6.79/2.16 % (7312)Time elapsed: 0.069 s
% 6.79/2.16 % (7312)Instructions burned: 269 (million)
% 6.79/2.16 % (7312)------------------------------
% 6.79/2.16 % (7312)------------------------------
% 6.79/2.16 % (7313)Instruction limit reached!
% 6.79/2.16 % (7313)------------------------------
% 6.79/2.16 % (7313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.16 % (7313)Termination reason: Unknown
% 6.79/2.16 % (7313)Termination phase: Saturation
% 6.79/2.16
% 6.79/2.16 % (7313)Memory used [KB]: 6652
% 6.79/2.16 % (7313)Time elapsed: 0.055 s
% 6.79/2.16 % (7313)Instructions burned: 204 (million)
% 6.79/2.16 % (7313)------------------------------
% 6.79/2.16 % (7313)------------------------------
% 6.79/2.17 % (7317)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_6848 for (2992ds/1539Mi)
% 6.79/2.17 % (7318)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_6848 for (2992ds/408Mi)
% 6.79/2.18 % (7310)Instruction limit reached!
% 6.79/2.18 % (7310)------------------------------
% 6.79/2.18 % (7310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.18 % (7310)Termination reason: Unknown
% 6.79/2.18 % (7310)Termination phase: Saturation
% 6.79/2.18
% 6.79/2.18 % (7310)Memory used [KB]: 7547
% 6.79/2.18 % (7310)Time elapsed: 0.099 s
% 6.79/2.18 % (7310)Instructions burned: 369 (million)
% 6.79/2.18 % (7310)------------------------------
% 6.79/2.18 % (7310)------------------------------
% 6.79/2.19 % (7319)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_6848 for (2992ds/5205Mi)
% 7.16/2.23 % (7299)Instruction limit reached!
% 7.16/2.23 % (7299)------------------------------
% 7.16/2.23 % (7299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.23 % (7299)Termination reason: Unknown
% 7.16/2.23 % (7299)Termination phase: Saturation
% 7.16/2.23
% 7.16/2.23 % (7299)Memory used [KB]: 7036
% 7.16/2.23 % (7299)Time elapsed: 0.255 s
% 7.16/2.23 % (7299)Instructions burned: 987 (million)
% 7.16/2.23 % (7299)------------------------------
% 7.16/2.23 % (7299)------------------------------
% 7.16/2.24 % (7320)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_6848 for (2991ds/1913Mi)
% 7.16/2.28 % (7318)Instruction limit reached!
% 7.16/2.28 % (7318)------------------------------
% 7.16/2.28 % (7318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.28 % (7318)Termination reason: Unknown
% 7.16/2.28 % (7318)Termination phase: Saturation
% 7.16/2.28
% 7.16/2.28 % (7318)Memory used [KB]: 6524
% 7.16/2.28 % (7318)Time elapsed: 0.109 s
% 7.16/2.28 % (7318)Instructions burned: 408 (million)
% 7.16/2.28 % (7318)------------------------------
% 7.16/2.28 % (7318)------------------------------
% 7.16/2.29 % (7321)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_6848 for (2991ds/4350Mi)
% 7.16/2.29 % (7306)Instruction limit reached!
% 7.16/2.29 % (7306)------------------------------
% 7.16/2.29 % (7306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.29 % (7306)Termination reason: Unknown
% 7.16/2.29 % (7306)Termination phase: Saturation
% 7.16/2.29
% 7.16/2.29 % (7306)Memory used [KB]: 10106
% 7.16/2.29 % (7306)Time elapsed: 0.247 s
% 7.16/2.29 % (7306)Instructions burned: 925 (million)
% 7.16/2.29 % (7306)------------------------------
% 7.16/2.29 % (7306)------------------------------
% 7.57/2.30 % (7322)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_6848 for (2991ds/68Mi)
% 7.57/2.32 % (7322)Instruction limit reached!
% 7.57/2.32 % (7322)------------------------------
% 7.57/2.32 % (7322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.32 % (7322)Termination reason: Unknown
% 7.57/2.32 % (7322)Termination phase: Saturation
% 7.57/2.32
% 7.57/2.32 % (7322)Memory used [KB]: 6140
% 7.57/2.32 % (7322)Time elapsed: 0.018 s
% 7.57/2.32 % (7322)Instructions burned: 68 (million)
% 7.57/2.32 % (7322)------------------------------
% 7.57/2.32 % (7322)------------------------------
% 7.57/2.33 % (7323)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_6848 for (2991ds/358Mi)
% 7.57/2.36 % (7311)Instruction limit reached!
% 7.57/2.36 % (7311)------------------------------
% 7.57/2.36 % (7311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.36 % (7311)Termination reason: Unknown
% 7.57/2.36 % (7311)Termination phase: Saturation
% 7.57/2.36
% 7.57/2.36 % (7311)Memory used [KB]: 9978
% 7.57/2.36 % (7311)Time elapsed: 0.275 s
% 7.57/2.36 % (7311)Instructions burned: 1024 (million)
% 7.57/2.36 % (7311)------------------------------
% 7.57/2.36 % (7311)------------------------------
% 7.57/2.37 % (7324)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6848 for (2990ds/31Mi)
% 7.57/2.38 % (7324)Instruction limit reached!
% 7.57/2.38 % (7324)------------------------------
% 7.57/2.38 % (7324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.57/2.38 % (7324)Termination reason: Unknown
% 7.57/2.38 % (7324)Termination phase: Property scanning
% 7.57/2.38
% 7.57/2.38 % (7324)Memory used [KB]: 1535
% 7.57/2.38 % (7324)Time elapsed: 0.009 s
% 7.57/2.38 % (7324)Instructions burned: 32 (million)
% 7.57/2.38 % (7324)------------------------------
% 7.57/2.38 % (7324)------------------------------
% 7.57/2.39 % (7325)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_6848 for (2990ds/279Mi)
% 7.90/2.41 % (7325)Refutation not found, incomplete strategy
% 7.90/2.41 % (7325)------------------------------
% 7.90/2.41 % (7325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.41 % (7325)Termination reason: Refutation not found, incomplete strategy
% 7.90/2.41
% 7.90/2.41
% 7.90/2.41 % (7325)Memory used [KB]: 6396
% 7.90/2.41 % (7325)Time elapsed: 0.019 s
% 7.90/2.41 % (7325)Instructions burned: 69 (million)
% 7.90/2.41 % (7325)------------------------------
% 7.90/2.41 % (7325)------------------------------
% 7.90/2.42 % (7326)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_6848 for (2990ds/258Mi)
% 7.90/2.42 % (7323)Instruction limit reached!
% 7.90/2.42 % (7323)------------------------------
% 7.90/2.42 % (7323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.42 % (7323)Termination reason: Unknown
% 7.90/2.42 % (7323)Termination phase: Saturation
% 7.90/2.42
% 7.90/2.42 % (7323)Memory used [KB]: 7291
% 7.90/2.42 % (7323)Time elapsed: 0.094 s
% 7.90/2.42 % (7323)Instructions burned: 358 (million)
% 7.90/2.42 % (7323)------------------------------
% 7.90/2.42 % (7323)------------------------------
% 7.90/2.43 % (7327)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_6848 for (2990ds/26Mi)
% 7.90/2.44 % (7327)Instruction limit reached!
% 7.90/2.44 % (7327)------------------------------
% 7.90/2.44 % (7327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.44 % (7327)Termination reason: Unknown
% 7.90/2.44 % (7327)Termination phase: Property scanning
% 7.90/2.44
% 7.90/2.44 % (7327)Memory used [KB]: 1407
% 7.90/2.44 % (7327)Time elapsed: 0.008 s
% 7.90/2.44 % (7327)Instructions burned: 28 (million)
% 7.90/2.44 % (7327)------------------------------
% 7.90/2.44 % (7327)------------------------------
% 7.90/2.45 % (7328)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_6848 for (2989ds/995Mi)
% 7.90/2.49 % (7326)Instruction limit reached!
% 7.90/2.49 % (7326)------------------------------
% 7.90/2.49 % (7326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.49 % (7326)Termination reason: Unknown
% 7.90/2.49 % (7326)Termination phase: Saturation
% 7.90/2.49
% 7.90/2.49 % (7326)Memory used [KB]: 6780
% 7.90/2.49 % (7326)Time elapsed: 0.074 s
% 7.90/2.49 % (7326)Instructions burned: 260 (million)
% 7.90/2.49 % (7326)------------------------------
% 7.90/2.49 % (7326)------------------------------
% 8.13/2.50 % (7329)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_6848 for (2989ds/373Mi)
% 8.13/2.58 % (7317)Instruction limit reached!
% 8.13/2.58 % (7317)------------------------------
% 8.13/2.58 % (7317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.13/2.58 % (7317)Termination reason: Unknown
% 8.13/2.58 % (7317)Termination phase: Saturation
% 8.13/2.58
% 8.13/2.58 % (7317)Memory used [KB]: 13176
% 8.13/2.58 % (7317)Time elapsed: 0.419 s
% 8.13/2.58 % (7317)Instructions burned: 1542 (million)
% 8.13/2.58 % (7317)------------------------------
% 8.13/2.58 % (7317)------------------------------
% 8.13/2.59 % (7330)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_6848 for (2988ds/253Mi)
% 8.57/2.60 % (7329)Instruction limit reached!
% 8.57/2.60 % (7329)------------------------------
% 8.57/2.60 % (7329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.60 % (7329)Termination reason: Unknown
% 8.57/2.60 % (7329)Termination phase: Saturation
% 8.57/2.60
% 8.57/2.60 % (7329)Memory used [KB]: 7164
% 8.57/2.60 % (7329)Time elapsed: 0.102 s
% 8.57/2.60 % (7329)Instructions burned: 373 (million)
% 8.57/2.60 % (7329)------------------------------
% 8.57/2.60 % (7329)------------------------------
% 8.57/2.61 % (7331)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_6848 for (2988ds/832Mi)
% 8.57/2.62 % (7331)Refutation not found, incomplete strategy
% 8.57/2.62 % (7331)------------------------------
% 8.57/2.62 % (7331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.62 % (7331)Termination reason: Refutation not found, incomplete strategy
% 8.57/2.62
% 8.57/2.62
% 8.57/2.62 % (7331)Memory used [KB]: 6140
% 8.57/2.62 % (7331)Time elapsed: 0.014 s
% 8.57/2.62 % (7331)Instructions burned: 49 (million)
% 8.57/2.62 % (7331)------------------------------
% 8.57/2.62 % (7331)------------------------------
% 8.57/2.63 % (7332)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_6848 for (2988ds/668Mi)
% 8.57/2.65 % (7330)Instruction limit reached!
% 8.57/2.65 % (7330)------------------------------
% 8.57/2.65 % (7330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.65 % (7330)Termination reason: Unknown
% 8.57/2.65 % (7330)Termination phase: Saturation
% 8.57/2.65
% 8.57/2.65 % (7330)Memory used [KB]: 6140
% 8.57/2.65 % (7330)Time elapsed: 0.061 s
% 8.57/2.65 % (7330)Instructions burned: 253 (million)
% 8.57/2.65 % (7330)------------------------------
% 8.57/2.65 % (7330)------------------------------
% 8.57/2.66 % (7333)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=40:si=on:rtra=on_0 on DTF2THF_6848 for (2987ds/40Mi)
% 8.57/2.68 % (7333)Instruction limit reached!
% 8.57/2.68 % (7333)------------------------------
% 8.57/2.68 % (7333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.68 % (7333)Termination reason: Unknown
% 8.57/2.68 % (7333)Termination phase: Saturation
% 8.57/2.68
% 8.57/2.68 % (7333)Memory used [KB]: 6012
% 8.57/2.68 % (7333)Time elapsed: 0.012 s
% 8.57/2.68 % (7333)Instructions burned: 42 (million)
% 8.57/2.68 % (7333)------------------------------
% 8.57/2.68 % (7333)------------------------------
% 8.57/2.68 % (7334)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_6848 for (2987ds/294Mi)
% 8.79/2.73 % (7328)Instruction limit reached!
% 8.79/2.73 % (7328)------------------------------
% 8.79/2.73 % (7328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.73 % (7328)Termination reason: Unknown
% 8.79/2.73 % (7328)Termination phase: Saturation
% 8.79/2.73
% 8.79/2.73 % (7328)Memory used [KB]: 7419
% 8.79/2.73 % (7328)Time elapsed: 0.284 s
% 8.79/2.73 % (7328)Instructions burned: 995 (million)
% 8.79/2.73 % (7328)------------------------------
% 8.79/2.73 % (7328)------------------------------
% 8.79/2.74 % (7335)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_6848 for (2986ds/187Mi)
% 8.79/2.76 % (7334)Instruction limit reached!
% 8.79/2.76 % (7334)------------------------------
% 8.79/2.76 % (7334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.76 % (7334)Termination reason: Unknown
% 8.79/2.76 % (7334)Termination phase: Saturation
% 8.79/2.76
% 8.79/2.76 % (7334)Memory used [KB]: 6524
% 8.79/2.76 % (7334)Time elapsed: 0.074 s
% 8.79/2.76 % (7334)Instructions burned: 297 (million)
% 8.79/2.76 % (7334)------------------------------
% 8.79/2.76 % (7334)------------------------------
% 8.79/2.77 % (7320)Instruction limit reached!
% 8.79/2.77 % (7320)------------------------------
% 8.79/2.77 % (7320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.77 % (7320)Termination reason: Unknown
% 8.79/2.77 % (7320)Termination phase: Saturation
% 8.79/2.77
% 8.79/2.77 % (7320)Memory used [KB]: 7291
% 8.79/2.77 % (7320)Time elapsed: 0.525 s
% 8.79/2.77 % (7320)Instructions burned: 1913 (million)
% 8.79/2.77 % (7320)------------------------------
% 8.79/2.77 % (7320)------------------------------
% 8.79/2.77 % (7336)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_6848 for (2986ds/371Mi)
% 8.79/2.78 % (7336)Refutation not found, incomplete strategy
% 8.79/2.78 % (7336)------------------------------
% 8.79/2.78 % (7336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.78 % (7336)Termination reason: Refutation not found, incomplete strategy
% 8.79/2.78
% 8.79/2.78
% 8.79/2.78 % (7336)Memory used [KB]: 6012
% 8.79/2.78 % (7336)Time elapsed: 0.009 s
% 8.79/2.78 % (7336)Instructions burned: 31 (million)
% 8.79/2.78 % (7336)------------------------------
% 8.79/2.78 % (7336)------------------------------
% 8.79/2.78 % (7337)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_6848 for (2986ds/1827Mi)
% 8.79/2.79 % (7338)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_6848 for (2986ds/70Mi)
% 8.79/2.79 % (7335)Instruction limit reached!
% 8.79/2.79 % (7335)------------------------------
% 8.79/2.79 % (7335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.79 % (7335)Termination reason: Unknown
% 8.79/2.79 % (7335)Termination phase: Saturation
% 8.79/2.79
% 8.79/2.79 % (7335)Memory used [KB]: 6524
% 8.79/2.79 % (7335)Time elapsed: 0.051 s
% 8.79/2.79 % (7335)Instructions burned: 190 (million)
% 8.79/2.79 % (7335)------------------------------
% 8.79/2.79 % (7335)------------------------------
% 9.78/2.80 % (7339)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_6848 for (2986ds/316Mi)
% 9.78/2.80 % (7338)Instruction limit reached!
% 9.78/2.80 % (7338)------------------------------
% 9.78/2.80 % (7338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.80 % (7338)Termination reason: Unknown
% 9.78/2.80 % (7338)Termination phase: Saturation
% 9.78/2.80
% 9.78/2.80 % (7338)Memory used [KB]: 1663
% 9.78/2.80 % (7338)Time elapsed: 0.019 s
% 9.78/2.80 % (7338)Instructions burned: 70 (million)
% 9.78/2.80 % (7338)------------------------------
% 9.78/2.80 % (7338)------------------------------
% 9.78/2.80 % (7332)Refutation not found, non-redundant clauses discarded% (7332)------------------------------
% 9.78/2.80 % (7332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.80 % (7332)Termination reason: Refutation not found, non-redundant clauses discarded
% 9.78/2.80
% 9.78/2.80 % (7332)Memory used [KB]: 11385
% 9.78/2.80 % (7332)Time elapsed: 0.173 s
% 9.78/2.80 % (7332)Instructions burned: 644 (million)
% 9.78/2.80 % (7332)------------------------------
% 9.78/2.80 % (7332)------------------------------
% 9.78/2.81 % (7340)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_6848 for (2986ds/932Mi)
% 9.78/2.81 % (7341)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_6848 for (2986ds/4714Mi)
% 9.78/2.82 % (7339)Refutation not found, incomplete strategy
% 9.78/2.82 % (7339)------------------------------
% 9.78/2.82 % (7339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.82 % (7339)Termination reason: Refutation not found, incomplete strategy
% 9.78/2.82
% 9.78/2.82
% 9.78/2.82 % (7339)Memory used [KB]: 6268
% 9.78/2.82 % (7339)Time elapsed: 0.021 s
% 9.78/2.82 % (7339)Instructions burned: 79 (million)
% 9.78/2.82 % (7339)------------------------------
% 9.78/2.82 % (7339)------------------------------
% 9.78/2.83 % (7341)Refutation not found, incomplete strategy
% 9.78/2.83 % (7341)------------------------------
% 9.78/2.83 % (7341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.83 % (7341)Termination reason: Refutation not found, incomplete strategy
% 9.78/2.83
% 9.78/2.83
% 9.78/2.83 % (7341)Memory used [KB]: 6396
% 9.78/2.83 % (7341)Time elapsed: 0.018 s
% 9.78/2.83 % (7341)Instructions burned: 64 (million)
% 9.78/2.83 % (7341)------------------------------
% 9.78/2.83 % (7341)------------------------------
% 9.78/2.83 % (7342)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_6848 for (2985ds/8250Mi)
% 9.78/2.84 % (7343)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_6848 for (2985ds/770Mi)
% 9.78/2.85 % (7343)Refutation not found, incomplete strategy
% 9.78/2.85 % (7343)------------------------------
% 9.78/2.85 % (7343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.85 % (7343)Termination reason: Refutation not found, incomplete strategy
% 9.78/2.85
% 9.78/2.85
% 9.78/2.85 % (7343)Memory used [KB]: 6012
% 9.78/2.85 % (7343)Time elapsed: 0.009 s
% 9.78/2.85 % (7343)Instructions burned: 28 (million)
% 9.78/2.85 % (7343)------------------------------
% 9.78/2.85 % (7343)------------------------------
% 9.78/2.86 % (7344)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_6848 for (2985ds/794Mi)
% 9.78/2.87 % (7344)Refutation not found, incomplete strategy
% 9.78/2.87 % (7344)------------------------------
% 9.78/2.87 % (7344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.87 % (7344)Termination reason: Refutation not found, incomplete strategy
% 9.78/2.87
% 9.78/2.87
% 9.78/2.87 % (7344)Memory used [KB]: 1535
% 9.78/2.87 % (7344)Time elapsed: 0.015 s
% 9.78/2.87 % (7344)Instructions burned: 52 (million)
% 9.78/2.87 % (7344)------------------------------
% 9.78/2.87 % (7344)------------------------------
% 9.78/2.88 % (7345)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_6848 for (2985ds/464Mi)
% 10.09/3.00 % (7345)Instruction limit reached!
% 10.09/3.00 % (7345)------------------------------
% 10.09/3.00 % (7345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/3.00 % (7345)Termination reason: Unknown
% 10.09/3.00 % (7345)Termination phase: Saturation
% 10.09/3.00
% 10.09/3.00 % (7345)Memory used [KB]: 7164
% 10.09/3.00 % (7345)Time elapsed: 0.123 s
% 10.09/3.00 % (7345)Instructions burned: 464 (million)
% 10.09/3.00 % (7345)------------------------------
% 10.09/3.00 % (7345)------------------------------
% 10.09/3.01 % (7346)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_6848 for (2984ds/1376Mi)
% 13.28/3.07 % (7340)Instruction limit reached!
% 13.28/3.07 % (7340)------------------------------
% 13.28/3.07 % (7340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.28/3.07 % (7340)Termination reason: Unknown
% 13.28/3.07 % (7340)Termination phase: Saturation
% 13.28/3.07
% 13.28/3.07 % (7340)Memory used [KB]: 7036
% 13.28/3.07 % (7340)Time elapsed: 0.276 s
% 13.28/3.07 % (7340)Instructions burned: 934 (million)
% 13.28/3.07 % (7340)------------------------------
% 13.28/3.07 % (7340)------------------------------
% 13.28/3.08 % (7347)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_6848 for (2983ds/906Mi)
% 14.72/3.30 % (7337)Instruction limit reached!
% 14.72/3.30 % (7337)------------------------------
% 14.72/3.30 % (7337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.30 % (7337)Termination reason: Unknown
% 14.72/3.30 % (7337)Termination phase: Saturation
% 14.72/3.30
% 14.72/3.30 % (7337)Memory used [KB]: 11641
% 14.72/3.30 % (7337)Time elapsed: 0.524 s
% 14.72/3.30 % (7337)Instructions burned: 1829 (million)
% 14.72/3.30 % (7337)------------------------------
% 14.72/3.30 % (7337)------------------------------
% 14.72/3.31 % (7348)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_6848 for (2981ds/434Mi)
% 14.72/3.32 % (7348)Refutation not found, incomplete strategy
% 14.72/3.32 % (7348)------------------------------
% 14.72/3.32 % (7348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.32 % (7348)Termination reason: Refutation not found, incomplete strategy
% 14.72/3.32
% 14.72/3.32
% 14.72/3.32 % (7348)Memory used [KB]: 6012
% 14.72/3.32 % (7348)Time elapsed: 0.010 s
% 14.72/3.32 % (7348)Instructions burned: 32 (million)
% 14.72/3.32 % (7348)------------------------------
% 14.72/3.32 % (7348)------------------------------
% 14.72/3.33 % (7347)Instruction limit reached!
% 14.72/3.33 % (7347)------------------------------
% 14.72/3.33 % (7347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.33 % (7347)Termination reason: Unknown
% 14.72/3.33 % (7347)Termination phase: Saturation
% 14.72/3.33
% 14.72/3.33 % (7347)Memory used [KB]: 10362
% 14.72/3.33 % (7347)Time elapsed: 0.250 s
% 14.72/3.33 % (7347)Instructions burned: 907 (million)
% 14.72/3.33 % (7347)------------------------------
% 14.72/3.33 % (7347)------------------------------
% 14.72/3.33 % (7349)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_6848 for (2981ds/865Mi)
% 14.72/3.34 % (7350)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_6848 for (2981ds/593Mi)
% 14.72/3.36 % (7346)Instruction limit reached!
% 14.72/3.36 % (7346)------------------------------
% 14.72/3.36 % (7346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.36 % (7346)Termination reason: Unknown
% 14.72/3.36 % (7346)Termination phase: Saturation
% 14.72/3.36
% 14.72/3.36 % (7346)Memory used [KB]: 7419
% 14.72/3.36 % (7346)Time elapsed: 0.346 s
% 14.72/3.36 % (7346)Instructions burned: 1378 (million)
% 14.72/3.36 % (7346)------------------------------
% 14.72/3.36 % (7346)------------------------------
% 14.72/3.37 % (7351)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_6848 for (2980ds/443Mi)
% 15.76/3.44 % (7316)Instruction limit reached!
% 15.76/3.44 % (7316)------------------------------
% 15.76/3.44 % (7316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.76/3.44 % (7316)Termination reason: Unknown
% 15.76/3.44 % (7316)Termination phase: Saturation
% 15.76/3.44
% 15.76/3.44 % (7316)Memory used [KB]: 19445
% 15.76/3.44 % (7316)Time elapsed: 1.291 s
% 15.76/3.44 % (7316)Instructions burned: 4437 (million)
% 15.76/3.44 % (7316)------------------------------
% 15.76/3.44 % (7316)------------------------------
% 15.76/3.45 % (7352)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_6848 for (2979ds/594Mi)
% 15.76/3.49 % (7351)Instruction limit reached!
