%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 69.45s 11.19s
% Output : Refutation 69.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 4
% Syntax : Number of formulae : 118 ( 71 unt; 0 typ; 2 def)
% Number of atoms : 6522 (1140 equ; 32 cnn)
% Maximal formula atoms : 33 ( 55 avg)
% Number of connectives : 32366 (4283 ~;4114 |; 889 &;18589 @)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 3 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 3836 (3836 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 59 usr; 11 con; 0-3 aty)
% (4418 !!; 31 ??; 0 @@+; 0 @@-)
% Number of variables : 5991 (5383 ^; 606 !; 2 ?;5991 :)
% 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_54,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_56,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
sK2: $i > $i > $o ).
thf(func_def_58,type,
sK3: $i > d_unsorted ).
thf(func_def_59,type,
sK4: ( $i > $i > $o ) > $i ).
thf(func_def_60,type,
sK5: ( $i > $i > $o ) > $i ).
thf(func_def_61,type,
sK6: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_62,type,
sK7: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_63,type,
sK8: ( $i > $i > $o ) > $i ).
thf(func_def_64,type,
sK9: ( $i > $i > $o ) > $i ).
thf(func_def_65,type,
sK10: ( $i > $i > $o ) > $i ).
thf(func_def_66,type,
sK11: ( $i > $i > $o ) > $i ).
thf(func_def_67,type,
sK12: ( $i > $i > $o ) > $i ).
thf(func_def_71,type,
sK16: ( $i > $i > $o ) > $i ).
thf(func_def_72,type,
sK17: ( ( $i > $i > $o ) > $i > $i > $o ) > $i > $i > $o ).
thf(func_def_73,type,
sK18: ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK19: ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK21: ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK22: ( $i > $i > $o ) > $i ).
thf(func_def_78,type,
sK23: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_79,type,
sK24: ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK25: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_81,type,
sK26: ( $i > $i > $o ) > $i ).
thf(f2789,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f136,f1822,f2788]) ).
thf(f2788,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f2787]) ).
thf(f2787,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f2782]) ).
thf(f2782,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f131,f2779]) ).
thf(f2779,plain,
! [X1: $i > $i > $o] :
( ( lconfl @ X1 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f2778,f192]) ).
thf(f192,plain,
! [X2: $i,X1: $i] : ( X1 = X2 ),
inference(superposition,[status(thm)],[f187,f187]) ).
thf(f187,plain,
! [X0: $i,X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 ),
inference(superposition,[status(thm)],[f185,f121]) ).
thf(f121,plain,
! [X0: d_unsorted,X1: d_unsorted] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f107,f107]) ).
thf(f107,plain,
! [X1: d_unsorted] : ( d_unsorted_0 = X1 ),
inference(equality_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X1: d_unsorted] :
( ( d_unsorted_0 = X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y3 @ Y5 )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ( Y1 @ Y4 @ Y5 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= sconfl ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y3 @ Y5 )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ( Y1 @ Y4 @ Y5 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= sconfl )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y3 @ Y5 )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ( Y1 @ Y4 @ Y5 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= sconfl )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] : ( d_unsorted_0 = Y0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y3 @