% 15.76/3.49 % (7351)------------------------------
% 15.76/3.49 % (7351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.76/3.49 % (7351)Termination reason: Unknown
% 15.76/3.49 % (7351)Termination phase: Saturation
% 15.76/3.49
% 15.76/3.49 % (7351)Memory used [KB]: 7547
% 15.76/3.49 % (7351)Time elapsed: 0.117 s
% 15.76/3.49 % (7351)Instructions burned: 445 (million)
% 15.76/3.49 % (7351)------------------------------
% 15.76/3.49 % (7351)------------------------------
% 15.76/3.49 % (7353)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_6848 for (2979ds/327Mi)
% 16.25/3.51 % (7350)Instruction limit reached!
% 16.25/3.51 % (7350)------------------------------
% 16.25/3.51 % (7350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.51 % (7350)Termination reason: Unknown
% 16.25/3.51 % (7350)Termination phase: Saturation
% 16.25/3.51
% 16.25/3.51 % (7350)Memory used [KB]: 7803
% 16.25/3.51 % (7350)Time elapsed: 0.171 s
% 16.25/3.51 % (7350)Instructions burned: 594 (million)
% 16.25/3.51 % (7350)------------------------------
% 16.25/3.51 % (7350)------------------------------
% 16.25/3.51 % (7354)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_6848 for (2979ds/5411Mi)
% 16.25/3.52 % (7354)Refutation not found, incomplete strategy
% 16.25/3.52 % (7354)------------------------------
% 16.25/3.52 % (7354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.52 % (7354)Termination reason: Refutation not found, incomplete strategy
% 16.25/3.52
% 16.25/3.52
% 16.25/3.52 % (7354)Memory used [KB]: 6012
% 16.25/3.52 % (7354)Time elapsed: 0.008 s
% 16.25/3.52 % (7354)Instructions burned: 28 (million)
% 16.25/3.52 % (7354)------------------------------
% 16.25/3.52 % (7354)------------------------------
% 16.25/3.53 % (7355)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_6848 for (2979ds/1762Mi)
% 16.25/3.53 % (7321)Instruction limit reached!
% 16.25/3.53 % (7321)------------------------------
% 16.25/3.53 % (7321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.53 % (7321)Termination reason: Unknown
% 16.25/3.53 % (7321)Termination phase: Saturation
% 16.25/3.53
% 16.25/3.53 % (7321)Memory used [KB]: 19573
% 16.25/3.53 % (7321)Time elapsed: 1.247 s
% 16.25/3.53 % (7321)Instructions burned: 4352 (million)
% 16.25/3.53 % (7321)------------------------------
% 16.25/3.53 % (7321)------------------------------
% 16.25/3.54 % (7356)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/96Mi)
% 16.25/3.55 % (7349)Instruction limit reached!
% 16.25/3.55 % (7349)------------------------------
% 16.25/3.55 % (7349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.55 % (7349)Termination reason: Unknown
% 16.25/3.55 % (7349)Termination phase: Saturation
% 16.25/3.55
% 16.25/3.55 % (7349)Memory used [KB]: 8699
% 16.25/3.55 % (7349)Time elapsed: 0.224 s
% 16.25/3.55 % (7349)Instructions burned: 865 (million)
% 16.25/3.55 % (7349)------------------------------
% 16.25/3.55 % (7349)------------------------------
% 16.25/3.56 % (7357)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/503Mi)
% 16.25/3.57 % (7357)Refutation not found, incomplete strategy
% 16.25/3.57 % (7357)------------------------------
% 16.25/3.57 % (7357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.57 % (7357)Termination reason: Refutation not found, incomplete strategy
% 16.25/3.57
% 16.25/3.57
% 16.25/3.57 % (7357)Memory used [KB]: 6012
% 16.25/3.57 % (7357)Time elapsed: 0.010 s
% 16.25/3.57 % (7357)Instructions burned: 31 (million)
% 16.25/3.57 % (7357)------------------------------
% 16.25/3.57 % (7357)------------------------------
% 16.25/3.57 % (7356)Instruction limit reached!
% 16.25/3.57 % (7356)------------------------------
% 16.25/3.57 % (7356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.57 % (7356)Termination reason: Unknown
% 16.25/3.57 % (7356)Termination phase: Saturation
% 16.25/3.57
% 16.25/3.57 % (7356)Memory used [KB]: 6268
% 16.25/3.57 % (7356)Time elapsed: 0.028 s
% 16.25/3.57 % (7356)Instructions burned: 98 (million)
% 16.25/3.57 % (7356)------------------------------
% 16.25/3.57 % (7356)------------------------------
% 16.25/3.58 % (7358)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/90Mi)
% 16.25/3.58 % (7359)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/593Mi)
% 16.25/3.58 % (7353)Instruction limit reached!
% 16.25/3.58 % (7353)------------------------------
% 16.25/3.58 % (7353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.58 % (7353)Termination reason: Unknown
% 16.25/3.58 % (7353)Termination phase: Saturation
% 16.25/3.58
% 16.25/3.58 % (7353)Memory used [KB]: 8187
% 16.25/3.58 % (7353)Time elapsed: 0.087 s
% 16.25/3.58 % (7353)Instructions burned: 328 (million)
% 16.25/3.58 % (7353)------------------------------
% 16.25/3.58 % (7353)------------------------------
% 16.25/3.59 % (7360)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/1512Mi)
% 17.09/3.61 % (7358)Instruction limit reached!
% 17.09/3.61 % (7358)------------------------------
% 17.09/3.61 % (7358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.61 % (7358)Termination reason: Unknown
% 17.09/3.61 % (7358)Termination phase: Saturation
% 17.09/3.61
% 17.09/3.61 % (7358)Memory used [KB]: 6268
% 17.09/3.61 % (7358)Time elapsed: 0.028 s
% 17.09/3.61 % (7358)Instructions burned: 91 (million)
% 17.09/3.61 % (7358)------------------------------
% 17.09/3.61 % (7358)------------------------------
% 17.09/3.61 % (7352)Instruction limit reached!
% 17.09/3.61 % (7352)------------------------------
% 17.09/3.61 % (7352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.61 % (7352)Termination reason: Unknown
% 17.09/3.61 % (7352)Termination phase: Saturation
% 17.09/3.61
% 17.09/3.61 % (7352)Memory used [KB]: 8187
% 17.09/3.61 % (7352)Time elapsed: 0.160 s
% 17.09/3.61 % (7352)Instructions burned: 597 (million)
% 17.09/3.61 % (7352)------------------------------
% 17.09/3.61 % (7352)------------------------------
% 17.09/3.61 % (7360)Refutation not found, incomplete strategy
% 17.09/3.61 % (7360)------------------------------
% 17.09/3.61 % (7360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.61 % (7360)Termination reason: Refutation not found, incomplete strategy
% 17.09/3.61
% 17.09/3.61
% 17.09/3.61 % (7360)Memory used [KB]: 6140
% 17.09/3.61 % (7360)Time elapsed: 0.024 s
% 17.09/3.61 % (7360)Instructions burned: 80 (million)
% 17.09/3.61 % (7360)------------------------------
% 17.09/3.61 % (7360)------------------------------
% 17.09/3.62 % (7361)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/569Mi)
% 17.09/3.62 % (7362)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/501Mi)
% 17.09/3.62 % (7363)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_6848 for (2978ds/562Mi)
% 17.09/3.63 % (7319)Instruction limit reached!
% 17.09/3.63 % (7319)------------------------------
% 17.09/3.63 % (7319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.63 % (7319)Termination reason: Unknown
% 17.09/3.63 % (7319)Termination phase: Saturation
% 17.09/3.63
% 17.09/3.63 % (7319)Memory used [KB]: 10618
% 17.09/3.63 % (7319)Time elapsed: 1.436 s
% 17.09/3.63 % (7319)Instructions burned: 5208 (million)
% 17.09/3.63 % (7319)------------------------------
% 17.09/3.63 % (7319)------------------------------
% 17.09/3.64 % (7362)Refutation not found, incomplete strategy
% 17.09/3.64 % (7362)------------------------------
% 17.09/3.64 % (7362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.64 % (7362)Termination reason: Refutation not found, incomplete strategy
% 17.09/3.64
% 17.09/3.64
% 17.09/3.64 % (7362)Memory used [KB]: 6012
% 17.09/3.64 % (7362)Time elapsed: 0.015 s
% 17.09/3.64 % (7362)Instructions burned: 54 (million)
% 17.09/3.64 % (7362)------------------------------
% 17.09/3.64 % (7362)------------------------------
% 17.09/3.64 % (7364)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_6848 for (2977ds/406Mi)
% 17.09/3.65 % (7365)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_6848 for (2977ds/582Mi)
% 17.09/3.67 % (7364)Refutation not found, incomplete strategy
% 17.09/3.67 % (7364)------------------------------
% 17.09/3.67 % (7364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.09/3.67 % (7364)Termination reason: Refutation not found, incomplete strategy
% 17.09/3.67
% 17.09/3.67
% 17.09/3.67 % (7364)Memory used [KB]: 6396
% 17.09/3.67 % (7364)Time elapsed: 0.028 s
% 17.09/3.67 % (7364)Instructions burned: 101 (million)
% 17.09/3.67 % (7364)------------------------------
% 17.09/3.67 % (7364)------------------------------
% 17.09/3.68 % (7366)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_6848 for (2977ds/456Mi)
% 17.53/3.74 % (7359)Instruction limit reached!
% 17.53/3.74 % (7359)------------------------------
% 17.53/3.74 % (7359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.53/3.74 % (7359)Termination reason: Unknown
% 17.53/3.74 % (7359)Termination phase: Saturation
% 17.53/3.74
% 17.53/3.74 % (7359)Memory used [KB]: 7931
% 17.53/3.74 % (7359)Time elapsed: 0.162 s
% 17.53/3.74 % (7359)Instructions burned: 596 (million)
% 17.53/3.74 % (7359)------------------------------
% 17.53/3.74 % (7359)------------------------------
% 17.53/3.76 % (7367)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_6848 for (2976ds/393Mi)
% 17.53/3.78 % (7363)Instruction limit reached!
% 17.53/3.78 % (7363)------------------------------
% 17.53/3.78 % (7363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.53/3.78 % (7363)Termination reason: Unknown
% 17.53/3.78 % (7363)Termination phase: Saturation
% 17.53/3.78
% 17.53/3.78 % (7363)Memory used [KB]: 7164
% 17.53/3.78 % (7363)Time elapsed: 0.158 s
% 17.53/3.78 % (7363)Instructions burned: 563 (million)
% 17.53/3.78 % (7363)------------------------------
% 17.53/3.78 % (7363)------------------------------
% 17.53/3.78 % (7361)Instruction limit reached!
% 17.53/3.78 % (7361)------------------------------
% 17.53/3.78 % (7361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.53/3.78 % (7361)Termination reason: Unknown
% 17.53/3.78 % (7361)Termination phase: Saturation
% 17.53/3.78
% 17.53/3.78 % (7361)Memory used [KB]: 6780
% 17.53/3.78 % (7361)Time elapsed: 0.165 s
% 17.53/3.78 % (7361)Instructions burned: 571 (million)
% 17.53/3.78 % (7361)------------------------------
% 17.53/3.78 % (7361)------------------------------
% 17.53/3.79 % (7368)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_6848 for (2976ds/1335Mi)
% 17.53/3.79 % (7369)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_6848 for (2976ds/3373Mi)
% 18.14/3.80 % (7366)Instruction limit reached!
% 18.14/3.80 % (7366)------------------------------
% 18.14/3.80 % (7366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.80 % (7366)Termination reason: Unknown
% 18.14/3.80 % (7366)Termination phase: Saturation
% 18.14/3.80
% 18.14/3.80 % (7366)Memory used [KB]: 7675
% 18.14/3.80 % (7366)Time elapsed: 0.124 s
% 18.14/3.80 % (7366)Instructions burned: 456 (million)
% 18.14/3.80 % (7366)------------------------------
% 18.14/3.80 % (7366)------------------------------
% 18.14/3.80 % (7368)Refutation not found, incomplete strategy
% 18.14/3.80 % (7368)------------------------------
% 18.14/3.80 % (7368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.80 % (7368)Termination reason: Refutation not found, incomplete strategy
% 18.14/3.80
% 18.14/3.80
% 18.14/3.80 % (7368)Memory used [KB]: 6012
% 18.14/3.80 % (7368)Time elapsed: 0.010 s
% 18.14/3.80 % (7368)Instructions burned: 36 (million)
% 18.14/3.80 % (7368)------------------------------
% 18.14/3.80 % (7368)------------------------------
% 18.14/3.80 % (7365)Instruction limit reached!
% 18.14/3.80 % (7365)------------------------------
% 18.14/3.80 % (7365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.80 % (7365)Termination reason: Unknown
% 18.14/3.80 % (7365)Termination phase: Saturation
% 18.14/3.80
% 18.14/3.80 % (7365)Memory used [KB]: 8187
% 18.14/3.80 % (7365)Time elapsed: 0.157 s
% 18.14/3.80 % (7365)Instructions burned: 584 (million)
% 18.14/3.80 % (7365)------------------------------
% 18.14/3.80 % (7365)------------------------------
% 18.14/3.81 % (7370)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_6848 for (2976ds/474Mi)
% 18.14/3.81 % (7371)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_6848 for (2976ds/157Mi)
% 18.14/3.81 % (7372)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_6848 for (2976ds/590Mi)
% 18.14/3.85 % (7371)Instruction limit reached!
% 18.14/3.85 % (7371)------------------------------
% 18.14/3.85 % (7371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.85 % (7371)Termination reason: Unknown
% 18.14/3.85 % (7371)Termination phase: Saturation
% 18.14/3.85
% 18.14/3.85 % (7371)Memory used [KB]: 6012
% 18.14/3.85 % (7371)Time elapsed: 0.039 s
% 18.14/3.85 % (7371)Instructions burned: 157 (million)
% 18.14/3.85 % (7371)------------------------------
% 18.14/3.85 % (7371)------------------------------
% 18.14/3.86 % (7373)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_6848 for (2975ds/104Mi)
% 18.14/3.88 % (7373)Instruction limit reached!
% 18.14/3.88 % (7373)------------------------------
% 18.14/3.88 % (7373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.88 % (7373)Termination reason: Unknown
% 18.14/3.88 % (7373)Termination phase: Saturation
% 18.14/3.88
% 18.14/3.88 % (7373)Memory used [KB]: 6140
% 18.14/3.88 % (7373)Time elapsed: 0.027 s
% 18.14/3.88 % (7373)Instructions burned: 106 (million)
% 18.14/3.88 % (7373)------------------------------
% 18.14/3.88 % (7373)------------------------------
% 18.14/3.89 % (7374)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_6848 for (2975ds/414Mi)
% 18.64/3.91 % (7367)Instruction limit reached!
% 18.64/3.91 % (7367)------------------------------
% 18.64/3.91 % (7367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.64/3.91 % (7367)Termination reason: Unknown
% 18.64/3.91 % (7367)Termination phase: Saturation
% 18.64/3.91
% 18.64/3.91 % (7367)Memory used [KB]: 6140
% 18.64/3.91 % (7367)Time elapsed: 0.153 s
% 18.64/3.91 % (7367)Instructions burned: 393 (million)
% 18.64/3.91 % (7367)------------------------------
% 18.64/3.91 % (7367)------------------------------
% 18.64/3.92 % (7375)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_6848 for (2975ds/715Mi)
% 18.64/3.93 % (7370)Instruction limit reached!
% 18.64/3.93 % (7370)------------------------------
% 18.64/3.93 % (7370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.64/3.93 % (7370)Termination reason: Unknown
% 18.64/3.93 % (7370)Termination phase: Saturation
% 18.64/3.93
% 18.64/3.93 % (7370)Memory used [KB]: 6524
% 18.64/3.93 % (7370)Time elapsed: 0.120 s
% 18.64/3.93 % (7370)Instructions burned: 474 (million)
% 18.64/3.93 % (7370)------------------------------
% 18.64/3.93 % (7370)------------------------------
% 18.64/3.94 % (7376)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_6848 for (2974ds/961Mi)
% 18.64/3.96 % (7355)Instruction limit reached!
% 18.64/3.96 % (7355)------------------------------
% 18.64/3.96 % (7355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.64/3.96 % (7355)Termination reason: Unknown
% 18.64/3.96 % (7355)Termination phase: Saturation
% 18.64/3.96
% 18.64/3.96 % (7355)Memory used [KB]: 8571
% 18.64/3.96 % (7355)Time elapsed: 0.426 s
% 18.64/3.96 % (7355)Instructions burned: 1763 (million)
% 18.64/3.96 % (7355)------------------------------
% 18.64/3.96 % (7355)------------------------------
% 18.64/3.96 % (7372)Instruction limit reached!
% 18.64/3.96 % (7372)------------------------------
% 18.64/3.96 % (7372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.64/3.96 % (7372)Termination reason: Unknown
% 18.64/3.96 % (7372)Termination phase: Saturation
% 18.64/3.96
% 18.64/3.96 % (7372)Memory used [KB]: 7036
% 18.64/3.96 % (7372)Time elapsed: 0.153 s
% 18.64/3.96 % (7372)Instructions burned: 593 (million)
% 18.64/3.96 % (7372)------------------------------
% 18.64/3.96 % (7372)------------------------------
% 18.64/3.97 % (7377)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_6848 for (2974ds/1213Mi)
% 18.64/3.97 % (7378)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_6848 for (2974ds/1979Mi)
% 18.64/4.01 % (7374)Instruction limit reached!
% 18.64/4.01 % (7374)------------------------------
% 18.64/4.01 % (7374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.64/4.01 % (7374)Termination reason: Unknown
% 18.64/4.01 % (7374)Termination phase: Saturation
% 18.64/4.01
% 18.64/4.01 % (7374)Memory used [KB]: 6524
% 18.64/4.01 % (7374)Time elapsed: 0.116 s
% 18.64/4.01 % (7374)Instructions burned: 415 (million)
% 18.64/4.01 % (7374)------------------------------
% 18.64/4.01 % (7374)------------------------------
% 20.26/4.02 % (7379)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_6848 for (2974ds/481Mi)
% 20.89/4.14 % (7379)Instruction limit reached!
% 20.89/4.14 % (7379)------------------------------
% 20.89/4.14 % (7379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.14 % (7379)Termination reason: Unknown
% 20.89/4.14 % (7379)Termination phase: Saturation
% 20.89/4.14
% 20.89/4.14 % (7379)Memory used [KB]: 6524
% 20.89/4.14 % (7379)Time elapsed: 0.120 s
% 20.89/4.14 % (7379)Instructions burned: 481 (million)
% 20.89/4.14 % (7379)------------------------------
% 20.89/4.14 % (7379)------------------------------
% 20.89/4.14 % (7380)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_6848 for (2972ds/783Mi)
% 20.89/4.16 % (7375)Instruction limit reached!
% 20.89/4.16 % (7375)------------------------------
% 20.89/4.16 % (7375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.16 % (7375)Termination reason: Unknown
% 20.89/4.16 % (7375)Termination phase: Saturation
% 20.89/4.16
% 20.89/4.16 % (7375)Memory used [KB]: 4477
% 20.89/4.16 % (7375)Time elapsed: 0.241 s
% 20.89/4.16 % (7375)Instructions burned: 717 (million)
% 20.89/4.16 % (7375)------------------------------
% 20.89/4.16 % (7375)------------------------------
% 20.89/4.17 % (7381)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_6848 for (2972ds/432Mi)
% 20.89/4.18 % (7381)Refutation not found, incomplete strategy
% 20.89/4.18 % (7381)------------------------------
% 20.89/4.18 % (7381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.18 % (7381)Termination reason: Refutation not found, incomplete strategy
% 20.89/4.18
% 20.89/4.18
% 20.89/4.18 % (7381)Memory used [KB]: 6012
% 20.89/4.18 % (7381)Time elapsed: 0.009 s
% 20.89/4.18 % (7381)Instructions burned: 30 (million)
% 20.89/4.18 % (7381)------------------------------
% 20.89/4.18 % (7381)------------------------------
% 20.89/4.19 % (7382)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_6848 for (2972ds/1670Mi)
% 20.89/4.19 % (7376)Instruction limit reached!
% 20.89/4.19 % (7376)------------------------------
% 20.89/4.19 % (7376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.89/4.19 % (7376)Termination reason: Unknown
% 20.89/4.19 % (7376)Termination phase: Saturation
% 20.89/4.19
% 20.89/4.19 % (7376)Memory used [KB]: 9850
% 20.89/4.19 % (7376)Time elapsed: 0.258 s
% 20.89/4.19 % (7376)Instructions burned: 961 (million)
% 20.89/4.19 % (7376)------------------------------
% 20.89/4.19 % (7376)------------------------------
% 21.49/4.20 % (7383)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_6848 for (2972ds/90Mi)
% 21.49/4.23 % (7383)Instruction limit reached!
% 21.49/4.23 % (7383)------------------------------
% 21.49/4.23 % (7383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.49/4.23 % (7383)Termination reason: Unknown
% 21.49/4.23 % (7383)Termination phase: Saturation
% 21.49/4.23
% 21.49/4.23 % (7383)Memory used [KB]: 6140
% 21.49/4.23 % (7383)Time elapsed: 0.024 s
% 21.49/4.23 % (7383)Instructions burned: 92 (million)
% 21.49/4.23 % (7383)------------------------------
% 21.49/4.23 % (7383)------------------------------
% 21.49/4.24 % (7384)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_6848 for (2972ds/346Mi)
% 21.93/4.32 % (7384)Instruction limit reached!
% 21.93/4.32 % (7384)------------------------------
% 21.93/4.32 % (7384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.32 % (7384)Termination reason: Unknown
% 21.93/4.32 % (7384)Termination phase: Saturation
% 21.93/4.32
% 21.93/4.32 % (7384)Memory used [KB]: 6524
% 21.93/4.32 % (7384)Time elapsed: 0.086 s
% 21.93/4.32 % (7384)Instructions burned: 348 (million)
% 21.93/4.32 % (7384)------------------------------
% 21.93/4.32 % (7384)------------------------------
% 21.93/4.33 % (7377)Instruction limit reached!
% 21.93/4.33 % (7377)------------------------------
% 21.93/4.33 % (7377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.33 % (7377)Termination reason: Unknown
% 21.93/4.33 % (7377)Termination phase: Saturation
% 21.93/4.33
% 21.93/4.33 % (7377)Memory used [KB]: 7036
% 21.93/4.33 % (7377)Time elapsed: 0.363 s
% 21.93/4.33 % (7377)Instructions burned: 1213 (million)
% 21.93/4.33 % (7377)------------------------------
% 21.93/4.33 % (7377)------------------------------
% 21.93/4.33 % (7385)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_6848 for (2971ds/401Mi)
% 21.93/4.34 % (7386)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_6848 for (2971ds/6454Mi)
% 21.93/4.38 % (7380)Instruction limit reached!
% 21.93/4.38 % (7380)------------------------------
% 21.93/4.38 % (7380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.93/4.38 % (7380)Termination reason: Unknown
% 21.93/4.38 % (7380)Termination phase: Saturation
% 21.93/4.38
% 21.93/4.38 % (7380)Memory used [KB]: 8827
% 21.93/4.38 % (7380)Time elapsed: 0.234 s
% 21.93/4.38 % (7380)Instructions burned: 784 (million)
% 21.93/4.38 % (7380)------------------------------
% 21.93/4.38 % (7380)------------------------------
% 21.93/4.39 % (7387)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_6848 for (2970ds/283Mi)
% 22.62/4.43 % (7385)Instruction limit reached!
% 22.62/4.43 % (7385)------------------------------
% 22.62/4.43 % (7385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.62/4.43 % (7385)Termination reason: Unknown
% 22.62/4.43 % (7385)Termination phase: Saturation
% 22.62/4.43
% 22.62/4.43 % (7385)Memory used [KB]: 6524
% 22.62/4.43 % (7385)Time elapsed: 0.103 s
% 22.62/4.43 % (7385)Instructions burned: 402 (million)
% 22.62/4.43 % (7385)------------------------------
% 22.62/4.43 % (7385)------------------------------
% 22.62/4.44 % (7388)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_6848 for (2970ds/865Mi)
% 22.62/4.46 % (7387)Instruction limit reached!
% 22.62/4.46 % (7387)------------------------------
% 22.62/4.46 % (7387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.62/4.46 % (7387)Termination reason: Unknown
% 22.62/4.46 % (7387)Termination phase: Saturation
% 22.62/4.46
% 22.62/4.46 % (7387)Memory used [KB]: 6780
% 22.62/4.46 % (7387)Time elapsed: 0.076 s
% 22.62/4.46 % (7387)Instructions burned: 285 (million)
% 22.62/4.46 % (7387)------------------------------
% 22.62/4.46 % (7387)------------------------------
% 22.62/4.47 % (7389)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_6848 for (2969ds/4528Mi)
% 22.62/4.48 % (7389)Refutation not found, incomplete strategy
% 22.62/4.48 % (7389)------------------------------
% 22.62/4.48 % (7389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.62/4.48 % (7389)Termination reason: Refutation not found, incomplete strategy
% 22.62/4.48
% 22.62/4.48
% 22.62/4.48 % (7389)Memory used [KB]: 1535
% 22.62/4.48 % (7389)Time elapsed: 0.008 s
% 22.62/4.48 % (7389)Instructions burned: 28 (million)
% 22.62/4.48 % (7389)------------------------------
% 22.62/4.48 % (7389)------------------------------
% 22.62/4.49 % (7390)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_6848 for (2969ds/1001Mi)
% 23.13/4.52 % (7378)Instruction limit reached!
% 23.13/4.52 % (7378)------------------------------
% 23.13/4.52 % (7378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.13/4.52 % (7378)Termination reason: Unknown
% 23.13/4.52 % (7378)Termination phase: Saturation
% 23.13/4.52
% 23.13/4.52 % (7378)Memory used [KB]: 11641
% 23.13/4.52 % (7378)Time elapsed: 0.548 s
% 23.13/4.52 % (7378)Instructions burned: 1981 (million)
% 23.13/4.52 % (7378)------------------------------
% 23.13/4.52 % (7378)------------------------------
% 23.13/4.53 % (7391)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_6848 for (2969ds/102Mi)
% 23.13/4.55 % (7391)Instruction limit reached!
% 23.13/4.55 % (7391)------------------------------
% 23.13/4.55 % (7391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.13/4.55 % (7391)Termination reason: Unknown
% 23.13/4.55 % (7391)Termination phase: Saturation
% 23.13/4.55
% 23.13/4.55 % (7391)Memory used [KB]: 6012
% 23.13/4.55 % (7391)Time elapsed: 0.026 s
% 23.13/4.55 % (7391)Instructions burned: 105 (million)
% 23.13/4.55 % (7391)------------------------------
% 23.13/4.55 % (7391)------------------------------
% 23.13/4.56 % (7392)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_6848 for (2968ds/952Mi)
% 23.41/4.63 % (7369)Instruction limit reached!
% 23.41/4.63 % (7369)------------------------------
% 23.41/4.63 % (7369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.41/4.63 % (7369)Termination reason: Unknown
% 23.41/4.63 % (7369)Termination phase: Saturation
% 23.41/4.63
% 23.41/4.63 % (7369)Memory used [KB]: 12537
% 23.41/4.63 % (7369)Time elapsed: 0.837 s
% 23.41/4.63 % (7369)Instructions burned: 3375 (million)
% 23.41/4.63 % (7369)------------------------------
% 23.41/4.63 % (7369)------------------------------
% 23.41/4.64 % (7393)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_6848 for (2967ds/578Mi)
% 23.41/4.68 % (7382)Instruction limit reached!
% 23.41/4.68 % (7382)------------------------------
% 23.41/4.68 % (7382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.41/4.68 % (7382)Termination reason: Unknown
% 23.41/4.68 % (7382)Termination phase: Saturation
% 23.41/4.68
% 23.41/4.68 % (7382)Memory used [KB]: 7803
% 23.41/4.68 % (7382)Time elapsed: 0.489 s
% 23.41/4.68 % (7382)Instructions burned: 1670 (million)
% 23.41/4.68 % (7382)------------------------------
% 23.41/4.68 % (7382)------------------------------
% 23.41/4.68 % (7388)Instruction limit reached!
% 23.41/4.68 % (7388)------------------------------
% 23.41/4.68 % (7388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.41/4.68 % (7388)Termination reason: Unknown
% 23.41/4.68 % (7388)Termination phase: Saturation
% 23.41/4.68
% 23.41/4.68 % (7388)Memory used [KB]: 7036
% 23.41/4.68 % (7388)Time elapsed: 0.258 s
% 23.41/4.68 % (7388)Instructions burned: 867 (million)
% 23.41/4.68 % (7388)------------------------------
% 23.41/4.68 % (7388)------------------------------
% 23.41/4.69 % (7394)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_6848 for (2967ds/643Mi)
% 23.41/4.69 % (7395)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_6848 for (2967ds/865Mi)
% 24.29/4.70 % (7395)Refutation not found, incomplete strategy
% 24.29/4.70 % (7395)------------------------------
% 24.29/4.70 % (7395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.29/4.70 % (7395)Termination reason: Refutation not found, incomplete strategy
% 24.29/4.70
% 24.29/4.70
% 24.29/4.70 % (7395)Memory used [KB]: 6012
% 24.29/4.70 % (7395)Time elapsed: 0.018 s
% 24.29/4.70 % (7395)Instructions burned: 68 (million)
% 24.29/4.70 % (7395)------------------------------
% 24.29/4.70 % (7395)------------------------------
% 24.29/4.71 % (7396)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_6848 for (2967ds/1174Mi)
% 24.29/4.76 % (7390)Instruction limit reached!
% 24.29/4.76 % (7390)------------------------------
% 24.29/4.76 % (7390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.29/4.76 % (7390)Termination reason: Unknown
% 24.29/4.76 % (7390)Termination phase: Saturation
% 24.29/4.76
% 24.29/4.76 % (7390)Memory used [KB]: 9978
% 24.29/4.76 % (7390)Time elapsed: 0.271 s
% 24.29/4.76 % (7390)Instructions burned: 1001 (million)
% 24.29/4.76 % (7390)------------------------------
% 24.29/4.76 % (7390)------------------------------
% 24.29/4.77 % (7397)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_6848 for (2966ds/644Mi)
% 24.29/4.79 % (7393)Instruction limit reached!
% 24.29/4.79 % (7393)------------------------------
% 24.29/4.79 % (7393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.29/4.79 % (7393)Termination reason: Unknown
% 24.29/4.79 % (7393)Termination phase: Saturation
% 24.29/4.79
% 24.29/4.79 % (7393)Memory used [KB]: 6780
% 24.29/4.79 % (7393)Time elapsed: 0.157 s
% 24.29/4.79 % (7393)Instructions burned: 579 (million)
% 24.29/4.79 % (7393)------------------------------
% 24.29/4.79 % (7393)------------------------------
% 24.86/4.80 % (7398)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_6848 for (2966ds/1201Mi)
% 24.86/4.82 % (7392)Instruction limit reached!
% 24.86/4.82 % (7392)------------------------------
% 24.86/4.82 % (7392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.86/4.82 % (7392)Termination reason: Unknown
% 24.86/4.82 % (7392)Termination phase: Saturation
% 24.86/4.82
% 24.86/4.82 % (7392)Memory used [KB]: 9466
% 24.86/4.82 % (7392)Time elapsed: 0.258 s
% 24.86/4.82 % (7392)Instructions burned: 952 (million)
% 24.86/4.82 % (7392)------------------------------
% 24.86/4.82 % (7392)------------------------------
% 24.86/4.83 % (7399)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_6848 for (2965ds/1046Mi)
% 24.86/4.86 % (7394)Instruction limit reached!
% 24.86/4.86 % (7394)------------------------------
% 24.86/4.86 % (7394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.86/4.86 % (7394)Termination reason: Unknown
% 24.86/4.86 % (7394)Termination phase: Saturation
% 24.86/4.86
% 24.86/4.86 % (7394)Memory used [KB]: 7164
% 24.86/4.86 % (7394)Time elapsed: 0.177 s
% 24.86/4.86 % (7394)Instructions burned: 643 (million)
% 24.86/4.86 % (7394)------------------------------
% 24.86/4.86 % (7394)------------------------------
% 24.86/4.87 % (7400)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_6848 for (2965ds/222Mi)
% 25.42/4.93 % (7400)Instruction limit reached!
% 25.42/4.93 % (7400)------------------------------
% 25.42/4.93 % (7400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.42/4.93 % (7400)Termination reason: Unknown
% 25.42/4.93 % (7400)Termination phase: Saturation
% 25.42/4.93
% 25.42/4.93 % (7400)Memory used [KB]: 6268
% 25.42/4.93 % (7400)Time elapsed: 0.059 s
% 25.42/4.93 % (7400)Instructions burned: 225 (million)
% 25.42/4.93 % (7400)------------------------------
% 25.42/4.93 % (7400)------------------------------
% 25.42/4.94 % (7401)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_6848 for (2964ds/68Mi)
% 25.42/4.94 % (7397)Instruction limit reached!
% 25.42/4.94 % (7397)------------------------------
% 25.42/4.94 % (7397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.42/4.94 % (7397)Termination reason: Unknown
% 25.42/4.94 % (7397)Termination phase: Saturation
% 25.42/4.94
% 25.42/4.94 % (7397)Memory used [KB]: 7419
% 25.42/4.94 % (7397)Time elapsed: 0.177 s
% 25.42/4.94 % (7397)Instructions burned: 644 (million)
% 25.42/4.94 % (7397)------------------------------
% 25.42/4.94 % (7397)------------------------------
% 25.42/4.95 % (7402)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_6848 for (2964ds/454Mi)
% 25.42/4.96 % (7401)Instruction limit reached!
% 25.42/4.96 % (7401)------------------------------
% 25.42/4.96 % (7401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.42/4.96 % (7401)Termination reason: Unknown
% 25.42/4.96 % (7401)Termination phase: Saturation
% 25.42/4.96
% 25.42/4.96 % (7401)Memory used [KB]: 6140
% 25.42/4.96 % (7401)Time elapsed: 0.018 s
% 25.42/4.96 % (7401)Instructions burned: 69 (million)
% 25.42/4.96 % (7401)------------------------------
% 25.42/4.96 % (7401)------------------------------
% 25.42/4.97 % (7403)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_6848 for (2964ds/360Mi)
% 25.42/5.02 % (7396)Instruction limit reached!
% 25.42/5.02 % (7396)------------------------------
% 25.42/5.02 % (7396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.42/5.02 % (7396)Termination reason: Unknown
% 25.42/5.02 % (7396)Termination phase: Saturation
% 25.42/5.02
% 25.42/5.02 % (7396)Memory used [KB]: 9978
% 25.42/5.02 % (7396)Time elapsed: 0.311 s
% 25.42/5.02 % (7396)Instructions burned: 1176 (million)
% 25.42/5.02 % (7396)------------------------------
% 25.42/5.02 % (7396)------------------------------
% 27.35/5.03 % (7404)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_6848 for (2963ds/157Mi)
% 27.35/5.06 % (7403)Instruction limit reached!
% 27.35/5.06 % (7403)------------------------------
% 27.35/5.06 % (7403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.06 % (7403)Termination reason: Unknown
% 27.35/5.06 % (7403)Termination phase: Saturation
% 27.35/5.06
% 27.35/5.06 % (7403)Memory used [KB]: 6396
% 27.35/5.06 % (7403)Time elapsed: 0.094 s
% 27.35/5.06 % (7403)Instructions burned: 360 (million)
% 27.35/5.06 % (7403)------------------------------
% 27.35/5.06 % (7403)------------------------------
% 27.35/5.07 % (7405)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_6848 for (2963ds/5061Mi)
% 27.35/5.07 % (7404)Instruction limit reached!
% 27.35/5.07 % (7404)------------------------------
% 27.35/5.07 % (7404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.07 % (7404)Termination reason: Unknown
% 27.35/5.07 % (7404)Termination phase: Saturation
% 27.35/5.07
% 27.35/5.07 % (7404)Memory used [KB]: 6012
% 27.35/5.07 % (7404)Time elapsed: 0.038 s
% 27.35/5.07 % (7404)Instructions burned: 157 (million)
% 27.35/5.07 % (7404)------------------------------
% 27.35/5.07 % (7404)------------------------------
% 27.35/5.08 % (7402)Instruction limit reached!
% 27.35/5.08 % (7402)------------------------------
% 27.35/5.08 % (7402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.08 % (7402)Termination reason: Unknown
% 27.35/5.08 % (7402)Termination phase: Saturation
% 27.35/5.08
% 27.35/5.08 % (7402)Memory used [KB]: 11129
% 27.35/5.08 % (7402)Time elapsed: 0.123 s
% 27.35/5.08 % (7402)Instructions burned: 454 (million)
% 27.35/5.08 % (7402)------------------------------
% 27.35/5.08 % (7402)------------------------------
% 27.35/5.08 % (7406)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_6848 for (2963ds/2401Mi)
% 27.35/5.09 % (7407)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_6848 for (2963ds/5798Mi)
% 27.35/5.10 % (7398)Instruction limit reached!
% 27.35/5.10 % (7398)------------------------------
% 27.35/5.10 % (7398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.10 % (7398)Termination reason: Unknown
% 27.35/5.10 % (7398)Termination phase: Saturation
% 27.35/5.10
% 27.35/5.10 % (7398)Memory used [KB]: 6780
% 27.35/5.10 % (7398)Time elapsed: 0.304 s
% 27.35/5.10 % (7398)Instructions burned: 1203 (million)
% 27.35/5.10 % (7398)------------------------------
% 27.35/5.10 % (7398)------------------------------
% 27.35/5.11 % (7408)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_6848 for (2963ds/346Mi)
% 27.93/5.13 % (7399)Instruction limit reached!
% 27.93/5.13 % (7399)------------------------------
% 27.93/5.13 % (7399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.13 % (7399)Termination reason: Unknown
% 27.93/5.13 % (7399)Termination phase: Saturation
% 27.93/5.13
% 27.93/5.13 % (7399)Memory used [KB]: 6652
% 27.93/5.13 % (7399)Time elapsed: 0.300 s
% 27.93/5.13 % (7399)Instructions burned: 1048 (million)
% 27.93/5.13 % (7399)------------------------------
% 27.93/5.13 % (7399)------------------------------
% 27.93/5.14 % (7409)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_6848 for (2962ds/1321Mi)
% 27.93/5.15 % (7409)Refutation not found, incomplete strategy
% 27.93/5.15 % (7409)------------------------------
% 27.93/5.15 % (7409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.15 % (7409)Termination reason: Refutation not found, incomplete strategy
% 27.93/5.15
% 27.93/5.15
% 27.93/5.15 % (7409)Memory used [KB]: 1535
% 27.93/5.15 % (7409)Time elapsed: 0.015 s
% 27.93/5.15 % (7409)Instructions burned: 50 (million)
% 27.93/5.15 % (7409)------------------------------
% 27.93/5.15 % (7409)------------------------------
% 27.93/5.16 % (7410)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_6848 for (2962ds/1312Mi)
% 27.93/5.19 % (7342)Instruction limit reached!
% 27.93/5.19 % (7342)------------------------------
% 27.93/5.19 % (7342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.93/5.19 % (7342)Termination reason: Unknown
% 27.93/5.19 % (7342)Termination phase: Saturation
% 27.93/5.19
% 27.93/5.19 % (7342)Memory used [KB]: 26737
% 27.93/5.19 % (7342)Time elapsed: 2.357 s
% 27.93/5.19 % (7342)Instructions burned: 8250 (million)
% 27.93/5.19 % (7342)------------------------------
% 27.93/5.19 % (7342)------------------------------
% 28.09/5.20 % (7411)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_6848 for (2962ds/672Mi)
% 28.09/5.20 % (7408)Instruction limit reached!
% 28.09/5.20 % (7408)------------------------------
% 28.09/5.20 % (7408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.20 % (7408)Termination reason: Unknown
% 28.09/5.20 % (7408)Termination phase: Saturation
% 28.09/5.20
% 28.09/5.20 % (7408)Memory used [KB]: 6396
% 28.09/5.20 % (7408)Time elapsed: 0.090 s
% 28.09/5.20 % (7408)Instructions burned: 349 (million)
% 28.09/5.20 % (7408)------------------------------
% 28.09/5.20 % (7408)------------------------------
% 28.09/5.21 % (7411)Refutation not found, incomplete strategy
% 28.09/5.21 % (7411)------------------------------
% 28.09/5.21 % (7411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.21 % (7411)Termination reason: Refutation not found, incomplete strategy
% 28.09/5.21
% 28.09/5.21
% 28.09/5.21 % (7411)Memory used [KB]: 6012
% 28.09/5.21 % (7411)Time elapsed: 0.009 s
% 28.09/5.21 % (7411)Instructions burned: 30 (million)
% 28.09/5.21 % (7411)------------------------------
% 28.09/5.21 % (7411)------------------------------
% 28.09/5.21 % (7412)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_6848 for (2962ds/1897Mi)
% 28.09/5.22 % (7413)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_6848 for (2962ds/1202Mi)
% 28.09/5.22 % (7412)Refutation not found, incomplete strategy
% 28.09/5.22 % (7412)------------------------------
% 28.09/5.22 % (7412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.22 % (7412)Termination reason: Refutation not found, incomplete strategy
% 28.09/5.22
% 28.09/5.22
% 28.09/5.22 % (7412)Memory used [KB]: 6012
% 28.09/5.22 % (7412)Time elapsed: 0.010 s
% 28.09/5.22 % (7412)Instructions burned: 30 (million)
% 28.09/5.22 % (7412)------------------------------
% 28.09/5.22 % (7412)------------------------------
% 28.09/5.23 % (7414)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_6848 for (2961ds/1493Mi)
% 28.09/5.24 % (7414)Refutation not found, incomplete strategy
% 28.09/5.24 % (7414)------------------------------
% 28.09/5.24 % (7414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.24 % (7414)Termination reason: Refutation not found, incomplete strategy
% 28.09/5.24
% 28.09/5.24
% 28.09/5.24 % (7414)Memory used [KB]: 6012
% 28.09/5.24 % (7414)Time elapsed: 0.010 s
% 28.09/5.24 % (7414)Instructions burned: 32 (million)
% 28.09/5.24 % (7414)------------------------------
% 28.09/5.24 % (7414)------------------------------
% 28.09/5.25 % (7415)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_6848 for (2961ds/7679Mi)
% 28.09/5.26 % (7415)Refutation not found, incomplete strategy
% 28.09/5.26 % (7415)------------------------------
% 28.09/5.26 % (7415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.26 % (7415)Termination reason: Refutation not found, incomplete strategy
% 28.09/5.26
% 28.09/5.26
% 28.09/5.26 % (7415)Memory used [KB]: 1535
% 28.09/5.26 % (7415)Time elapsed: 0.010 s
% 28.09/5.26 % (7415)Instructions burned: 34 (million)
% 28.09/5.26 % (7415)------------------------------
% 28.09/5.26 % (7415)------------------------------
% 28.09/5.27 % (7416)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_6848 for (2961ds/340Mi)
% 28.09/5.29 % (7416)Refutation not found, incomplete strategy
% 28.09/5.29 % (7416)------------------------------
% 28.09/5.29 % (7416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.29 % (7416)Termination reason: Refutation not found, incomplete strategy
% 28.09/5.29
% 28.09/5.29
% 28.09/5.29 % (7416)Memory used [KB]: 6140
% 28.09/5.29 % (7416)Time elapsed: 0.023 s
% 28.09/5.29 % (7416)Instructions burned: 88 (million)
% 28.09/5.29 % (7416)------------------------------
% 28.09/5.29 % (7416)------------------------------
% 28.40/5.30 % (7417)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_6848 for (2961ds/3672Mi)
% 28.61/5.50 % (7410)Instruction limit reached!
% 28.61/5.50 % (7410)------------------------------
% 28.61/5.50 % (7410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.61/5.50 % (7410)Termination reason: Unknown
% 28.61/5.50 % (7410)Termination phase: Saturation
% 28.61/5.50
% 28.61/5.50 % (7410)Memory used [KB]: 6780
% 28.61/5.50 % (7410)Time elapsed: 0.335 s
% 28.61/5.50 % (7410)Instructions burned: 1312 (million)
% 28.61/5.50 % (7410)------------------------------
% 28.61/5.50 % (7410)------------------------------
% 28.61/5.51 % (7418)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_6848 for (2959ds/1535Mi)
% 28.61/5.58 % (7413)Instruction limit reached!
% 28.61/5.58 % (7413)------------------------------
% 28.61/5.58 % (7413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.61/5.58 % (7413)Termination reason: Unknown
% 28.61/5.58 % (7413)Termination phase: Saturation
% 28.61/5.58
% 28.61/5.58 % (7413)Memory used [KB]: 2686
% 28.61/5.58 % (7413)Time elapsed: 0.363 s
% 28.61/5.58 % (7413)Instructions burned: 1202 (million)
% 28.61/5.58 % (7413)------------------------------
% 28.61/5.58 % (7413)------------------------------
% 28.61/5.59 % (7419)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_6848 for (2958ds/4637Mi)
% 29.53/5.75 % (7406)Instruction limit reached!
% 29.53/5.75 % (7406)------------------------------
% 29.53/5.75 % (7406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.53/5.75 % (7406)Termination reason: Unknown
% 29.53/5.75 % (7406)Termination phase: Saturation
% 29.53/5.75
% 29.53/5.75 % (7406)Memory used [KB]: 10618
% 29.53/5.75 % (7406)Time elapsed: 0.673 s
% 29.53/5.75 % (7406)Instructions burned: 2404 (million)
% 29.53/5.75 % (7406)------------------------------
% 29.53/5.75 % (7406)------------------------------
% 29.53/5.76 % (7420)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_6848 for (2956ds/3174Mi)
% 30.32/5.86 % (7418)Instruction limit reached!
% 30.32/5.86 % (7418)------------------------------
% 30.32/5.86 % (7418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.86 % (7418)Termination reason: Unknown
% 30.32/5.86 % (7418)Termination phase: Saturation
% 30.32/5.86
% 30.32/5.86 % (7418)Memory used [KB]: 8571
% 30.32/5.86 % (7418)Time elapsed: 0.356 s
% 30.32/5.86 % (7418)Instructions burned: 1538 (million)
% 30.32/5.86 % (7418)------------------------------
% 30.32/5.86 % (7418)------------------------------
% 30.32/5.87 % (7421)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_6848 for (2955ds/307Mi)
% 30.80/5.95 % (7421)Instruction limit reached!
% 30.80/5.95 % (7421)------------------------------
% 30.80/5.95 % (7421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.80/5.95 % (7421)Termination reason: Unknown
% 30.80/5.95 % (7421)Termination phase: Saturation
% 30.80/5.95
% 30.80/5.95 % (7421)Memory used [KB]: 6268
% 30.80/5.95 % (7421)Time elapsed: 0.079 s
% 30.80/5.95 % (7421)Instructions burned: 307 (million)
% 30.80/5.95 % (7421)------------------------------
% 30.80/5.95 % (7421)------------------------------
% 30.80/5.96 % (7422)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_6848 for (2954ds/3619Mi)
% 30.80/5.97 % (7422)Refutation not found, incomplete strategy
% 30.80/5.97 % (7422)------------------------------
% 30.80/5.97 % (7422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.80/5.97 % (7422)Termination reason: Refutation not found, incomplete strategy
% 30.80/5.97
% 30.80/5.97
% 30.80/5.97 % (7422)Memory used [KB]: 6140
% 30.80/5.97 % (7422)Time elapsed: 0.013 s
% 30.80/5.97 % (7422)Instructions burned: 48 (million)
% 30.80/5.97 % (7422)------------------------------
% 30.80/5.97 % (7422)------------------------------
% 30.80/5.98 % (7423)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_6848 for (2954ds/2325Mi)
% 35.13/6.19 % (7386)Instruction limit reached!
% 35.13/6.19 % (7386)------------------------------
% 35.13/6.19 % (7386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.13/6.19 % (7386)Termination reason: Unknown
% 35.13/6.19 % (7386)Termination phase: Saturation
% 35.13/6.19
% 35.13/6.19 % (7386)Memory used [KB]: 27376
% 35.13/6.19 % (7386)Time elapsed: 1.853 s
% 35.13/6.19 % (7386)Instructions burned: 6457 (million)
% 35.13/6.19 % (7386)------------------------------
% 35.13/6.19 % (7386)------------------------------
% 35.62/6.20 % (7424)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_6848 for (2952ds/2341Mi)
% 36.21/6.33 % (7417)Instruction limit reached!
% 36.21/6.33 % (7417)------------------------------
% 36.21/6.33 % (7417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.21/6.33 % (7417)Termination reason: Unknown
% 36.21/6.33 % (7417)Termination phase: Saturation
% 36.21/6.33
% 36.21/6.33 % (7417)Memory used [KB]: 17526
% 36.21/6.33 % (7417)Time elapsed: 1.031 s
% 36.21/6.33 % (7417)Instructions burned: 3673 (million)
% 36.21/6.33 % (7417)------------------------------
% 36.21/6.33 % (7417)------------------------------
% 36.21/6.34 % (7425)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_6848 for (2951ds/7257Mi)
% 36.21/6.35 % (7425)Refutation not found, incomplete strategy
% 36.21/6.35 % (7425)------------------------------
% 36.21/6.35 % (7425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.21/6.35 % (7425)Termination reason: Refutation not found, incomplete strategy
% 36.21/6.35
% 36.21/6.35
% 36.21/6.35 % (7425)Memory used [KB]: 6012
% 36.21/6.35 % (7425)Time elapsed: 0.032 s
% 36.21/6.35 % (7425)Instructions burned: 29 (million)
% 36.21/6.35 % (7425)------------------------------
% 36.21/6.35 % (7425)------------------------------
% 36.21/6.36 % (7426)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_6848 for (2950ds/3710Mi)
% 36.78/6.49 % (7405)Instruction limit reached!
% 36.78/6.49 % (7405)------------------------------
% 36.78/6.49 % (7405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.78/6.49 % (7405)Termination reason: Unknown
% 36.78/6.49 % (7405)Termination phase: Saturation
% 36.78/6.49
% 36.78/6.49 % (7405)Memory used [KB]: 7931
% 36.78/6.49 % (7405)Time elapsed: 1.422 s
% 36.78/6.49 % (7405)Instructions burned: 5066 (million)
% 36.78/6.49 % (7405)------------------------------
% 36.78/6.49 % (7405)------------------------------
% 37.28/6.50 % (7427)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_6848 for (2949ds/326Mi)
% 37.28/6.51 % (7427)Refutation not found, incomplete strategy
% 37.28/6.51 % (7427)------------------------------
% 37.28/6.51 % (7427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.28/6.51 % (7427)Termination reason: Refutation not found, incomplete strategy
% 37.28/6.51
% 37.28/6.51
% 37.28/6.51 % (7427)Memory used [KB]: 6012
% 37.28/6.51 % (7427)Time elapsed: 0.010 s
% 37.28/6.51 % (7427)Instructions burned: 28 (million)
% 37.28/6.51 % (7427)------------------------------
% 37.28/6.51 % (7427)------------------------------
% 37.28/6.52 % (7428)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_6848 for (2949ds/1100Mi)
% 37.28/6.53 % (7428)Refutation not found, incomplete strategy
% 37.28/6.53 % (7428)------------------------------
% 37.28/6.53 % (7428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.28/6.53 % (7428)Termination reason: Refutation not found, incomplete strategy
% 37.28/6.53
% 37.28/6.53
% 37.28/6.53 % (7428)Memory used [KB]: 6012
% 37.28/6.53 % (7428)Time elapsed: 0.015 s
% 37.28/6.53 % (7428)Instructions burned: 54 (million)
% 37.28/6.53 % (7428)------------------------------
% 37.28/6.53 % (7428)------------------------------
% 37.28/6.54 % (7429)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_6848 for (2948ds/406Mi)
% 37.28/6.57 % (7429)Refutation not found, incomplete strategy
% 37.28/6.57 % (7429)------------------------------
% 37.28/6.57 % (7429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.28/6.57 % (7429)Termination reason: Refutation not found, incomplete strategy
% 37.28/6.57
% 37.28/6.57
% 37.28/6.57 % (7429)Memory used [KB]: 6396
% 37.28/6.57 % (7429)Time elapsed: 0.029 s
% 37.28/6.57 % (7429)Instructions burned: 100 (million)
% 37.28/6.57 % (7429)------------------------------
% 37.28/6.57 % (7429)------------------------------
% 37.28/6.58 % (7430)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_6848 for (2948ds/1871Mi)
% 37.76/6.64 % (7423)Instruction limit reached!
% 37.76/6.64 % (7423)------------------------------
% 37.76/6.64 % (7423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.76/6.64 % (7423)Termination reason: Unknown
% 37.76/6.64 % (7423)Termination phase: Saturation
% 37.76/6.64
% 37.76/6.64 % (7423)Memory used [KB]: 14583
% 37.76/6.64 % (7423)Time elapsed: 0.659 s
% 37.76/6.64 % (7423)Instructions burned: 2327 (million)
% 37.76/6.64 % (7423)------------------------------
% 37.76/6.64 % (7423)------------------------------
% 37.76/6.65 % (7420)Instruction limit reached!
% 37.76/6.65 % (7420)------------------------------
% 37.76/6.65 % (7420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.76/6.65 % (7420)Termination reason: Unknown
% 37.76/6.65 % (7420)Termination phase: Saturation
% 37.76/6.65
% 37.76/6.65 % (7420)Memory used [KB]: 16758
% 37.76/6.65 % (7420)Time elapsed: 0.888 s
% 37.76/6.65 % (7420)Instructions burned: 3176 (million)
% 37.76/6.65 % (7420)------------------------------
% 37.76/6.65 % (7420)------------------------------
% 37.76/6.65 % (7431)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_6848 for (2947ds/1194Mi)
% 37.76/6.66 % (7432)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_6848 for (2947ds/474Mi)
% 38.07/6.71 % (7407)Instruction limit reached!
% 38.07/6.71 % (7407)------------------------------
% 38.07/6.71 % (7407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.07/6.71 % (7407)Termination reason: Unknown
% 38.07/6.71 % (7407)Termination phase: Saturation
% 38.07/6.71
% 38.07/6.71 % (7407)Memory used [KB]: 18293
% 38.07/6.71 % (7407)Time elapsed: 1.625 s
% 38.07/6.71 % (7407)Instructions burned: 5801 (million)
% 38.07/6.71 % (7407)------------------------------
% 38.07/6.71 % (7407)------------------------------
% 38.07/6.72 % (7433)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_6848 for (2947ds/3115Mi)
% 38.07/6.78 % (7432)Instruction limit reached!
% 38.07/6.78 % (7432)------------------------------
% 38.07/6.78 % (7432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.07/6.78 % (7432)Termination reason: Unknown
% 38.07/6.78 % (7432)Termination phase: Saturation
% 38.07/6.78
% 38.07/6.78 % (7432)Memory used [KB]: 6652
% 38.07/6.78 % (7432)Time elapsed: 0.121 s
% 38.07/6.78 % (7432)Instructions burned: 474 (million)
% 38.07/6.78 % (7432)------------------------------
% 38.07/6.78 % (7432)------------------------------
% 38.07/6.79 % (7434)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_6848 for (2946ds/831Mi)
% 38.33/6.85 % (7424)Instruction limit reached!
% 38.33/6.85 % (7424)------------------------------
% 38.33/6.85 % (7424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.33/6.85 % (7424)Termination reason: Unknown
% 38.33/6.85 % (7424)Termination phase: Saturation
% 38.33/6.85
% 38.33/6.85 % (7424)Memory used [KB]: 12025
% 38.33/6.85 % (7424)Time elapsed: 0.670 s
% 38.33/6.85 % (7424)Instructions burned: 2344 (million)
% 38.33/6.85 % (7424)------------------------------
% 38.33/6.85 % (7424)------------------------------
% 38.33/6.86 % (7435)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_6848 for (2945ds/1188Mi)
% 39.08/6.90 % (7419)Instruction limit reached!
% 39.08/6.90 % (7419)------------------------------
% 39.08/6.90 % (7419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/6.90 % (7419)Termination reason: Unknown
% 39.08/6.90 % (7419)Termination phase: Saturation
% 39.08/6.90
% 39.08/6.90 % (7419)Memory used [KB]: 20084
% 39.08/6.90 % (7419)Time elapsed: 1.313 s
% 39.08/6.90 % (7419)Instructions burned: 4637 (million)
% 39.08/6.90 % (7419)------------------------------
% 39.08/6.90 % (7419)------------------------------
% 39.08/6.91 % (7436)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_6848 for (2945ds/2868Mi)
% 39.08/6.93 % (7436)Refutation not found, incomplete strategy
% 39.08/6.93 % (7436)------------------------------
% 39.08/6.93 % (7436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/6.93 % (7436)Termination reason: Refutation not found, incomplete strategy
% 39.08/6.93
% 39.08/6.93
% 39.08/6.93 % (7436)Memory used [KB]: 6396
% 39.08/6.93 % (7436)Time elapsed: 0.020 s
% 39.08/6.93 % (7436)Instructions burned: 74 (million)
% 39.08/6.93 % (7436)------------------------------
% 39.08/6.93 % (7436)------------------------------
% 39.08/6.94 % (7437)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_6848 for (2944ds/1516Mi)
% 39.08/6.95 % (7437)Refutation not found, incomplete strategy
% 39.08/6.95 % (7437)------------------------------
% 39.08/6.95 % (7437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/6.95 % (7437)Termination reason: Refutation not found, incomplete strategy
% 39.08/6.95
% 39.08/6.95
% 39.08/6.95 % (7437)Memory used [KB]: 6012
% 39.08/6.95 % (7437)Time elapsed: 0.009 s
% 39.08/6.95 % (7437)Instructions burned: 30 (million)
% 39.08/6.95 % (7437)------------------------------
% 39.08/6.95 % (7437)------------------------------
% 39.08/6.96 % (7438)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_6848 for (2944ds/2321Mi)
% 39.08/6.97 % (7431)Instruction limit reached!
% 39.08/6.97 % (7431)------------------------------
% 39.08/6.97 % (7431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/6.97 % (7431)Termination reason: Unknown
% 39.08/6.97 % (7431)Termination phase: Saturation
% 39.08/6.97
% 39.08/6.97 % (7431)Memory used [KB]: 10106
% 39.08/6.97 % (7431)Time elapsed: 0.317 s
% 39.08/6.97 % (7431)Instructions burned: 1197 (million)
% 39.08/6.97 % (7431)------------------------------
% 39.08/6.97 % (7431)------------------------------
% 39.08/6.98 % (7438)Refutation not found, incomplete strategy
% 39.08/6.98 % (7438)------------------------------
% 39.08/6.98 % (7438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/6.98 % (7438)Termination reason: Refutation not found, incomplete strategy
% 39.08/6.98
% 39.08/6.98
% 39.08/6.98 % (7438)Memory used [KB]: 6268
% 39.08/6.98 % (7438)Time elapsed: 0.016 s
% 39.08/6.98 % (7438)Instructions burned: 62 (million)
% 39.08/6.98 % (7438)------------------------------
% 39.08/6.98 % (7438)------------------------------
% 39.08/6.98 % (7439)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_6848 for (2944ds/2812Mi)
% 39.08/6.98 % (7440)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_6848 for (2944ds/4604Mi)
% 39.08/7.01 % (7434)Instruction limit reached!
% 39.08/7.01 % (7434)------------------------------
% 39.08/7.01 % (7434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/7.01 % (7434)Termination reason: Unknown
% 39.08/7.01 % (7434)Termination phase: Saturation
% 39.08/7.01
% 39.08/7.01 % (7434)Memory used [KB]: 9466
% 39.08/7.01 % (7434)Time elapsed: 0.220 s
% 39.08/7.01 % (7434)Instructions burned: 831 (million)
% 39.08/7.01 % (7434)------------------------------
% 39.08/7.01 % (7434)------------------------------
% 39.08/7.02 % (7441)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_6848 for (2944ds/2678Mi)
% 41.38/7.11 % (7430)Instruction limit reached!
% 41.38/7.11 % (7430)------------------------------
% 41.38/7.11 % (7430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.38/7.11 % (7430)Termination reason: Unknown
% 41.38/7.11 % (7430)Termination phase: Saturation
% 41.38/7.11
% 41.38/7.11 % (7430)Memory used [KB]: 13304
% 41.38/7.11 % (7430)Time elapsed: 0.530 s
% 41.38/7.11 % (7430)Instructions burned: 1873 (million)
% 41.38/7.11 % (7430)------------------------------
% 41.38/7.11 % (7430)------------------------------
% 41.38/7.12 % (7442)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_6848 for (2943ds/643Mi)
% 42.01/7.15 % (7435)Instruction limit reached!
% 42.01/7.15 % (7435)------------------------------
% 42.01/7.15 % (7435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.01/7.15 % (7435)Termination reason: Unknown
% 42.01/7.15 % (7435)Termination phase: Saturation
% 42.01/7.15
% 42.01/7.15 % (7435)Memory used [KB]: 6780
% 42.01/7.15 % (7435)Time elapsed: 0.296 s
% 42.01/7.15 % (7435)Instructions burned: 1190 (million)
% 42.01/7.15 % (7435)------------------------------
% 42.01/7.15 % (7435)------------------------------
% 42.01/7.16 % (7443)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_6848 for (2942ds/458Mi)
% 42.33/7.25 % (7426)Instruction limit reached!
% 42.33/7.25 % (7426)------------------------------
% 42.33/7.25 % (7426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.33/7.25 % (7426)Termination reason: Unknown
% 42.33/7.25 % (7426)Termination phase: Saturation
% 42.33/7.25
% 42.33/7.25 % (7426)Memory used [KB]: 9210
% 42.33/7.25 % (7426)Time elapsed: 0.893 s
% 42.33/7.25 % (7426)Instructions burned: 3711 (million)
% 42.33/7.25 % (7426)------------------------------
% 42.33/7.25 % (7426)------------------------------
% 42.33/7.26 % (7444)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_6848 for (2941ds/2546Mi)
% 42.33/7.28 % (7443)Instruction limit reached!
% 42.33/7.28 % (7443)------------------------------
% 42.33/7.28 % (7443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.33/7.28 % (7443)Termination reason: Unknown
% 42.33/7.28 % (7443)Termination phase: Saturation
% 42.33/7.28
% 42.33/7.28 % (7443)Memory used [KB]: 6524
% 42.33/7.28 % (7443)Time elapsed: 0.123 s
% 42.33/7.28 % (7443)Instructions burned: 458 (million)
% 42.33/7.28 % (7443)------------------------------
% 42.33/7.28 % (7443)------------------------------
% 42.33/7.29 % (7442)Instruction limit reached!
% 42.33/7.29 % (7442)------------------------------
% 42.33/7.29 % (7442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.33/7.29 % (7442)Termination reason: Unknown
% 42.33/7.29 % (7442)Termination phase: Saturation
% 42.33/7.29
% 42.33/7.29 % (7442)Memory used [KB]: 7036
% 42.33/7.29 % (7442)Time elapsed: 0.171 s
% 42.33/7.29 % (7442)Instructions burned: 644 (million)
% 42.33/7.29 % (7442)------------------------------
% 42.33/7.29 % (7442)------------------------------
% 42.33/7.29 % (7445)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_6848 for (2941ds/1432Mi)
% 43.01/7.30 % (7446)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_6848 for (2941ds/386Mi)
% 43.01/7.40 % (7446)Instruction limit reached!
% 43.01/7.40 % (7446)------------------------------
% 43.01/7.40 % (7446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.01/7.40 % (7446)Termination reason: Unknown
% 43.01/7.40 % (7446)Termination phase: Saturation
% 43.01/7.40
% 43.01/7.40 % (7446)Memory used [KB]: 6396
% 43.01/7.40 % (7446)Time elapsed: 0.099 s
% 43.01/7.40 % (7446)Instructions burned: 388 (million)
% 43.01/7.40 % (7446)------------------------------
% 43.01/7.40 % (7446)------------------------------
% 43.31/7.41 % (7447)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_6848 for (2940ds/360Mi)
% 43.31/7.48 % (7433)Instruction limit reached!
% 43.31/7.48 % (7433)------------------------------
% 43.31/7.48 % (7433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.31/7.48 % (7433)Termination reason: Unknown
% 43.31/7.48 % (7433)Termination phase: Saturation
% 43.31/7.48
% 43.31/7.48 % (7433)Memory used [KB]: 6780
% 43.31/7.48 % (7433)Time elapsed: 0.762 s
% 43.31/7.48 % (7433)Instructions burned: 3118 (million)
% 43.31/7.48 % (7433)------------------------------
% 43.31/7.48 % (7433)------------------------------
% 43.31/7.49 % (7448)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_6848 for (2939ds/5446Mi)
% 43.70/7.50 % (7447)Instruction limit reached!
% 43.70/7.50 % (7447)------------------------------
% 43.70/7.50 % (7447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.70/7.50 % (7447)Termination reason: Unknown
% 43.70/7.50 % (7447)Termination phase: Saturation
% 43.70/7.50
% 43.70/7.50 % (7447)Memory used [KB]: 6780
% 43.70/7.50 % (7447)Time elapsed: 0.098 s
% 43.70/7.50 % (7447)Instructions burned: 360 (million)
% 43.70/7.50 % (7447)------------------------------
% 43.70/7.50 % (7447)------------------------------
% 43.70/7.51 % (7449)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_6848 for (2939ds/2573Mi)
% 43.70/7.59 % (7445)Instruction limit reached!
% 43.70/7.59 % (7445)------------------------------
% 43.70/7.59 % (7445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.70/7.59 % (7445)Termination reason: Unknown
% 43.70/7.59 % (7445)Termination phase: Saturation
% 43.70/7.59
% 43.70/7.59 % (7445)Memory used [KB]: 8315
% 43.70/7.59 % (7445)Time elapsed: 0.303 s
% 43.70/7.59 % (7445)Instructions burned: 1436 (million)
% 43.70/7.59 % (7445)------------------------------
% 43.70/7.59 % (7445)------------------------------
% 44.34/7.60 % (7450)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_6848 for (2938ds/2655Mi)
% 44.54/7.76 % (7439)Instruction limit reached!
% 44.54/7.76 % (7439)------------------------------
% 44.54/7.76 % (7439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.54/7.76 % (7439)Termination reason: Unknown
% 44.54/7.76 % (7439)Termination phase: Saturation
% 44.54/7.76
% 44.54/7.76 % (7439)Memory used [KB]: 16247
% 44.54/7.76 % (7439)Time elapsed: 0.781 s
% 44.54/7.76 % (7439)Instructions burned: 2814 (million)
% 44.54/7.76 % (7439)------------------------------
% 44.54/7.76 % (7439)------------------------------
% 44.54/7.76 % (7441)Instruction limit reached!
% 44.54/7.76 % (7441)------------------------------
% 44.54/7.76 % (7441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.54/7.76 % (7441)Termination reason: Unknown
% 44.54/7.76 % (7441)Termination phase: Saturation
% 44.54/7.76
% 44.54/7.76 % (7441)Memory used [KB]: 17270
% 44.54/7.76 % (7441)Time elapsed: 0.742 s
% 44.54/7.76 % (7441)Instructions burned: 2681 (million)
% 44.54/7.76 % (7441)------------------------------
% 44.54/7.76 % (7441)------------------------------
% 44.54/7.77 % (7451)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_6848 for (2936ds/2781Mi)
% 44.54/7.77 % (7452)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_6848 for (2936ds/307Mi)
% 45.46/7.85 % (7452)Instruction limit reached!
% 45.46/7.85 % (7452)------------------------------
% 45.46/7.85 % (7452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.46/7.85 % (7452)Termination reason: Unknown
% 45.46/7.85 % (7452)Termination phase: Saturation
% 45.46/7.85
% 45.46/7.85 % (7452)Memory used [KB]: 6268
% 45.46/7.85 % (7452)Time elapsed: 0.081 s
% 45.46/7.85 % (7452)Instructions burned: 309 (million)
% 45.46/7.85 % (7452)------------------------------
% 45.46/7.85 % (7452)------------------------------
% 45.46/7.86 % (7453)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_6848 for (2935ds/1548Mi)
% 45.46/7.87 % (7453)Refutation not found, incomplete strategy
% 45.46/7.87 % (7453)------------------------------
% 45.46/7.87 % (7453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.46/7.87 % (7453)Termination reason: Refutation not found, incomplete strategy
% 45.46/7.87
% 45.46/7.87
% 45.46/7.87 % (7453)Memory used [KB]: 6012
% 45.46/7.87 % (7453)Time elapsed: 0.009 s
% 45.46/7.87 % (7453)Instructions burned: 29 (million)
% 45.46/7.87 % (7453)------------------------------
% 45.46/7.87 % (7453)------------------------------
% 45.46/7.88 % (7454)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_6848 for (2935ds/5214Mi)
% 48.39/8.04 % (7444)Instruction limit reached!
% 48.39/8.04 % (7444)------------------------------
% 48.39/8.04 % (7444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.39/8.04 % (7444)Termination reason: Unknown
% 48.39/8.04 % (7444)Termination phase: Saturation
% 48.39/8.04
% 48.39/8.04 % (7444)Memory used [KB]: 9722
% 48.39/8.04 % (7444)Time elapsed: 0.781 s
% 48.39/8.04 % (7444)Instructions burned: 2548 (million)
% 48.39/8.04 % (7444)------------------------------
% 48.39/8.04 % (7444)------------------------------
% 48.39/8.05 % (7455)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_6848 for (2933ds/3201Mi)
% 49.07/8.17 % (7449)Instruction limit reached!
% 49.07/8.17 % (7449)------------------------------
% 49.07/8.17 % (7449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.07/8.17 % (7449)Termination reason: Unknown
% 49.07/8.17 % (7449)Termination phase: Saturation
% 49.07/8.17
% 49.07/8.17 % (7449)Memory used [KB]: 7419
% 49.07/8.17 % (7449)Time elapsed: 0.663 s
% 49.07/8.17 % (7449)Instructions burned: 2575 (million)
% 49.07/8.17 % (7449)------------------------------
% 49.07/8.17 % (7449)------------------------------
% 49.07/8.18 % (7456)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_6848 for (2932ds/454Mi)
% 49.48/8.28 % (7450)Instruction limit reached!
% 49.48/8.28 % (7450)------------------------------
% 49.48/8.28 % (7450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.48/8.28 % (7450)Termination reason: Unknown
% 49.48/8.28 % (7450)Termination phase: Saturation
% 49.48/8.28
% 49.48/8.28 % (7450)Memory used [KB]: 8059
% 49.48/8.28 % (7450)Time elapsed: 0.681 s
% 49.48/8.28 % (7450)Instructions burned: 2655 (million)
% 49.48/8.28 % (7450)------------------------------
% 49.48/8.28 % (7450)------------------------------
% 49.48/8.29 % (7440)Instruction limit reached!
% 49.48/8.29 % (7440)------------------------------
% 49.48/8.29 % (7440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.48/8.29 % (7440)Termination reason: Unknown
% 49.48/8.29 % (7440)Termination phase: Saturation
% 49.48/8.29
% 49.48/8.29 % (7440)Memory used [KB]: 18421
% 49.48/8.29 % (7440)Time elapsed: 1.309 s
% 49.48/8.29 % (7440)Instructions burned: 4606 (million)
% 49.48/8.29 % (7440)------------------------------
% 49.48/8.29 % (7440)------------------------------
% 49.48/8.29 % (7457)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_6848 for (2931ds/3049Mi)
% 49.98/8.30 % (7458)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_6848 for (2931ds/7311Mi)
% 49.98/8.31 % (7457)Refutation not found, incomplete strategy
% 49.98/8.31 % (7457)------------------------------
% 49.98/8.31 % (7457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.98/8.31 % (7457)Termination reason: Refutation not found, incomplete strategy
% 49.98/8.31
% 49.98/8.31
% 49.98/8.31 % (7457)Memory used [KB]: 6012
% 49.98/8.31 % (7457)Time elapsed: 0.015 s
% 49.98/8.31 % (7457)Instructions burned: 54 (million)
% 49.98/8.31 % (7457)------------------------------
% 49.98/8.31 % (7457)------------------------------
% 49.98/8.31 % (7456)Instruction limit reached!
% 49.98/8.31 % (7456)------------------------------
% 49.98/8.31 % (7456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.98/8.31 % (7456)Termination reason: Unknown
% 49.98/8.31 % (7456)Termination phase: Saturation
% 49.98/8.31
% 49.98/8.31 % (7456)Memory used [KB]: 11129
% 49.98/8.31 % (7456)Time elapsed: 0.125 s
% 49.98/8.31 % (7456)Instructions burned: 457 (million)
% 49.98/8.31 % (7456)------------------------------
% 49.98/8.31 % (7456)------------------------------
% 49.98/8.31 % (7458)Refutation not found, incomplete strategy
% 49.98/8.31 % (7458)------------------------------
% 49.98/8.31 % (7458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.98/8.31 % (7458)Termination reason: Refutation not found, incomplete strategy
% 49.98/8.31
% 49.98/8.31
% 49.98/8.31 % (7458)Memory used [KB]: 6012
% 49.98/8.31 % (7458)Time elapsed: 0.008 s
% 49.98/8.31 % (7458)Instructions burned: 28 (million)
% 49.98/8.31 % (7458)------------------------------
% 49.98/8.31 % (7458)------------------------------
% 49.98/8.32 % (7459)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_6848 for (2931ds/6804Mi)
% 49.98/8.32 % (7460)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_6848 for (2931ds/1683Mi)
% 49.98/8.32 % (7461)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_6848 for (2931ds/4688Mi)
% 49.98/8.33 % (7459)Refutation not found, incomplete strategy
% 49.98/8.33 % (7459)------------------------------
% 49.98/8.33 % (7459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.98/8.33 % (7459)Termination reason: Refutation not found, incomplete strategy
% 49.98/8.33
% 49.98/8.33
% 49.98/8.33 % (7459)Memory used [KB]: 6140
% 49.98/8.33 % (7459)Time elapsed: 0.014 s
% 49.98/8.33 % (7459)Instructions burned: 49 (million)
% 49.98/8.33 % (7459)------------------------------
% 49.98/8.33 % (7459)------------------------------
% 49.98/8.34 % (7462)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_6848 for (2930ds/2207Mi)
% 50.80/8.59 % (7451)Instruction limit reached!
% 50.80/8.59 % (7451)------------------------------
% 50.80/8.59 % (7451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.80/8.59 % (7451)Termination reason: Unknown
% 50.80/8.59 % (7451)Termination phase: Saturation
% 50.80/8.59
% 50.80/8.59 % (7451)Memory used [KB]: 2814
% 50.80/8.59 % (7451)Time elapsed: 0.823 s
% 50.80/8.59 % (7451)Instructions burned: 2783 (million)
% 50.80/8.59 % (7451)------------------------------
% 50.80/8.59 % (7451)------------------------------
% 51.10/8.60 % (7463)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=8216:si=on:rtra=on_0 on DTF2THF_6848 for (2928ds/8216Mi)
% 51.30/8.78 % (7460)Instruction limit reached!
% 51.30/8.78 % (7460)------------------------------
% 51.30/8.78 % (7460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.30/8.78 % (7460)Termination reason: Unknown
% 51.30/8.78 % (7460)Termination phase: Saturation
% 51.30/8.78
% 51.30/8.78 % (7460)Memory used [KB]: 12409
% 51.30/8.78 % (7460)Time elapsed: 0.467 s
% 51.30/8.78 % (7460)Instructions burned: 1683 (million)
% 51.30/8.78 % (7460)------------------------------
% 51.30/8.78 % (7460)------------------------------
% 51.30/8.79 % (7464)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_6848 for (2926ds/430Mi)
% 52.19/8.91 % (7464)Instruction limit reached!
% 52.19/8.91 % (7464)------------------------------
% 52.19/8.91 % (7464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.19/8.91 % (7464)Termination reason: Unknown
% 52.19/8.91 % (7464)Termination phase: Saturation
% 52.19/8.91
% 52.19/8.91 % (7464)Memory used [KB]: 6524
% 52.19/8.91 % (7464)Time elapsed: 0.113 s
% 52.19/8.91 % (7464)Instructions burned: 431 (million)
% 52.19/8.91 % (7464)------------------------------
% 52.19/8.91 % (7464)------------------------------
% 52.19/8.92 % (7465)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_6848 for (2925ds/2012Mi)
% 52.19/8.95 % (7462)Instruction limit reached!
% 52.19/8.95 % (7462)------------------------------
% 52.19/8.95 % (7462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.19/8.95 % (7462)Termination reason: Unknown
% 52.19/8.95 % (7462)Termination phase: Saturation
% 52.19/8.95
% 52.19/8.95 % (7462)Memory used [KB]: 13560
% 52.19/8.95 % (7462)Time elapsed: 0.608 s
% 52.19/8.95 % (7462)Instructions burned: 2210 (million)
% 52.19/8.95 % (7462)------------------------------
% 52.19/8.95 % (7462)------------------------------
% 52.19/8.95 % (7455)Instruction limit reached!
% 52.19/8.95 % (7455)------------------------------
% 52.19/8.95 % (7455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.19/8.95 % (7455)Termination reason: Unknown
% 52.19/8.95 % (7455)Termination phase: Saturation
% 52.19/8.95
% 52.19/8.95 % (7455)Memory used [KB]: 17142
% 52.19/8.95 % (7455)Time elapsed: 0.926 s
% 52.19/8.95 % (7455)Instructions burned: 3202 (million)
% 52.19/8.95 % (7455)------------------------------
% 52.19/8.95 % (7455)------------------------------
% 52.19/8.96 % (7466)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_6848 for (2924ds/631Mi)
% 52.19/8.96 % (7467)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_6848 for (2924ds/8785Mi)
% 55.45/9.04 % (7448)Instruction limit reached!
% 55.45/9.04 % (7448)------------------------------
% 55.45/9.04 % (7448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.45/9.04 % (7448)Termination reason: Unknown
% 55.45/9.04 % (7448)Termination phase: Saturation
% 55.45/9.04
% 55.45/9.04 % (7448)Memory used [KB]: 22387
% 55.45/9.04 % (7448)Time elapsed: 1.550 s
% 55.45/9.04 % (7448)Instructions burned: 5447 (million)
% 55.45/9.04 % (7448)------------------------------
% 55.45/9.04 % (7448)------------------------------
% 55.45/9.05 % (7468)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_6848 for (2923ds/739Mi)
% 56.11/9.13 % (7466)Instruction limit reached!
% 56.11/9.13 % (7466)------------------------------
% 56.11/9.13 % (7466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.11/9.13 % (7466)Termination reason: Unknown
% 56.11/9.13 % (7466)Termination phase: Saturation
% 56.11/9.13
% 56.11/9.13 % (7466)Memory used [KB]: 7291
% 56.11/9.13 % (7466)Time elapsed: 0.172 s
% 56.11/9.13 % (7466)Instructions burned: 632 (million)
% 56.11/9.13 % (7466)------------------------------
% 56.11/9.13 % (7466)------------------------------
% 56.11/9.14 % (7469)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_6848 for (2922ds/5473Mi)
% 56.48/9.27 % (7468)Instruction limit reached!
% 56.48/9.27 % (7468)------------------------------
% 56.48/9.27 % (7468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.48/9.27 % (7468)Termination reason: Unknown
% 56.48/9.27 % (7468)Termination phase: Saturation
% 56.48/9.27
% 56.48/9.27 % (7468)Memory used [KB]: 6780
% 56.48/9.27 % (7468)Time elapsed: 0.221 s
% 56.48/9.27 % (7468)Instructions burned: 740 (million)
% 56.48/9.27 % (7468)------------------------------
% 56.48/9.27 % (7468)------------------------------
% 56.48/9.28 % (7470)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_6848 for (2921ds/43570Mi)
% 56.48/9.29 % (7470)Refutation not found, incomplete strategy
% 56.48/9.29 % (7470)------------------------------
% 56.48/9.29 % (7470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.48/9.29 % (7470)Termination reason: Refutation not found, incomplete strategy
% 56.48/9.29
% 56.48/9.29
% 56.48/9.29 % (7470)Memory used [KB]: 6012
% 56.48/9.29 % (7470)Time elapsed: 0.009 s
% 56.48/9.29 % (7470)Instructions burned: 30 (million)
% 56.48/9.29 % (7470)------------------------------
% 56.48/9.29 % (7470)------------------------------
% 57.23/9.30 % (7471)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_6848 for (2921ds/8382Mi)
% 57.23/9.32 % (7454)Instruction limit reached!
% 57.23/9.32 % (7454)------------------------------
% 57.23/9.32 % (7454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.23/9.32 % (7454)Termination reason: Unknown
% 57.23/9.32 % (7454)Termination phase: Saturation
% 57.23/9.32
% 57.23/9.32 % (7454)Memory used [KB]: 18293
% 57.23/9.32 % (7454)Time elapsed: 1.441 s
% 57.23/9.32 % (7454)Instructions burned: 5216 (million)
% 57.23/9.32 % (7454)------------------------------
% 57.23/9.32 % (7454)------------------------------
% 57.23/9.33 % (7472)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_6848 for (2921ds/407Mi)
% 57.66/9.44 % (7472)Instruction limit reached!
% 57.66/9.44 % (7472)------------------------------
% 57.66/9.44 % (7472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.66/9.44 % (7472)Termination reason: Unknown
% 57.66/9.44 % (7472)Termination phase: Saturation
% 57.66/9.44
% 57.66/9.44 % (7472)Memory used [KB]: 7931
% 57.66/9.44 % (7472)Time elapsed: 0.114 s
% 57.66/9.44 % (7472)Instructions burned: 408 (million)
% 57.66/9.44 % (7472)------------------------------
% 57.66/9.44 % (7472)------------------------------
% 57.66/9.45 % (7473)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_6848 for (2919ds/2971Mi)
% 57.66/9.47 % (7465)Instruction limit reached!
% 57.66/9.47 % (7465)------------------------------
% 57.66/9.47 % (7465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.66/9.47 % (7465)Termination reason: Unknown
% 57.66/9.47 % (7465)Termination phase: Saturation
% 57.66/9.47
% 57.66/9.47 % (7465)Memory used [KB]: 21492
% 57.66/9.47 % (7465)Time elapsed: 0.554 s
% 57.66/9.47 % (7465)Instructions burned: 2013 (million)
% 57.66/9.47 % (7465)------------------------------
% 57.66/9.47 % (7465)------------------------------
% 57.66/9.47 % (7473)Refutation not found, incomplete strategy
% 57.66/9.47 % (7473)------------------------------
% 57.66/9.47 % (7473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.66/9.47 % (7473)Termination reason: Refutation not found, incomplete strategy
% 57.66/9.47
% 57.66/9.47
% 57.66/9.47 % (7473)Memory used [KB]: 6524
% 57.66/9.47 % (7473)Time elapsed: 0.020 s
% 57.66/9.47 % (7473)Instructions burned: 70 (million)
% 57.66/9.47 % (7473)------------------------------
% 57.66/9.47 % (7473)------------------------------
% 57.66/9.48 % (7474)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_6848 for (2919ds/9822Mi)
% 57.66/9.48 % (7475)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_6848 for (2919ds/8425Mi)
% 57.66/9.49 % (7474)Refutation not found, incomplete strategy
% 57.66/9.49 % (7474)------------------------------
% 57.66/9.49 % (7474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.66/9.49 % (7474)Termination reason: Refutation not found, incomplete strategy
% 57.66/9.49
% 57.66/9.49
% 57.66/9.49 % (7474)Memory used [KB]: 6012
% 57.66/9.49 % (7474)Time elapsed: 0.014 s
% 57.66/9.49 % (7474)Instructions burned: 50 (million)
% 57.66/9.49 % (7474)------------------------------
% 57.66/9.49 % (7474)------------------------------
% 58.22/9.50 % (7476)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_6848 for (2919ds/3107Mi)
% 58.53/9.69 % (7461)Instruction limit reached!
% 58.53/9.69 % (7461)------------------------------
% 58.53/9.69 % (7461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.53/9.69 % (7461)Termination reason: Unknown
% 58.53/9.69 % (7461)Termination phase: Saturation
% 58.53/9.69
% 58.53/9.69 % (7461)Memory used [KB]: 8827
% 58.53/9.69 % (7461)Time elapsed: 1.373 s
% 58.53/9.69 % (7461)Instructions burned: 4690 (million)
% 58.53/9.69 % (7461)------------------------------
% 58.53/9.69 % (7461)------------------------------
% 58.83/9.70 % (7477)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_6848 for (2917ds/7967Mi)
% 58.83/9.72 % (7477)Refutation not found, incomplete strategy
% 58.83/9.72 % (7477)------------------------------
% 58.83/9.72 % (7477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.83/9.72 % (7477)Termination reason: Refutation not found, incomplete strategy
% 58.83/9.72
% 58.83/9.72
% 58.83/9.72 % (7477)Memory used [KB]: 6268
% 58.83/9.72 % (7477)Time elapsed: 0.017 s
% 58.83/9.72 % (7477)Instructions burned: 59 (million)
% 58.83/9.72 % (7477)------------------------------
% 58.83/9.72 % (7477)------------------------------
% 58.83/9.73 % (7478)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_6848 for (2917ds/3629Mi)
% 64.39/10.39 % (7476)Instruction limit reached!
% 64.39/10.39 % (7476)------------------------------
% 64.39/10.39 % (7476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.39/10.39 % (7476)Termination reason: Unknown
% 64.39/10.39 % (7476)Termination phase: Saturation
% 64.39/10.39
% 64.39/10.39 % (7476)Memory used [KB]: 11641
% 64.39/10.39 % (7476)Time elapsed: 0.893 s
% 64.39/10.39 % (7476)Instructions burned: 3109 (million)
% 64.39/10.39 % (7476)------------------------------
% 64.39/10.39 % (7476)------------------------------
% 65.10/10.40 % (7479)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_6848 for (2910ds/939Mi)
% 66.30/10.69 % (7479)Instruction limit reached!
% 66.30/10.69 % (7479)------------------------------
% 66.30/10.69 % (7479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.30/10.69 % (7479)Termination reason: Unknown
% 66.30/10.69 % (7479)Termination phase: Saturation
% 66.30/10.69
% 66.30/10.69 % (7479)Memory used [KB]: 6268
% 66.30/10.69 % (7479)Time elapsed: 0.289 s
% 66.30/10.69 % (7479)Instructions burned: 942 (million)
% 66.30/10.69 % (7479)------------------------------
% 66.30/10.69 % (7479)------------------------------
% 67.19/10.70 % (7469)Instruction limit reached!
% 67.19/10.70 % (7469)------------------------------
% 67.19/10.70 % (7469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.19/10.70 % (7469)Termination reason: Unknown
% 67.19/10.70 % (7469)Termination phase: Saturation
% 67.19/10.70
% 67.19/10.70 % (7469)Memory used [KB]: 21875
% 67.19/10.70 % (7469)Time elapsed: 1.563 s
% 67.19/10.70 % (7469)Instructions burned: 5475 (million)
% 67.19/10.70 % (7469)------------------------------
% 67.19/10.70 % (7469)------------------------------
% 67.19/10.70 % (7480)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_6848 for (2907ds/1188Mi)
% 67.19/10.71 % (7481)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_6848 for (2907ds/3205Mi)
% 67.73/10.81 % (7478)Instruction limit reached!
% 67.73/10.81 % (7478)------------------------------
% 67.73/10.81 % (7478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.73/10.81 % (7478)Termination reason: Unknown
% 67.73/10.81 % (7478)Termination phase: Saturation
% 67.73/10.81
% 67.73/10.81 % (7478)Memory used [KB]: 12665
% 67.73/10.81 % (7478)Time elapsed: 1.078 s
% 67.73/10.81 % (7478)Instructions burned: 3630 (million)
% 67.73/10.81 % (7478)------------------------------
% 67.73/10.81 % (7478)------------------------------
% 67.73/10.82 % (7482)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_6848 for (2906ds/865Mi)
% 67.73/10.83 % (7482)Refutation not found, incomplete strategy
% 67.73/10.83 % (7482)------------------------------
% 67.73/10.83 % (7482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.73/10.83 % (7482)Termination reason: Refutation not found, incomplete strategy
% 67.73/10.83
% 67.73/10.83
% 67.73/10.83 % (7482)Memory used [KB]: 6012
% 67.73/10.83 % (7482)Time elapsed: 0.017 s
% 67.73/10.83 % (7482)Instructions burned: 61 (million)
% 67.73/10.83 % (7482)------------------------------
% 67.73/10.83 % (7482)------------------------------
% 67.73/10.84 % (7483)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_6848 for (2905ds/7469Mi)
% 68.17/11.00 % (7480)Instruction limit reached!
% 68.17/11.00 % (7480)------------------------------
% 68.17/11.00 % (7480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.17/11.00 % (7480)Termination reason: Unknown
% 68.17/11.00 % (7480)Termination phase: Saturation
% 68.17/11.00
% 68.17/11.00 % (7480)Memory used [KB]: 6780
% 68.17/11.00 % (7480)Time elapsed: 0.296 s
% 68.17/11.00 % (7480)Instructions burned: 1188 (million)
% 68.17/11.00 % (7480)------------------------------
% 68.17/11.00 % (7480)------------------------------
% 68.17/11.01 % (7484)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_6848 for (2904ds/4165Mi)
% 69.47/11.05 % (7463)Instruction limit reached!
% 69.47/11.05 % (7463)------------------------------
% 69.47/11.05 % (7463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.47/11.05 % (7463)Termination reason: Unknown
% 69.47/11.05 % (7463)Termination phase: Saturation
% 69.47/11.05
% 69.47/11.05 % (7463)Memory used [KB]: 15479
% 69.47/11.05 % (7463)Time elapsed: 2.458 s
% 69.47/11.05 % (7463)Instructions burned: 8217 (million)
% 69.47/11.05 % (7463)------------------------------
% 69.47/11.05 % (7463)------------------------------
% 69.47/11.07 % (7485)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_6848 for (2903ds/13468Mi)
% 69.47/11.07 % (7485)Refutation not found, incomplete strategy
% 69.47/11.07 % (7485)------------------------------
% 69.47/11.07 % (7485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.47/11.07 % (7485)Termination reason: Refutation not found, incomplete strategy
% 69.47/11.07
% 69.47/11.07
% 69.47/11.07 % (7485)Memory used [KB]: 6012
% 69.47/11.07 % (7485)Time elapsed: 0.010 s
% 69.47/11.07 % (7485)Instructions burned: 34 (million)
% 69.47/11.07 % (7485)------------------------------
% 69.47/11.07 % (7485)------------------------------
% 69.47/11.08 % (7486)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_6848 for (2903ds/2635Mi)
% 71.81/11.46 % (7467)Instruction limit reached!
% 71.81/11.46 % (7467)------------------------------
% 71.81/11.46 % (7467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.81/11.46 % (7467)Termination reason: Unknown
% 71.81/11.46 % (7467)Termination phase: Saturation
% 71.81/11.46
% 71.81/11.46 % (7467)Memory used [KB]: 33645
% 71.81/11.46 % (7467)Time elapsed: 2.495 s
% 71.81/11.46 % (7467)Instructions burned: 8785 (million)
% 71.81/11.46 % (7467)------------------------------
% 71.81/11.46 % (7467)------------------------------
% 71.81/11.47 % (7487)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_6848 for (2899ds/631Mi)
% 72.39/11.59 % (7471)Instruction limit reached!
% 72.39/11.59 % (7471)------------------------------
% 72.39/11.59 % (7471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.39/11.59 % (7471)Termination reason: Unknown
% 72.39/11.59 % (7471)Termination phase: Saturation
% 72.39/11.59
% 72.39/11.59 % (7471)Memory used [KB]: 11769
% 72.39/11.59 % (7471)Time elapsed: 2.293 s
% 72.39/11.59 % (7471)Instructions burned: 8383 (million)
% 72.39/11.59 % (7471)------------------------------
% 72.39/11.59 % (7471)------------------------------
% 72.88/11.60 % (7488)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_6848 for (2898ds/15557Mi)
% 72.88/11.62 % (7481)Instruction limit reached!
% 72.88/11.62 % (7481)------------------------------
% 72.88/11.62 % (7481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.88/11.62 % (7481)Termination reason: Unknown
% 72.88/11.62 % (7481)Termination phase: Saturation
% 72.88/11.62
% 72.88/11.62 % (7481)Memory used [KB]: 16502
% 72.88/11.62 % (7481)Time elapsed: 0.908 s
% 72.88/11.62 % (7481)Instructions burned: 3206 (million)
% 72.88/11.62 % (7481)------------------------------
% 72.88/11.62 % (7481)------------------------------
% 72.88/11.63 % (7489)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_6848 for (2898ds/2142Mi)
% 72.88/11.64 % (7487)Instruction limit reached!
% 72.88/11.64 % (7487)------------------------------
% 72.88/11.64 % (7487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.88/11.64 % (7487)Termination reason: Unknown
% 72.88/11.64 % (7487)Termination phase: Saturation
% 72.88/11.64
% 72.88/11.64 % (7487)Memory used [KB]: 7164
% 72.88/11.64 % (7487)Time elapsed: 0.176 s
% 72.88/11.64 % (7487)Instructions burned: 631 (million)
% 72.88/11.64 % (7487)------------------------------
% 72.88/11.64 % (7487)------------------------------
% 72.88/11.65 % (7490)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_6848 for (2897ds/5624Mi)
% 73.70/11.82 % (7486)Instruction limit reached!
% 73.70/11.82 % (7486)------------------------------
% 73.70/11.82 % (7486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.70/11.82 % (7486)Termination reason: Unknown
% 73.70/11.82 % (7486)Termination phase: Saturation
% 73.70/11.82
% 73.70/11.82 % (7486)Memory used [KB]: 15863
% 73.70/11.82 % (7486)Time elapsed: 0.741 s
% 73.70/11.82 % (7486)Instructions burned: 2636 (million)
% 73.70/11.82 % (7486)------------------------------
% 73.70/11.82 % (7486)------------------------------
% 73.70/11.83 % (7491)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_6848 for (2895ds/1665Mi)
% 73.70/11.89 % (7475)Instruction limit reached!
% 73.70/11.89 % (7475)------------------------------
% 73.70/11.89 % (7475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.70/11.89 % (7475)Termination reason: Unknown
% 73.70/11.89 % (7475)Termination phase: Saturation
% 73.70/11.89
% 73.70/11.89 % (7475)Memory used [KB]: 21236
% 73.70/11.89 % (7475)Time elapsed: 2.416 s
% 73.70/11.89 % (7475)Instructions burned: 8427 (million)
% 73.70/11.89 % (7475)------------------------------
% 73.70/11.89 % (7475)------------------------------
% 74.76/11.91 % (7492)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_6848 for (2895ds/64912Mi)
% 74.76/11.92 % (7492)Refutation not found, incomplete strategy
% 74.76/11.92 % (7492)------------------------------
% 74.76/11.92 % (7492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.76/11.92 % (7492)Termination reason: Refutation not found, incomplete strategy
% 74.76/11.92
% 74.76/11.92
% 74.76/11.92 % (7492)Memory used [KB]: 1535
% 74.76/11.92 % (7492)Time elapsed: 0.011 s
% 74.76/11.92 % (7492)Instructions burned: 34 (million)
% 74.76/11.92 % (7492)------------------------------
% 74.76/11.92 % (7492)------------------------------
% 74.76/11.93 % (7493)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_6848 for (2895ds/7801Mi)
% 77.22/12.19 % (7484)Instruction limit reached!
% 77.22/12.19 % (7484)------------------------------
% 77.22/12.19 % (7484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.22/12.19 % (7484)Termination reason: Unknown
% 77.22/12.19 % (7484)Termination phase: Saturation
% 77.22/12.19
% 77.22/12.19 % (7484)Memory used [KB]: 13944
% 77.22/12.19 % (7484)Time elapsed: 1.184 s
% 77.22/12.19 % (7484)Instructions burned: 4167 (million)
% 77.22/12.19 % (7484)------------------------------
% 77.22/12.19 % (7484)------------------------------
% 77.76/12.20 % (7494)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_6848 for (2892ds/15194Mi)
% 77.76/12.20 % (7489)Instruction limit reached!
% 77.76/12.20 % (7489)------------------------------
% 77.76/12.20 % (7489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.76/12.20 % (7489)Termination reason: Unknown
% 77.76/12.20 % (7489)Termination phase: Saturation
% 77.76/12.20
% 77.76/12.20 % (7489)Memory used [KB]: 11257
% 77.76/12.20 % (7489)Time elapsed: 0.575 s
% 77.76/12.20 % (7489)Instructions burned: 2142 (million)
% 77.76/12.20 % (7489)------------------------------
% 77.76/12.20 % (7489)------------------------------
% 77.76/12.21 % (7495)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_6848 for (2892ds/6753Mi)
% 77.76/12.23 % (7495)Refutation not found, incomplete strategy
% 77.76/12.23 % (7495)------------------------------
% 77.76/12.23 % (7495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.76/12.23 % (7495)Termination reason: Refutation not found, incomplete strategy
% 77.76/12.23
% 77.76/12.23
% 77.76/12.23 % (7495)Memory used [KB]: 6012
% 77.76/12.23 % (7495)Time elapsed: 0.014 s
% 77.76/12.23 % (7495)Instructions burned: 50 (million)
% 77.76/12.23 % (7495)------------------------------
% 77.76/12.23 % (7495)------------------------------
% 77.76/12.23 % (7496)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_6848 for (2891ds/1003Mi)
% 78.28/12.31 % (7491)Instruction limit reached!
% 78.28/12.31 % (7491)------------------------------
% 78.28/12.31 % (7491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.28/12.31 % (7491)Termination reason: Unknown
% 78.28/12.31 % (7491)Termination phase: Saturation
% 78.28/12.31
% 78.28/12.31 % (7491)Memory used [KB]: 7803
% 78.28/12.31 % (7491)Time elapsed: 0.479 s
% 78.28/12.31 % (7491)Instructions burned: 1666 (million)
% 78.28/12.31 % (7491)------------------------------
% 78.28/12.31 % (7491)------------------------------
% 78.28/12.32 % (7497)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_6848 for (2891ds/13018Mi)
% 79.10/12.53 % (7496)Instruction limit reached!
% 79.10/12.53 % (7496)------------------------------
% 79.10/12.53 % (7496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.10/12.53 % (7496)Termination reason: Unknown
% 79.10/12.53 % (7496)Termination phase: Saturation
% 79.10/12.53
% 79.10/12.53 % (7496)Memory used [KB]: 7675
% 79.10/12.53 % (7496)Time elapsed: 0.293 s
% 79.10/12.53 % (7496)Instructions burned: 1005 (million)
% 79.10/12.53 % (7496)------------------------------
% 79.10/12.53 % (7496)------------------------------
% 79.10/12.54 % (7498)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_6848 for (2888ds/1267Mi)
% 79.10/12.55 % (7498)Refutation not found, incomplete strategy
% 79.10/12.55 % (7498)------------------------------
% 79.10/12.55 % (7498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.10/12.55 % (7498)Termination reason: Refutation not found, incomplete strategy
% 79.10/12.55
% 79.10/12.55
% 79.10/12.55 % (7498)Memory used [KB]: 6012
% 79.10/12.55 % (7498)Time elapsed: 0.010 s
% 79.10/12.55 % (7498)Instructions burned: 31 (million)
% 79.10/12.55 % (7498)------------------------------
% 79.10/12.55 % (7498)------------------------------
% 79.10/12.56 % (7499)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_6848 for (2888ds/2570Mi)
% 81.03/12.92 % (7483)Instruction limit reached!
% 81.03/12.92 % (7483)------------------------------
% 81.03/12.92 % (7483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.03/12.92 % (7483)Termination reason: Unknown
% 81.03/12.92 % (7483)Termination phase: Saturation
% 81.03/12.92
% 81.03/12.92 % (7483)Memory used [KB]: 11129
% 81.03/12.92 % (7483)Time elapsed: 2.076 s
% 81.03/12.92 % (7483)Instructions burned: 7472 (million)
% 81.03/12.92 % (7483)------------------------------
% 81.03/12.92 % (7483)------------------------------
% 81.03/12.93 % (7500)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_6848 for (2885ds/13163Mi)
% 84.24/13.17 % (7499)Instruction limit reached!
% 84.24/13.17 % (7499)------------------------------
% 84.24/13.17 % (7499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.24/13.17 % (7499)Termination reason: Unknown
% 84.24/13.17 % (7499)Termination phase: Saturation
% 84.24/13.17
% 84.24/13.17 % (7499)Memory used [KB]: 10234
% 84.24/13.17 % (7499)Time elapsed: 0.620 s
% 84.24/13.17 % (7499)Instructions burned: 2572 (million)
% 84.24/13.17 % (7499)------------------------------
% 84.24/13.17 % (7499)------------------------------
% 84.24/13.18 % (7501)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_6848 for (2882ds/5087Mi)
% 85.34/13.33 % (7490)Instruction limit reached!
% 85.34/13.33 % (7490)------------------------------
% 85.34/13.33 % (7490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.34/13.33 % (7490)Termination reason: Unknown
% 85.34/13.33 % (7490)Termination phase: Saturation
% 85.34/13.33
% 85.34/13.33 % (7490)Memory used [KB]: 11385
% 85.34/13.33 % (7490)Time elapsed: 1.683 s
% 85.34/13.33 % (7490)Instructions burned: 5624 (million)
% 85.34/13.33 % (7490)------------------------------
% 85.34/13.33 % (7490)------------------------------
% 85.34/13.34 % (7502)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_6848 for (2881ds/10380Mi)
% 87.89/13.80 % (7502)First to succeed.
% 87.89/13.84 % (7502)Refutation found. Thanks to Tanya!
% 87.89/13.84 % SZS status Theorem for DTF2THF_6848
% 87.89/13.84 % SZS output start Proof for DTF2THF_6848
% 87.89/13.84 thf(type_def_6, type, d_unsorted: $tType).
% 87.89/13.84 thf(func_def_0, type, unsorted: $tType).
% 87.89/13.84 thf(func_def_1, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 87.89/13.84 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 87.89/13.84 thf(func_def_30, type, d_unsorted: $tType).
% 87.89/13.84 thf(func_def_31, type, d2unsorted: d_unsorted > $i).
% 87.89/13.84 thf(func_def_32, type, d_unsorted_0: d_unsorted).
% 87.89/13.84 thf(func_def_55, type, ph1: !>[X0: $tType]:(X0)).
% 87.89/13.84 thf(func_def_56, type, sK2: $i > $i > $o).
% 87.89/13.84 thf(func_def_57, type, sK3: $i > d_unsorted).
% 87.89/13.84 thf(func_def_58, type, sK4: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_59, type, sK5: ($i > $i > $o) > ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_60, type, sK6: ($i > $i > $o) > ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_61, type, sK7: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_62, type, sK8: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_63, type, sK9: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_64, type, sK10: $i > ($i > $i > $o) > $i > $i > $i > $o).
% 87.89/13.84 thf(func_def_68, type, sK14: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_69, type, sK15: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_70, type, sK16: ($i > $i > $o) > $i > $i).
% 87.89/13.84 thf(func_def_71, type, sK17: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_72, type, sK18: ($i > $i > $o) > $i > $o).
% 87.89/13.84 thf(func_def_73, type, sK19: ($i > $o) > ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_74, type, sK20: ($i > $i > $o) > $i > $i).
% 87.89/13.84 thf(func_def_75, type, sK21: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_76, type, sK22: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_77, type, sK23: ($i > $i > $o) > $i > $i > $o).
% 87.89/13.84 thf(func_def_78, type, sK24: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_79, type, sK25: $i > $i > $o).
% 87.89/13.84 thf(func_def_80, type, sK26: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_81, type, sK27: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_82, type, sK28: ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_83, type, sK29: ($i > $i > $o) > ($i > $i > $o) > $i).
% 87.89/13.84 thf(func_def_84, type, sK30: ($i > $i > $o) > ($i > $i > $o) > $i).
% 87.89/13.84 thf(f5875,plain,(
% 87.89/13.84 $false),
% 87.89/13.84 inference(avatar_sat_refutation,[status(thm)],[f148,f4810,f4819,f4823,f5873])).
% 87.89/13.84 thf(f5873,plain,(
% 87.89/13.84 ~spl0_4),
% 87.89/13.84 inference(avatar_contradiction_clause,[status(thm)],[f5872])).
% 87.89/13.84 thf(f5872,plain,(
% 87.89/13.84 $false | ~spl0_4),
% 87.89/13.84 inference(trivial_inequality_removal,[status(thm)],[f5789])).
% 87.89/13.84 thf(f5789,plain,(
% 87.89/13.84 ($false = $true) | ~spl0_4),
% 87.89/13.84 inference(superposition,[status(thm)],[f4848,f5753])).
% 87.89/13.84 thf(f5753,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((join @ X1 @ X2 @ X3) = $true)) )),
% 87.89/13.84 inference(subsumption_resolution,[status(thm)],[f5752,f152])).
% 87.89/13.84 thf(f152,plain,(
% 87.89/13.84 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 87.89/13.84 inference(superposition,[status(thm)],[f141,f141])).
% 87.89/13.84 thf(f141,plain,(
% 87.89/13.84 ( ! [X1 : $i] : (((d2unsorted @ d_unsorted_0) = X1)) )),
% 87.89/13.84 inference(equality_proxy_clausification,[status(thm)],[f140])).
% 87.89/13.84 thf(f140,plain,(
% 87.89/13.84 ( ! [X1 : $i] : ((((d2unsorted @ d_unsorted_0) = X1) = $true)) )),
% 87.89/13.84 inference(forward_demodulation,[status(thm)],[f139,f110])).
% 87.89/13.84 thf(f110,plain,(
% 87.89/13.84 ( ! [X1 : d_unsorted] : ((d_unsorted_0 = X1)) )),
% 87.89/13.84 inference(equality_proxy_clausification,[status(thm)],[f109])).
% 87.89/13.84 thf(f109,plain,(
% 87.89/13.84 ( ! [X1 : d_unsorted] : (((d_unsorted_0 = X1) = $true)) )),
% 87.89/13.84 inference(pi_clausification,[status(thm)],[f17])).
% 87.89/13.84 thf(f17,plain,(
% 87.89/13.84 ((!! @ d_unsorted @ (= @ d_unsorted_0)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 87.89/13.84 thf(f16,plain,(
% 87.89/13.84 (((((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) = trans)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (!! @ d_unsorted @ (= @ d_unsorted_0))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 87.89/13.84 thf(f13,plain,(
% 87.89/13.84 ((((((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) = trans)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 87.89/13.84 thf(f11,plain,(
% 87.89/13.84 (((((((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) = trans)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) = $true)),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f10])).
% 87.89/13.84 thf(f10,plain,(
% 87.89/13.84 (((((((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) = trans)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (d_unsorted_0 = Y0)))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) = $true)),
% 87.89/13.84 inference(cnf_transformation,[status(thm)],[f8])).
% 87.89/13.84 thf(f8,plain,(
% 87.89/13.84 (((((((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) = trans)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (d_unsorted_0 = Y0)))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) = $true)),
% 87.89/13.84 inference(fool_elimination,[status(thm)],[f7])).
% 87.89/13.84 thf(f7,plain,(
% 87.89/13.84 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2 : $i,X3 : $i] : ((X1 @ X2 @ X3) | ~(X0 @ X2 @ X3))))) & (trsc = (^[X4 : $i > $i > $o, X5 : $i, X6 : $i] : (! [X7 : $i > $i > $o] : (~! [X8 : $i,X9 : $i] : ((X7 @ X9 @ X8) | ~(X4 @ X9 @ X8)) | ~! [X10 : $i,X11 : $i,X12 : $i] : (~(X7 @ X10 @ X11) | ~(X7 @ X12 @ X10) | (X7 @ X12 @ X11)) | (X7 @ X6 @ X5)) | (X5 = X6) | ! [X13 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : (~(X4 @ X15 @ X14) | (X13 @ X15 @ X14)) | ~! [X16 : $i,X17 : $i,X18 : $i] : ((X13 @ X16 @ X18) | ~(X13 @ X16 @ X17) | ~(X13 @ X17 @ X18)) | (X13 @ X5 @ X6))))) & ! [X19 : d_unsorted] : (d_unsorted_0 = X19) & ((^[X20 : $i > $i > $o, X21 : $i, X22 : $i] : (X20 @ X22 @ X21)) = inv) & ((^[X23 : $i > $i > $o] : (! [X24 : $i,X25 : $i,X26 : $i] : (~(X23 @ X24 @ X25) | ~(X23 @ X26 @ X24) | (X23 @ X26 @ X25)))) = trans) & (nfof = (^[X27 : $i > $i > $o, X28 : $i, X29 : $i] : (! [X30 : $i] : ~(X27 @ X28 @ X30) & (! [X31 : $i > $i > $o] : (~! [X32 : $i,X33 : $i,X34 : $i] : ((X31 @ X32 @ X33) | ~(X31 @ X34 @ X33) | ~(X31 @ X32 @ X34)) | ~! [X35 : $i,X36 : $i] : (~(X27 @ X36 @ X35) | (X31 @ X36 @ X35)) | (X31 @ X29 @ X28)) | (X28 = X29))))) & (total = (^[X37 : $i > $i > $o] : (! [X38 : $i,X39 : $i] : ((X38 = X39) | (X37 @ X39 @ X38) | (X37 @ X38 @ X39))))) & ! [X40 : d_unsorted,X41 : d_unsorted] : (((d2unsorted @ X41) = (d2unsorted @ X40)) => (X40 = X41)) & (ind = (^[X42 : $i > $i > $o] : (! [X43 : $i > $o,X44 : $i] : ((X43 @ X44) | ~! [X45 : $i] : ((X43 @ X45) | ~! [X46 : $i] : ((X43 @ X46) | ~! [X47 : $i > $i > $o] : (~! [X48 : $i,X49 : $i,X50 : $i] : ((X47 @ X49 @ X48) | ~(X47 @ X49 @ X50) | ~(X47 @ X50 @ X48)) | ~! [X51 : $i,X52 : $i] : ((X47 @ X52 @ X51) | ~(X42 @ X52 @ X51)) | (X47 @ X45 @ X46)))))))) & (confl = (^[X53 : $i > $i > $o] : (! [X54 : $i > $i > $o,X55 : $i,X56 : $i > $i > $o,X57 : $i,X58 : $i] : ((X56 @ X55 @ X57) | ~! [X59 : $i,X60 : $i] : ((X56 @ X59 @ X60) | ~(X53 @ X59 @ X60)) | (~! [X61 : $i > $i > $o] : (~! [X62 : $i,X63 : $i,X64 : $i] : ((X61 @ X64 @ X63) | ~(X61 @ X62 @ X63) | ~(X61 @ X64 @ X62)) | (X61 @ X58 @ X55) | ~! [X65 : $i,X66 : $i] : (~(X53 @ X65 @ X66) | (X61 @ X65 @ X66))) & (X55 != X58)) | (X55 = X57) | ~! [X67 : $i,X68 : $i,X69 : $i] : ((X54 @ X67 @ X68) | ~(X54 @ X67 @ X69) | ~(X54 @ X69 @ X68)) | ~! [X70 : $i,X71 : $i] : (~(X53 @ X71 @ X70) | (X54 @ X71 @ X70)) | ~! [X72 : $i,X73 : $i,X74 : $i] : ((X56 @ X74 @ X72) | ~(X56 @ X73 @ X72) | ~(X56 @ X74 @ X73)) | ((X57 != X58) & ~! [X75 : $i > $i > $o] : (~! [X76 : $i,X77 : $i,X78 : $i] : ((X75 @ X78 @ X76) | ~(X75 @ X77 @ X76) | ~(X75 @ X78 @ X77)) | (X75 @ X58 @ X57) | ~! [X79 : $i,X80 : $i] : (~(X53 @ X80 @ X79) | (X75 @ X80 @ X79)))) | (X54 @ X57 @ X55) | ~! [X81 : $i] : (~! [X82 : $i > $i > $o] : (~! [X83 : $i,X84 : $i] : ((X82 @ X84 @ X83) | ~(X53 @ X84 @ X83)) | (X82 @ X57 @ X81) | ~! [X85 : $i,X86 : $i,X87 : $i] : ((X82 @ X85 @ X87) | ~(X82 @ X85 @ X86) | ~(X82 @ X86 @ X87))) | ~! [X88 : $i > $i > $o] : (~! [X89 : $i,X90 : $i] : ((X88 @ X89 @ X90) | ~(X53 @ X89 @ X90)) | ~! [X91 : $i,X92 : $i,X93 : $i] : (~(X88 @ X93 @ X92) | (X88 @ X91 @ X92) | ~(X88 @ X91 @ X93)) | (X88 @ X55 @ X81))))))) & ((^[X94 : $i > $i > $o, X95 : $i, X96 : $i] : (~(! [X97 : $i] : (~! [X98 : $i > $i > $o] : (~! [X99 : $i,X100 : $i] : ((X98 @ X100 @ X99) | ~(X94 @ X100 @ X99)) | ~! [X101 : $i,X102 : $i,X103 : $i] : (~(X98 @ X103 @ X102) | (X98 @ X103 @ X101) | ~(X98 @ X102 @ X101)) | (X98 @ X96 @ X97)) | ~! [X104 : $i > $i > $o] : (~! [X105 : $i,X106 : $i,X107 : $i] : ((X104 @ X106 @ X107) | ~(X104 @ X106 @ X105) | ~(X104 @ X105 @ X107)) | (X104 @ X95 @ X97) | ~! [X108 : $i,X109 : $i] : (~(X94 @ X109 @ X108) | (X104 @ X109 @ X108)))) & ~! [X110 : $i > $i > $o] : (~! [X111 : $i,X112 : $i] : ((X110 @ X112 @ X111) | ~(X94 @ X112 @ X111)) | ~! [X113 : $i,X114 : $i,X115 : $i] : (~(X110 @ X113 @ X114) | (X110 @ X115 @ X114) | ~(X110 @ X115 @ X113)) | (X110 @ X95 @ X96)) & ~! [X116 : $i > $i > $o] : ((X116 @ X96 @ X95) | ~! [X117 : $i,X118 : $i,X119 : $i] : (~(X116 @ X118 @ X117) | ~(X116 @ X117 @ X119) | (X116 @ X118 @ X119)) | ~! [X120 : $i,X121 : $i] : (~(X94 @ X120 @ X121) | (X116 @ X120 @ X121))) & (X95 != X96)))) = join) & (sc = (^[X122 : $i > $i > $o, X123 : $i, X124 : $i] : ((X122 @ X123 @ X124) | (X122 @ X124 @ X123)))) & (trc = (^[X125 : $i > $i > $o, X126 : $i, X127 : $i] : (! [X128 : $i > $i > $o] : ((X128 @ X126 @ X127) | ~! [X129 : $i,X130 : $i] : (~(X125 @ X129 @ X130) | (X128 @ X129 @ X130)) | ~! [X131 : $i,X132 : $i,X133 : $i] : ((X128 @ X132 @ X131) | ~(X128 @ X133 @ X131) | ~(X128 @ X132 @ X133))) | (X126 = X127)))) & ((^[X134 : $i > $i > $o] : (! [X135 : $i,X136 : $i] : (~(X134 @ X135 @ X136) | ~(X134 @ X136 @ X135)) & ! [X137 : $i,X138 : $i,X139 : $i] : (~(X134 @ X137 @ X139) | (X134 @ X138 @ X139) | ~(X134 @ X138 @ X137)))) = so) & (lconfl = (^[X140 : $i > $i > $o] : (! [X141 : $i > $i > $o,X142 : $i,X143 : $i,X144 : $i,X145 : $i > $i > $o] : (~! [X146 : $i,X147 : $i,X148 : $i] : (~(X145 @ X148 @ X147) | (X145 @ X148 @ X146) | ~(X145 @ X147 @ X146)) | ~! [X149 : $i] : (~! [X150 : $i > $i > $o] : ((X150 @ X144 @ X149) | ~! [X151 : $i,X152 : $i] : (~(X140 @ X152 @ X151) | (X150 @ X152 @ X151)) | ~! [X153 : $i,X154 : $i,X155 : $i] : (~(X150 @ X155 @ X153) | ~(X150 @ X154 @ X155) | (X150 @ X154 @ X153))) | ~! [X156 : $i > $i > $o] : (~! [X157 : $i,X158 : $i,X159 : $i] : (~(X156 @ X157 @ X159) | (X156 @ X158 @ X159) | ~(X156 @ X158 @ X157)) | ~! [X160 : $i,X161 : $i] : ((X156 @ X161 @ X160) | ~(X140 @ X161 @ X160)) | (X156 @ X142 @ X149))) | ~! [X162 : $i,X163 : $i] : (~(X140 @ X163 @ X162) | (X141 @ X163 @ X162)) | (X142 = X144) | ~(X140 @ X143 @ X144) | (X141 @ X142 @ X144) | ~! [X164 : $i,X165 : $i] : ((X145 @ X164 @ X165) | ~(X140 @ X164 @ X165)) | ~! [X166 : $i,X167 : $i,X168 : $i] : ((X141 @ X166 @ X168) | ~(X141 @ X167 @ X168) | ~(X141 @ X166 @ X167)) | (X145 @ X144 @ X142) | ~(X140 @ X143 @ X142))))) & ((^[X169 : $i > $i > $o] : (! [X170 : $i,X171 : $i > $i > $o,X172 : $i > $i > $o,X173 : $i] : (~! [X174 : $i,X175 : $i,X176 : $i] : (~(X172 @ X175 @ X174) | (X172 @ X175 @ X176) | ~(X172 @ X174 @ X176)) | ~! [X177 : $i,X178 : $i,X179 : $i] : (~(X171 @ X179 @ X177) | (X171 @ X178 @ X177) | ~(X171 @ X178 @ X179)) | ~! [X180 : $i,X181 : $i] : (~(X169 @ X181 @ X180) | (X172 @ X181 @ X180)) | (~! [X182 : $i > $i > $o] : ((X182 @ X170 @ X173) | ~! [X183 : $i,X184 : $i] : ((X182 @ X184 @ X183) | ~(X169 @ X184 @ X183)) | ~! [X185 : $i,X186 : $i,X187 : $i] : (~(X182 @ X185 @ X186) | ~(X182 @ X187 @ X185) | (X182 @ X187 @ X186))) & ~! [X188 : $i > $i > $o] : (~! [X189 : $i,X190 : $i] : ((X188 @ X189 @ X190) | ~(X169 @ X189 @ X190)) | ~! [X191 : $i,X192 : $i,X193 : $i] : (~(X188 @ X192 @ X191) | (X188 @ X192 @ X193) | ~(X188 @ X191 @ X193)) | (X188 @ X173 @ X170)) & (X170 != X173)) | ~! [X194 : $i] : (~! [X195 : $i > $i > $o] : (~! [X196 : $i,X197 : $i,X198 : $i] : (~(X195 @ X198 @ X196) | (X195 @ X197 @ X196) | ~(X195 @ X197 @ X198)) | ~! [X199 : $i,X200 : $i] : ((X195 @ X199 @ X200) | ~(X169 @ X199 @ X200)) | (X195 @ X173 @ X194)) | ~! [X201 : $i > $i > $o] : (~! [X202 : $i,X203 : $i] : ((X201 @ X202 @ X203) | ~(X169 @ X202 @ X203)) | ~! [X204 : $i,X205 : $i,X206 : $i] : (~(X201 @ X205 @ X206) | (X201 @ X204 @ X206) | ~(X201 @ X204 @ X205)) | (X201 @ X170 @ X194))) | (X172 @ X170 @ X173) | (X170 = X173) | ~! [X207 : $i,X208 : $i] : (~(X169 @ X208 @ X207) | (X171 @ X208 @ X207)) | (X171 @ X173 @ X170)))) = cr) & ((^[X209 : $i > $i > $o] : (! [X210 : $i] : (X209 @ X210 @ X210))) = refl) & (infl = (^[X211 : ($i > $i > $o) > $i > $i > $o] : (! [X212 : $i > $i > $o,X213 : $i,X214 : $i] : ((X211 @ X212 @ X214 @ X213) | ~(X212 @ X214 @ X213))))) & (po = (^[X215 : $i > $i > $o] : (! [X216 : $i] : (X215 @ X216 @ X216) & ! [X217 : $i,X218 : $i] : ((X217 = X218) | ~(X215 @ X217 @ X218) | ~(X215 @ X218 @ X217)) & ! [X219 : $i,X220 : $i,X221 : $i] : (~(X215 @ X219 @ X220) | ~(X215 @ X221 @ X219) | (X215 @ X221 @ X220))))) & (tc = (^[X222 : $i > $i > $o, X223 : $i, X224 : $i] : (! [X225 : $i > $i > $o] : ((X225 @ X223 @ X224) | ~! [X226 : $i,X227 : $i] : (~(X222 @ X226 @ X227) | (X225 @ X226 @ X227)) | ~! [X228 : $i,X229 : $i,X230 : $i] : (~(X225 @ X228 @ X229) | (X225 @ X230 @ X229) | ~(X225 @ X230 @ X228)))))) & ((^[X231 : ($i > $i > $o) > $i > $i > $o] : (! [X232 : $i,X233 : $i > $i > $o,X234 : $i,X235 : $i > $i > $o] : ((X231 @ X235 @ X234 @ X232) | ~! [X236 : $i,X237 : $i] : ((X235 @ X236 @ X237) | ~(X233 @ X236 @ X237)) | ~(X231 @ X233 @ X234 @ X232)))) = mono) & (norm = (^[X238 : $i > $i > $o] : (! [X239 : $i,X240 : $i] : (~! [X241 : $i] : (~! [X242 : $i] : ~(X238 @ X241 @ X242) | ~! [X243 : $i > $i > $o] : (~! [X244 : $i,X245 : $i,X246 : $i] : (~(X243 @ X246 @ X244) | (X243 @ X245 @ X244) | ~(X243 @ X245 @ X246)) | ~! [X247 : $i,X248 : $i] : (~(X238 @ X248 @ X247) | (X243 @ X248 @ X247)) | (X243 @ X240 @ X241))) | ~(X238 @ X240 @ X239))))) & ((^[X249 : $i > $i > $o] : (! [X250 : $i,X251 : $i] : (~(X249 @ X251 @ X250) | ~(X249 @ X250 @ X251)))) = asymm) & ((^[X252 : $i > $i > $o, X253 : $i] : (! [X254 : $i] : ~(X252 @ X253 @ X254))) = innf) & (sconfl = (^[X255 : $i > $i > $o] : (! [X256 : $i,X257 : $i > $i > $o,X258 : $i,X259 : $i > $i > $o,X260 : $i] : (~! [X261 : $i,X262 : $i,X263 : $i] : (~(X257 @ X261 @ X262) | ~(X257 @ X262 @ X263) | (X257 @ X261 @ X263)) | (X257 @ X260 @ X256) | (X259 @ X256 @ X260) | ~! [X264 : $i,X265 : $i,X266 : $i] : (~(X259 @ X265 @ X264) | (X259 @ X266 @ X264) | ~(X259 @ X266 @ X265)) | ~! [X267 : $i] : (~! [X268 : $i > $i > $o] : (~! [X269 : $i,X270 : $i] : (~(X255 @ X269 @ X270) | (X268 @ X269 @ X270)) | (X268 @ X256 @ X267) | ~! [X271 : $i,X272 : $i,X273 : $i] : (~(X268 @ X273 @ X272) | (X268 @ X271 @ X272) | ~(X268 @ X271 @ X273))) | ~! [X274 : $i > $i > $o] : ((X274 @ X260 @ X267) | ~! [X275 : $i,X276 : $i] : (~(X255 @ X276 @ X275) | (X274 @ X276 @ X275)) | ~! [X277 : $i,X278 : $i,X279 : $i] : (~(X274 @ X279 @ X278) | (X274 @ X279 @ X277) | ~(X274 @ X278 @ X277)))) | ~(X255 @ X258 @ X260) | ~! [X280 : $i,X281 : $i] : (~(X255 @ X280 @ X281) | (X257 @ X280 @ X281)) | ~! [X282 : $i,X283 : $i] : (~(X255 @ X282 @ X283) | (X259 @ X282 @ X283)) | ((X256 != X258) & ~! [X284 : $i > $i > $o] : (~! [X285 : $i,X286 : $i,X287 : $i] : (~(X284 @ X287 @ X285) | ~(X284 @ X286 @ X287) | (X284 @ X286 @ X285)) | (X284 @ X258 @ X256) | ~! [X288 : $i,X289 : $i] : (~(X255 @ X288 @ X289) | (X284 @ X288 @ X289)))) | (X256 = X260))))) & ((^[X290 : $i > $i > $o] : (! [X291 : $i] : ~(X290 @ X291 @ X291))) = irrefl) & (symm = (^[X292 : $i > $i > $o] : (! [X293 : $i,X294 : $i] : ((X292 @ X293 @ X294) | ~(X292 @ X294 @ X293))))) & (rc = (^[X295 : $i > $i > $o, X296 : $i, X297 : $i] : ((X296 = X297) | (X295 @ X296 @ X297)))) & (idem = (^[X298 : ($i > $i > $o) > $i > $i > $o] : (! [X299 : $i > $i > $o] : ((X298 @ X299) = (X298 @ (X298 @ X299)))))) & (antisymm = (^[X300 : $i > $i > $o] : (! [X301 : $i,X302 : $i] : ((X301 = X302) | ~(X300 @ X302 @ X301) | ~(X300 @ X301 @ X302))))) & ((^[X303 : $i > $i > $o] : (! [X304 : $i,X305 : $i > $o] : (~(X305 @ X304) | ~! [X306 : $i] : (~! [X307 : $i] : (~(X305 @ X307) | ~(X303 @ X306 @ X307)) | ~(X305 @ X306))))) = term) & ! [X308 : $i] : ? [X309 : d_unsorted] : ((d2unsorted @ X309) = X308)),
% 87.89/13.84 inference(rectify,[status(thm)],[f1])).
% 87.89/13.84 thf(f1,axiom,(
% 87.89/13.84 (subrel = (^[X4 : $i > $i > $o, X5 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & (trsc = (^[X4 : $i > $i > $o, X16 : $i, X17 : $i] : (! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)) | (X5 @ X17 @ X16)) | (X16 = X17) | ! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11)) | (X5 @ X16 @ X17))))) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (X4 @ X7 @ X6)) = inv) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X11 : $i,X6 : $i] : (~(X4 @ X7 @ X11) | ~(X4 @ X6 @ X7) | (X4 @ X6 @ X11)))) = trans) & (nfof = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (! [X22 : $i] : ~(X4 @ X6 @ X22) & (! [X5 : $i > $i > $o] : (~! [X12 : $i,X11 : $i,X13 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X7 @ X6)) | (X6 = X7))))) & (total = (^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : ((X6 = X7) | (X4 @ X6 @ X7) | (X4 @ X7 @ X6))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (ind = (^[X4 : $i > $i > $o] : (! [X20 : $i > $o,X21 : $i] : ((X20 @ X21) | ~! [X6 : $i] : ((X20 @ X6) | ~! [X7 : $i] : ((X20 @ X7) | ~! [X5 : $i > $i > $o] : (~! [X11 : $i,X12 : $i,X13 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11)) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X7)))))))) & (confl = (^[X4 : $i > $i > $o] : (! [X33 : $i > $i > $o,X11 : $i,X34 : $i > $i > $o,X7 : $i,X6 : $i] : ((X34 @ X11 @ X7) | ~! [X14 : $i,X15 : $i] : ((X34 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (~! [X5 : $i > $i > $o] : (~! [X13 : $i,X26 : $i,X12 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X11) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) & (X6 != X11)) | (X7 = X11) | ~! [X12 : $i,X25 : $i,X13 : $i] : ((X33 @ X12 @ X25) | ~(X33 @ X12 @ X13) | ~(X33 @ X13 @ X25)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X33 @ X14 @ X15)) | ~! [X26 : $i,X13 : $i,X12 : $i] : ((X34 @ X12 @ X26) | ~(X34 @ X13 @ X26) | ~(X34 @ X12 @ X13)) | ((X6 != X7) & ~! [X5 : $i > $i > $o] : (~! [X35 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X35) | ~(X5 @ X13 @ X35) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X7) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | (X33 @ X7 @ X11) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X7 @ X27) | ~! [X12 : $i,X13 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25))) | ~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X26 : $i,X13 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X11 @ X27))))))) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (~(! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X25) | ~(X5 @ X13 @ X25)) | (X5 @ X7 @ X27)) | ~! [X5 : $i > $i > $o] : (~! [X13 : $i,X12 : $i,X26 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26)) | (X5 @ X6 @ X27) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) & ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X26 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X7)) & ~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X13 : $i,X12 : $i,X25 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25) | (X5 @ X12 @ X25)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) & (X6 != X7)))) = join) & (sc = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X4 @ X6 @ X7) | (X4 @ X7 @ X6)))) & (trc = (^[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 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13))) | (X16 = X17)))) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6)) & ! [X7 : $i,X6 : $i,X11 : $i] : (~(X4 @ X7 @ X11) | (X4 @ X6 @ X11) | ~(X4 @ X6 @ X7)))) = so) & (lconfl = (^[X4 : $i > $i > $o] : (! [X29 : $i > $i > $o,X11 : $i,X6 : $i,X7 : $i,X28 : $i > $i > $o] : (~! [X25 : $i,X13 : $i,X12 : $i] : (~(X28 @ X12 @ X13) | (X28 @ X12 @ X25) | ~(X28 @ X13 @ X25)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X27) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X25 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X25))) | ~! [X5 : $i > $i > $o] : (~! [X13 : $i,X12 : $i,X26 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X11 @ X27))) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X29 @ X14 @ X15)) | (X7 = X11) | ~(X4 @ X6 @ X7) | (X29 @ X11 @ X7) | ~! [X14 : $i,X15 : $i] : ((X28 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X26 : $i] : ((X29 @ X12 @ X26) | ~(X29 @ X13 @ X26) | ~(X29 @ X12 @ X13)) | (X28 @ X7 @ X11) | ~(X4 @ X6 @ X11))))) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X36 : $i > $i > $o,X37 : $i > $i > $o,X7 : $i] : (~! [X13 : $i,X12 : $i,X26 : $i] : (~(X37 @ X12 @ X13) | (X37 @ X12 @ X26) | ~(X37 @ X13 @ X26)) | ~! [X25 : $i,X12 : $i,X13 : $i] : (~(X36 @ X13 @ X25) | (X36 @ X12 @ X25) | ~(X36 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X37 @ X14 @ X15)) | (~! [X5 : $i > $i > $o] : ((X5 @ X6 @ X7) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11))) & ~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X11 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X11) | ~(X5 @ X13 @ X11)) | (X5 @ X7 @ X6)) & (X6 != X7)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X25 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X25) | (X5 @ X12 @ X25) | ~(X5 @ X12 @ X13)) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X7 @ X27)) | ~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X26 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X27))) | (X37 @ X6 @ X7) | (X6 = X7) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X36 @ X14 @ X15)) | (X36 @ X7 @ X6)))) = cr) & ((^[X4 : $i > $i > $o] : (! [X6 : $i] : (X4 @ X6 @ X6))) = refl) & (infl = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X4 : $i > $i > $o,X7 : $i,X6 : $i] : ((X8 @ X4 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & (po = (^[X4 : $i > $i > $o] : (! [X6 : $i] : (X4 @ X6 @ X6) & ! [X6 : $i,X7 : $i] : ((X6 = X7) | ~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6)) & ! [X7 : $i,X11 : $i,X6 : $i] : (~(X4 @ X7 @ X11) | ~(X4 @ X6 @ X7) | (X4 @ X6 @ X11))))) & (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 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13)))))) & ((^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X10 : $i,X4 : $i > $i > $o,X9 : $i,X5 : $i > $i > $o] : ((X8 @ X5 @ X9 @ X10) | ~! [X6 : $i,X7 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7)) | ~(X8 @ X4 @ X9 @ X10)))) = mono) & (norm = (^[X4 : $i > $i > $o] : (! [X23 : $i,X6 : $i] : (~! [X24 : $i] : (~! [X22 : $i] : ~(X4 @ X24 @ X22) | ~! [X5 : $i > $i > $o] : (~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X24))) | ~(X4 @ X6 @ X23))))) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6)))) = asymm) & ((^[X4 : $i > $i > $o, X6 : $i] : (! [X7 : $i] : ~(X4 @ X6 @ X7))) = innf) & (sconfl = (^[X4 : $i > $i > $o] : (! [X7 : $i,X31 : $i > $i > $o,X6 : $i,X30 : $i > $i > $o,X11 : $i] : (~! [X12 : $i,X13 : $i,X26 : $i] : (~(X31 @ X12 @ X13) | ~(X31 @ X13 @ X26) | (X31 @ X12 @ X26)) | (X31 @ X11 @ X7) | (X30 @ X7 @ X11) | ~! [X25 : $i,X13 : $i,X12 : $i] : (~(X30 @ X13 @ X25) | (X30 @ X12 @ X25) | ~(X30 @ X12 @ X13)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X7 @ X27) | ~! [X12 : $i,X25 : $i,X13 : $i] : (~(X5 @ X13 @ X25) | (X5 @ X12 @ X25) | ~(X5 @ X12 @ X13))) | ~! [X5 : $i > $i > $o] : ((X5 @ X11 @ X27) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X26 : $i,X13 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X26) | ~(X5 @ X13 @ X26)))) | ~(X4 @ X6 @ X11) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X31 @ X14 @ X15)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X30 @ X14 @ X15)) | ((X6 != X7) & ~! [X5 : $i > $i > $o] : (~! [X32 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X32) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X32)) | (X5 @ X6 @ X7) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | (X7 = X11))))) & ((^[X4 : $i > $i > $o] : (! [X6 : $i] : ~(X4 @ X6 @ X6))) = irrefl) & (symm = (^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : ((X4 @ X7 @ X6) | ~(X4 @ X6 @ X7))))) & (rc = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X6 = X7) | (X4 @ X6 @ X7)))) & (idem = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X4 : $i > $i > $o] : ((X8 @ X4) = (X8 @ (X8 @ X4)))))) & (antisymm = (^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : ((X6 = X7) | ~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7))))) & ((^[X4 : $i > $i > $o] : (! [X19 : $i,X18 : $i > $o] : (~(X18 @ X19) | ~! [X6 : $i] : (~! [X7 : $i] : (~(X18 @ X7) | ~(X4 @ X6 @ X7)) | ~(X18 @ X6))))) = term) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0)),
% 87.89/13.84 file('/export/starexec/sandbox2/tmp/tmp.oJoehLhDex/DTF2THF_6848.p',sev441_1)).
% 87.89/13.84 thf(f139,plain,(
% 87.89/13.84 ( ! [X1 : $i] : ((((d2unsorted @ (sK3 @ X1)) = X1) = $true)) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f138])).
% 87.89/13.84 thf(f138,plain,(
% 87.89/13.84 ( ! [X1 : $i] : ((((^[Y0 : d_unsorted]: ((d2unsorted @ Y0) = X1)) @ (sK3 @ X1)) = $true)) )),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f135])).
% 87.89/13.84 thf(f135,plain,(
% 87.89/13.84 ( ! [X1 : $i] : (((?? @ d_unsorted @ (^[Y0 : d_unsorted]: ((d2unsorted @ Y0) = X1))) = $true)) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f134])).
% 87.89/13.84 thf(f134,plain,(
% 87.89/13.84 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))) @ X1) = $true)) )),
% 87.89/13.84 inference(pi_clausification,[status(thm)],[f89])).
% 87.89/13.84 thf(f89,plain,(
% 87.89/13.84 ((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 87.89/13.84 thf(f86,plain,(
% 87.89/13.84 (((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 87.89/13.84 thf(f84,plain,(
% 87.89/13.84 ((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 87.89/13.84 thf(f82,plain,(
% 87.89/13.84 (((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 87.89/13.84 thf(f79,plain,(
% 87.89/13.84 ((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 87.89/13.84 thf(f77,plain,(
% 87.89/13.84 (((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 87.89/13.84 thf(f74,plain,(
% 87.89/13.84 ((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 87.89/13.84 thf(f72,plain,(
% 87.89/13.84 (((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 87.89/13.84 thf(f70,plain,(
% 87.89/13.84 ((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 87.89/13.84 thf(f68,plain,(
% 87.89/13.84 (((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 87.89/13.84 thf(f65,plain,(
% 87.89/13.84 ((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 87.89/13.84 thf(f62,plain,(
% 87.89/13.84 (((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 87.89/13.84 thf(f59,plain,(
% 87.89/13.84 ((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 87.89/13.84 thf(f56,plain,(
% 87.89/13.84 (((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 87.89/13.84 thf(f54,plain,(
% 87.89/13.84 ((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 87.89/13.84 thf(f51,plain,(
% 87.89/13.84 (((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 87.89/13.84 thf(f48,plain,(
% 87.89/13.84 ((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 87.89/13.84 thf(f45,plain,(
% 87.89/13.84 (((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 87.89/13.84 thf(f42,plain,(
% 87.89/13.84 ((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 87.89/13.84 thf(f40,plain,(
% 87.89/13.84 (((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 87.89/13.84 thf(f37,plain,(
% 87.89/13.84 ((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 87.89/13.84 thf(f35,plain,(
% 87.89/13.84 (((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 87.89/13.84 thf(f33,plain,(
% 87.89/13.84 ((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 87.89/13.84 thf(f31,plain,(
% 87.89/13.84 (((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 87.89/13.84 thf(f29,plain,(
% 87.89/13.84 ((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 87.89/13.84 thf(f26,plain,(
% 87.89/13.84 (((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 87.89/13.84 thf(f23,plain,(
% 87.89/13.84 ((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 87.89/13.84 thf(f20,plain,(
% 87.89/13.84 (((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) = trans)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 87.89/13.84 thf(f18,plain,(
% 87.89/13.84 ((((((((((((((((((((((((((((((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2)))))))) = term)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))) | (Y2 = Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))) = irrefl)) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y1) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y9) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y5 = Y3)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (Y0 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y8 @ Y10)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9)))))))))) | (Y7 @ Y5 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y6 @ Y7)) | (Y2 @ Y6 @ Y8)) | (~ (Y2 @ Y7 @ Y8))))))))))) | (Y2 @ Y5 @ Y1)) | (Y4 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y8 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))) = innf)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y7)))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))))))))))))))) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y3 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5)))))))) | (Y0 @ Y1 @ Y2 @ Y4))))))))))) = mono)) & (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 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))) | (Y2 = Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))))) & (infl = (^[Y0 : ($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))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) = refl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 = Y1)) | (Y2 @ Y4 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))))))))))) | (((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y4 @ Y1))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y7 @ Y5)) | (Y2 @ Y6 @ Y5)) | (~ (Y2 @ Y6 @ Y7)))))))))))))))))))) = cr)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: ((((((((((~ (Y0 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (Y5 @ Y4 @ Y2)) | (~ (Y0 @ Y3 @ Y2))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y8)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y8)) | (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y6 @ Y7)))))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y3)) | (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y3 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) = so)) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (Y3 @ Y1 @ Y2)))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join)) & (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y7 @ Y8))))))))))))) | (Y2 @ Y4))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y0) = (d2unsorted @ Y1)) => (Y1 = Y0))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2)))))))))) = trans)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 87.89/13.84 thf(f5752,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : ((X2 != X3) | ((join @ X1 @ X2 @ X3) = $true)) )),
% 87.89/13.84 inference(equality_proxy_clausification,[status(thm)],[f5751])).
% 87.89/13.84 thf(f5751,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($false = (X2 = X3)) | ((join @ X1 @ X2 @ X3) = $true)) )),
% 87.89/13.84 inference(not_proxy_clausification,[status(thm)],[f5749])).
% 87.89/13.84 thf(f5749,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((~ (X2 = X3)) = $true) | ((join @ X1 @ X2 @ X3) = $true)) )),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f5747])).
% 87.89/13.84 thf(f5747,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : ((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))))) | (Y0 @ X3 @ X2)))))) = $true) | ((join @ X1 @ X2 @ X3) = $true)) )),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f5745])).
% 87.89/13.84 thf(f5745,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))))) | (Y0 @ X3 @ X2)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ X3) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))))))) = $true) | ((join @ X1 @ X2 @ X3) = $true)) )),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f5743])).
% 87.89/13.84 thf(f5743,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((join @ X1 @ X2 @ X3) = $true) | (((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))))) | (Y0 @ X3 @ X2)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ X3) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ X2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y3 @ Y2))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X3 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y2 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3))))))))))))))) = $true)) )),
% 87.89/13.84 inference(not_proxy_clausification,[status(thm)],[f5742])).
% 87.89/13.84 thf(f5742,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((join @ X1 @ X2 @ X3) = $true) | ($false = (~ ((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))))) | (Y0 @ X3 @ X2)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ X3) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ X2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y3 @ Y2))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X3 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y2 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))))))))))) )),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f5740])).
% 87.89/13.84 thf(f5740,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((~ ((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))))) | (Y0 @ X3 @ X2)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ X2 @ X3) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ X2 @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y3 @ Y2))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X3 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y4)) | (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y2 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))))))))) = (join @ X1 @ X2 @ X3))) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f5739])).
% 87.89/13.84 thf(f5739,plain,(
% 87.89/13.84 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : ((((^[Y0 : $i]: (~ ((((~ (X2 = Y0)) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y4 @ Y2))) | (~ (Y1 @ Y3 @ Y4))))))))))) | (Y1 @ Y0 @ X2)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4)))))))) | (Y2 @ X2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y4 @ Y3))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y5)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))))) @ X3) = (join @ X1 @ X2 @ X3))) )),
% 87.89/13.84 inference(argument_congruence,[status(thm)],[f4629])).
% 87.89/13.84 thf(f4629,plain,(
% 87.89/13.84 ( ! [X2 : $i,X1 : $i > $i > $o] : (((^[Y0 : $i]: (~ ((((~ (X2 = Y0)) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y4 @ Y2))) | (~ (Y1 @ Y3 @ Y4))))))))))) | (Y1 @ Y0 @ X2)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y4 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4)))))))) | (Y2 @ X2 @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y4 @ Y3))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y5)) | (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))))) = (join @ X1 @ X2))) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4628])).
% 87.89/13.84 thf(f4628,plain,(
% 87.89/13.84 ( ! [X2 : $i,X1 : $i > $i > $o] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (~ ((((~ (Y0 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y5 @ Y3))) | (~ (Y2 @ Y4 @ Y5))))))))))) | (Y2 @ Y1 @ Y0)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5)))))))) | (Y3 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y4 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))))))))))) @ X2) = (join @ X1 @ X2))) )),
% 87.89/13.84 inference(argument_congruence,[status(thm)],[f4226])).
% 87.89/13.84 thf(f4226,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: (~ ((((~ (Y0 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y5 @ Y3))) | (~ (Y2 @ Y4 @ Y5))))))))))) | (Y2 @ Y1 @ Y0)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5)))))))) | (Y3 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y4 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))))))))))) = (join @ X1))) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4225])).
% 87.89/13.84 thf(f4225,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) @ X1) = (join @ X1))) )),
% 87.89/13.84 inference(argument_congruence,[status(thm)],[f38])).
% 87.89/13.84 thf(f38,plain,(
% 87.89/13.84 (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))))),
% 87.89/13.84 inference(equality_proxy_clausification,[status(thm)],[f36])).
% 87.89/13.84 thf(f36,plain,(
% 87.89/13.84 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (Y1 = Y2)) & (~ (!! @ ($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 : $i]: (((Y3 @ Y5 @ Y4) | (~ (Y3 @ Y6 @ Y4))) | (~ (Y3 @ Y5 @ Y6))))))))))) | (Y3 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y6 @ Y5))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) = join) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 87.89/13.84 thf(f4848,plain,(
% 87.89/13.84 ( ! [X0 : $i] : (($false = (join @ sK2 @ sK13 @ X0))) ) | ~spl0_4),
% 87.89/13.84 inference(superposition,[status(thm)],[f4843,f152])).
% 87.89/13.84 thf(f4843,plain,(
% 87.89/13.84 ($false = (join @ sK2 @ sK13 @ sK12)) | ~spl0_4),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f4838])).
% 87.89/13.84 thf(f4838,plain,(
% 87.89/13.84 ((((trc @ sK2 @ sK11 @ sK12) & (trc @ sK2 @ sK11 @ sK13)) => (join @ sK2 @ sK13 @ sK12)) = $false) | ~spl0_4),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4837])).
% 87.89/13.84 thf(f4837,plain,(
% 87.89/13.84 ($false = ((^[Y0 : $i]: (((trc @ sK2 @ sK11 @ sK12) & (trc @ sK2 @ sK11 @ Y0)) => (join @ sK2 @ Y0 @ sK12))) @ sK13)) | ~spl0_4),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f4836])).
% 87.89/13.84 thf(f4836,plain,(
% 87.89/13.84 ($false = (!! @ $i @ (^[Y0 : $i]: (((trc @ sK2 @ sK11 @ sK12) & (trc @ sK2 @ sK11 @ Y0)) => (join @ sK2 @ Y0 @ sK12))))) | ~spl0_4),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4835])).
% 87.89/13.84 thf(f4835,plain,(
% 87.89/13.84 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((trc @ sK2 @ sK11 @ Y0) & (trc @ sK2 @ sK11 @ Y1)) => (join @ sK2 @ Y1 @ Y0))))) @ sK12)) | ~spl0_4),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f4834])).
% 87.89/13.84 thf(f4834,plain,(
% 87.89/13.84 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((trc @ sK2 @ sK11 @ Y0) & (trc @ sK2 @ sK11 @ Y1)) => (join @ sK2 @ Y1 @ Y0)))))) = $false) | ~spl0_4),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4827])).
% 87.89/13.84 thf(f4827,plain,(
% 87.89/13.84 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((trc @ sK2 @ Y0 @ Y1) & (trc @ sK2 @ Y0 @ Y2)) => (join @ sK2 @ Y2 @ Y1))))))) @ sK11)) | ~spl0_4),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f147])).
% 87.89/13.84 thf(f147,plain,(
% 87.89/13.84 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((trc @ sK2 @ Y0 @ Y1) & (trc @ sK2 @ Y0 @ Y2)) => (join @ sK2 @ Y2 @ Y1))))))))) | ~spl0_4),
% 87.89/13.84 inference(avatar_component_clause,[status(thm)],[f146])).
% 87.89/13.84 thf(f146,definition,(
% 87.89/13.84 spl0_4 <=> ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((trc @ sK2 @ Y0 @ Y1) & (trc @ sK2 @ Y0 @ Y2)) => (join @ sK2 @ Y2 @ Y1)))))))))),
% 87.89/13.84 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 87.89/13.84 thf(f4823,plain,(
% 87.89/13.84 ~spl0_17),
% 87.89/13.84 inference(avatar_contradiction_clause,[status(thm)],[f4822])).
% 87.89/13.84 thf(f4822,plain,(
% 87.89/13.84 $false | ~spl0_17),
% 87.89/13.84 inference(trivial_inequality_removal,[status(thm)],[f4821])).
% 87.89/13.84 thf(f4821,plain,(
% 87.89/13.84 ($false = $true) | ~spl0_17),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4820])).
% 87.89/13.84 thf(f4820,plain,(
% 87.89/13.84 ($false = ((^[Y0 : $i > $i > $o]: ($true)) @ sK25)) | ~spl0_17),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f4809])).
% 87.89/13.84 thf(f4809,plain,(
% 87.89/13.84 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ($true))) = $false) | ~spl0_17),
% 87.89/13.84 inference(avatar_component_clause,[status(thm)],[f4808])).
% 87.89/13.84 thf(f4808,definition,(
% 87.89/13.84 spl0_17 <=> ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ($true))) = $false)),
% 87.89/13.84 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 87.89/13.84 thf(f4819,plain,(
% 87.89/13.84 ~spl0_3 | ~spl0_16),
% 87.89/13.84 inference(avatar_contradiction_clause,[status(thm)],[f4818])).
% 87.89/13.84 thf(f4818,plain,(
% 87.89/13.84 $false | (~spl0_3 | ~spl0_16)),
% 87.89/13.84 inference(trivial_inequality_removal,[status(thm)],[f4813])).
% 87.89/13.84 thf(f4813,plain,(
% 87.89/13.84 ($false = $true) | (~spl0_3 | ~spl0_16)),
% 87.89/13.84 inference(superposition,[status(thm)],[f144,f4806])).
% 87.89/13.84 thf(f4806,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true)) ) | ~spl0_16),
% 87.89/13.84 inference(avatar_component_clause,[status(thm)],[f4805])).
% 87.89/13.84 thf(f4805,definition,(
% 87.89/13.84 spl0_16 <=> ! [X1 : $i > $i > $o] : ((confl @ X1) = $true)),
% 87.89/13.84 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 87.89/13.84 thf(f144,plain,(
% 87.89/13.84 ((confl @ sK2) = $false) | ~spl0_3),
% 87.89/13.84 inference(avatar_component_clause,[status(thm)],[f143])).
% 87.89/13.84 thf(f143,definition,(
% 87.89/13.84 spl0_3 <=> ((confl @ sK2) = $false)),
% 87.89/13.84 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 87.89/13.84 thf(f4810,plain,(
% 87.89/13.84 spl0_16 | spl0_17),
% 87.89/13.84 inference(avatar_split_clause,[status(thm)],[f4803,f4808,f4805])).
% 87.89/13.84 thf(f4803,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ($true))) = $false)) )),
% 87.89/13.84 inference(boolean_simplification,[status(thm)],[f4802])).
% 87.89/13.84 thf(f4802,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ($true | (sK23 @ X1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))))) )),
% 87.89/13.84 inference(boolean_simplification,[status(thm)],[f4801])).
% 87.89/13.84 thf(f4801,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (($true | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK23 @ X1 @ Y2 @ Y1)))))))) | (sK23 @ X1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))) = $false) | ((confl @ X1) = $true)) )),
% 87.89/13.84 inference(boolean_simplification,[status(thm)],[f4800])).
% 87.89/13.84 thf(f4800,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((($true | ((~ ((d2unsorted @ d_unsorted_0) = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))) | (Y1 @ (sK21 @ X1) @ (d2unsorted @ d_unsorted_0))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK23 @ X1 @ Y2 @ Y1)))))))) | (sK23 @ X1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)))))) | ((confl @ X1) = $true)) )),
% 87.89/13.84 inference(boolean_simplification,[status(thm)],[f4799])).
% 87.89/13.84 thf(f4799,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ (d2unsorted @ d_unsorted_0) @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ (d2unsorted @ d_unsorted_0) @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))) | (Y0 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ (sK21 @ X1) @ (d2unsorted @ d_unsorted_0))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4))))))))))))) & (~ ((d2unsorted @ d_unsorted_0) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK23 @ X1 @ Y1 @ Y2)) | (~ (sK23 @ X1 @ Y2 @ Y3))) | (sK23 @ X1 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) | $true) | ((~ ((d2unsorted @ d_unsorted_0) = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))) | (Y1 @ (sK21 @ X1) @ (d2unsorted @ d_unsorted_0))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK23 @ X1 @ Y2 @ Y1)))))))) | (sK23 @ X1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))))) )),
% 87.89/13.84 inference(boolean_simplification,[status(thm)],[f4798])).
% 87.89/13.84 thf(f4798,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ (d2unsorted @ d_unsorted_0) @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ (d2unsorted @ d_unsorted_0) @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))) | (Y0 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) | ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ (sK21 @ X1) @ (d2unsorted @ d_unsorted_0))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4))))))))))))) & (~ ((d2unsorted @ d_unsorted_0) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK23 @ X1 @ Y1 @ Y2)) | (~ (sK23 @ X1 @ Y2 @ Y3))) | (sK23 @ X1 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) | ((d2unsorted @ d_unsorted_0) = (d2unsorted @ d_unsorted_0))) | ((~ ((d2unsorted @ d_unsorted_0) = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))) | (Y1 @ (sK21 @ X1) @ (d2unsorted @ d_unsorted_0))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK23 @ X1 @ Y2 @ Y1)))))))) | (sK23 @ X1 @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))))))) )),
% 87.89/13.84 inference(forward_demodulation,[status(thm)],[f4797,f141])).
% 87.89/13.84 thf(f4797,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ (d2unsorted @ d_unsorted_0) @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ (sK22 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))) | (Y0 @ (sK22 @ X1) @ (d2unsorted @ d_unsorted_0))) | ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ (sK21 @ X1) @ (sK22 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4))))))))))))) & (~ ((sK22 @ X1) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK23 @ X1 @ Y1 @ Y2)) | (~ (sK23 @ X1 @ Y2 @ Y3))) | (sK23 @ X1 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) | ((d2unsorted @ d_unsorted_0) = (sK22 @ X1))) | ((~ ((d2unsorted @ d_unsorted_0) = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))) | (Y1 @ (sK21 @ X1) @ (d2unsorted @ d_unsorted_0))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK23 @ X1 @ Y2 @ Y1)))))))) | (sK23 @ X1 @ (d2unsorted @ d_unsorted_0) @ (sK22 @ X1))))))) )),
% 87.89/13.84 inference(forward_demodulation,[status(thm)],[f4796,f141])).
% 87.89/13.84 thf(f4796,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ (sK24 @ X1) @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y5 @ Y3))))))))) | (Y2 @ (sK22 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))) | (Y0 @ (sK22 @ X1) @ (sK24 @ X1))) | ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ (sK21 @ X1) @ (sK22 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4))))))))))))) & (~ ((sK22 @ X1) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK23 @ X1 @ Y1 @ Y2)) | (~ (sK23 @ X1 @ Y2 @ Y3))) | (sK23 @ X1 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) | ((sK24 @ X1) = (sK22 @ X1))) | ((~ ((sK24 @ X1) = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))) | (Y1 @ (sK21 @ X1) @ (sK24 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK23 @ X1 @ Y2 @ Y1)))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1)))))) | ((confl @ X1) = $true)) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4791])).
% 87.89/13.84 thf(f4791,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ($false = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ (sK22 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))))))) | (Y1 @ (sK22 @ X1) @ Y0)) | ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4)))))))) | (Y2 @ (sK21 @ X1) @ (sK22 @ X1))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y3 @ Y5))))))))))))) & (~ ((sK22 @ X1) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (sK23 @ X1 @ Y2 @ Y3)) | (~ (sK23 @ X1 @ Y3 @ Y4))) | (sK23 @ X1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y4 @ Y2))) | (Y1 @ Y4 @ Y3)))))))))) | (Y0 = (sK22 @ X1))) | ((~ (Y0 = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3)))))))) | (Y2 @ (sK21 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y3 @ Y4))))))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (sK23 @ X1 @ Y3 @ Y2)))))))) | (sK23 @ X1 @ Y0 @ (sK22 @ X1)))))) @ (sK24 @ X1)))) )),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f4789])).
% 87.89/13.84 thf(f4789,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y6 @ Y4))))))))) | (Y3 @ (sK22 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))))))) | (Y1 @ (sK22 @ X1) @ Y0)) | ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4)))))))) | (Y2 @ (sK21 @ X1) @ (sK22 @ X1))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y3 @ Y5))))))))))))) & (~ ((sK22 @ X1) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (sK23 @ X1 @ Y2 @ Y3)) | (~ (sK23 @ X1 @ Y3 @ Y4))) | (sK23 @ X1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y4 @ Y2))) | (Y1 @ Y4 @ Y3)))))))))) | (Y0 = (sK22 @ X1))) | ((~ (Y0 = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3)))))))) | (Y2 @ (sK21 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y3 @ Y4))))))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (sK23 @ X1 @ Y3 @ Y2)))))))) | (sK23 @ X1 @ Y0 @ (sK22 @ X1))))))) = $false) | ((confl @ X1) = $true)) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4785])).
% 87.89/13.84 thf(f4785,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y7 @ Y5))))))))) | (Y4 @ (sK22 @ X1) @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))) | (Y2 @ (sK22 @ X1) @ Y1)) | ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5)))))))) | (Y3 @ (sK21 @ X1) @ (sK22 @ X1))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6))))))))))))) & (~ ((sK22 @ X1) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y4 @ Y5))) | (Y0 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y5 @ Y3))) | (Y2 @ Y5 @ Y4)))))))))) | (Y1 = (sK22 @ X1))) | ((~ (Y1 = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4)))))))) | (Y3 @ (sK21 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y0 @ Y4 @ Y3)))))))) | (Y0 @ Y1 @ (sK22 @ X1)))))))) @ (sK23 @ X1)) = $false)) )),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f4782])).
% 87.89/13.84 thf(f4782,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y7 @ Y5))))))))) | (Y4 @ (sK22 @ X1) @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))) | (Y2 @ (sK22 @ X1) @ Y1)) | ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5)))))))) | (Y3 @ (sK21 @ X1) @ (sK22 @ X1))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6))))))))))))) & (~ ((sK22 @ X1) = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y0 @ Y3 @ Y4)) | (~ (Y0 @ Y4 @ Y5))) | (Y0 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y5 @ Y3))) | (Y2 @ Y5 @ Y4)))))))))) | (Y1 = (sK22 @ X1))) | ((~ (Y1 = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4)))))))) | (Y3 @ (sK21 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y0 @ Y4 @ Y3)))))))) | (Y0 @ Y1 @ (sK22 @ X1))))))))) = $false) | ((confl @ X1) = $true)) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4779])).
% 87.89/13.84 thf(f4779,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ($false = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y0 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))))))))))) | (Y3 @ Y0 @ Y2)) | ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6)))))))) | (Y4 @ (sK21 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y5 @ Y7))))))))))))) & (~ (Y0 = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y1 @ Y4 @ Y5)) | (~ (Y1 @ Y5 @ Y6))) | (Y1 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5)))))))))) | (Y2 = Y0)) | ((~ (Y2 = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (X1 @ Y6 @ Y5)))))))) | (Y4 @ (sK21 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6))))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (Y1 @ Y5 @ Y4)))))))) | (Y1 @ Y2 @ Y0))))))))) @ (sK22 @ X1)))) )),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f4644])).
% 87.89/13.84 thf(f4644,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6))))))))) | (Y5 @ Y0 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))))))))))) | (Y3 @ Y0 @ Y2)) | ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6)))))))) | (Y4 @ (sK21 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y6 @ Y7))) | (Y4 @ Y5 @ Y7))))))))))))) & (~ (Y0 = (sK21 @ X1))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y1 @ Y4 @ Y5)) | (~ (Y1 @ Y5 @ Y6))) | (Y1 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y4))) | (Y3 @ Y6 @ Y5)))))))))) | (Y2 = Y0)) | ((~ (Y2 = (sK21 @ X1))) & (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (X1 @ Y6 @ Y5)))))))) | (Y4 @ (sK21 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6))))))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (Y1 @ Y5 @ Y4)))))))) | (Y1 @ Y2 @ Y0)))))))))) = $false) | ((confl @ X1) = $true)) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4643])).
% 87.89/13.84 thf(f4643,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = $true) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))))) | (Y4 @ Y1 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (X1 @ Y6 @ Y7)))))))) | (Y5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y6 @ Y8))))))))))))) & (~ (Y1 = Y0)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y5 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y5 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (Y3 = Y1)) | ((~ (Y3 = Y0)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (X1 @ Y7 @ Y6)))))))) | (Y5 @ Y0 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5)))))))) | (Y2 @ Y3 @ Y1))))))))))) @ (sK21 @ X1)))) )),
% 87.89/13.84 inference(sigma_clausification,[status(thm)],[f4040])).
% 87.89/13.84 thf(f4040,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))))) | (Y4 @ Y1 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (X1 @ Y6 @ Y7)))))))) | (Y5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y6 @ Y8))))))))))))) & (~ (Y1 = Y0)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y5 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y5 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (Y3 = Y1)) | ((~ (Y3 = Y0)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (X1 @ Y7 @ Y6)))))))) | (Y5 @ Y0 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5)))))))) | (Y2 @ Y3 @ Y1))))))))))))) | ((confl @ X1) = $true)) )),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f4039])).
% 87.89/13.84 thf(f4039,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : (((confl @ X1) = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((((((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y3 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y9 @ Y7))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))))) | (Y4 @ Y1 @ Y3)) | ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (X1 @ Y6 @ Y7)))))))) | (Y5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y6 @ Y8))))))))))))) & (~ (Y1 = Y0)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y2 @ Y5 @ Y6)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y5 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y5))) | (Y4 @ Y7 @ Y6)))))))))) | (Y3 = Y1)) | ((~ (Y3 = Y0)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (X1 @ Y7 @ Y6)))))))) | (Y5 @ Y0 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7))))))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y2 @ Y6 @ Y5)))))))) | (Y2 @ Y3 @ Y1)))))))))))))) )),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f4038])).
% 87.89/13.84 thf(f4038,plain,(
% 87.89/13.84 ( ! [X1 : $i > $i > $o] : ((((^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))) @ X1) = (confl @ X1))) )),
% 87.89/13.84 inference(argument_congruence,[status(thm)],[f99])).
% 87.89/13.84 thf(f99,plain,(
% 87.89/13.84 (confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2))))))))))))))),
% 87.89/13.84 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 87.89/13.84 thf(f34,plain,(
% 87.89/13.84 ((confl = (^[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]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y10 @ Y9))) | (Y7 @ Y10 @ Y8))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))))))) | (Y5 @ Y2 @ Y4)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y7 @ Y9))))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y7)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y8 @ Y7)))))))))) | (Y4 = Y2)) | ((~ (Y4 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (Y6 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y9 @ Y8))) | (Y6 @ Y7 @ Y8))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (Y3 @ Y4 @ Y2)))))))))))))) = $true)),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 87.89/13.84 thf(f148,plain,(
% 87.89/13.84 spl0_3 | spl0_4),
% 87.89/13.84 inference(avatar_split_clause,[status(thm)],[f108,f146,f143])).
% 87.89/13.84 thf(f108,plain,(
% 87.89/13.84 ((confl @ sK2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((trc @ sK2 @ Y0 @ Y1) & (trc @ sK2 @ Y0 @ Y2)) => (join @ sK2 @ Y2 @ Y1)))))))))),
% 87.89/13.84 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 87.89/13.84 thf(f106,plain,(
% 87.89/13.84 ((confl @ sK2) != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((trc @ sK2 @ Y0 @ Y1) & (trc @ sK2 @ Y0 @ Y2)) => (join @ sK2 @ Y2 @ Y1)))))))))),
% 87.89/13.84 inference(beta_eta_normalization,[status(thm)],[f105])).
% 87.89/13.84 thf(f105,plain,(
% 87.89/13.84 ((confl @ sK2) != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((trc @ Y0 @ Y1 @ Y2) & (trc @ Y0 @ Y1 @ Y3)) => (join @ Y0 @ Y3 @ Y2))))))))) @ sK2))),
% 87.89/13.84 inference(negative_extensionality,[status(thm)],[f104])).
% 87.89/13.84 thf(f104,plain,(
% 87.89/13.84 (confl != (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((trc @ Y0 @ Y1 @ Y2) & (trc @ Y0 @ Y1 @ Y3)) => (join @ Y0 @ Y3 @ Y2))))))))))),
% 87.89/13.84 inference(equality_proxy_clausification,[status(thm)],[f103])).
% 87.89/13.84 thf(f103,plain,(
% 87.89/13.84 ($false = (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((trc @ Y0 @ Y1 @ Y2) & (trc @ Y0 @ Y1 @ Y3)) => (join @ Y0 @ Y3 @ Y2)))))))))))),
% 87.89/13.84 inference(not_proxy_clausification,[status(thm)],[f9])).
% 87.89/13.84 thf(f9,plain,(
% 87.89/13.84 ((~ (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((trc @ Y0 @ Y1 @ Y2) & (trc @ Y0 @ Y1 @ Y3)) => (join @ Y0 @ Y3 @ Y2))))))))))) = $true)),
% 87.89/13.84 inference(cnf_transformation,[status(thm)],[f6])).
% 87.89/13.84 thf(f6,plain,(
% 87.89/13.84 ((~ (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((trc @ Y0 @ Y1 @ Y2) & (trc @ Y0 @ Y1 @ Y3)) => (join @ Y0 @ Y3 @ Y2))))))))))) = $true)),
% 87.89/13.84 inference(fool_elimination,[status(thm)],[f5])).
% 87.89/13.84 thf(f5,plain,(
% 87.89/13.84 ~(confl = (^[X0 : $i > $i > $o] : (! [X1 : $i,X2 : $i,X3 : $i] : (((trc @ X0 @ X3 @ X1) & (trc @ X0 @ X3 @ X2)) => (join @ X0 @ X1 @ X2)))))),
% 87.89/13.84 inference(rectify,[status(thm)],[f3])).
% 87.89/13.84 thf(f3,negated_conjecture,(
% 87.89/13.84 ~(confl = (^[X4 : $i > $i > $o] : (! [X11 : $i,X7 : $i,X6 : $i] : (((trc @ X4 @ X6 @ X11) & (trc @ X4 @ X6 @ X7)) => (join @ X4 @ X11 @ X7)))))),
% 87.89/13.84 inference(negated_conjecture,[status(cth)],[f2])).
% 87.89/13.84 thf(f2,conjecture,(
% 87.89/13.84 (confl = (^[X4 : $i > $i > $o] : (! [X11 : $i,X7 : $i,X6 : $i] : (((trc @ X4 @ X6 @ X11) & (trc @ X4 @ X6 @ X7)) => (join @ X4 @ X11 @ X7)))))),
% 87.89/13.84 file('/export/starexec/sandbox2/tmp/tmp.oJoehLhDex/DTF2THF_6848.p',confluent)).
% 87.89/13.84 % SZS output end Proof for DTF2THF_6848
% 87.89/13.84 % (7502)------------------------------
% 87.89/13.84 % (7502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.89/13.84 % (7502)Termination reason: Refutation
% 87.89/13.84
% 87.89/13.84 % (7502)Memory used [KB]: 11641
% 87.89/13.84 % (7502)Time elapsed: 0.519 s
% 87.89/13.84 % (7502)Instructions burned: 1601 (million)
% 87.89/13.84 % (7502)------------------------------
% 87.89/13.84 % (7502)------------------------------
% 87.89/13.84 % (7220)Success in time 12.408 s
%------------------------------------------------------------------------------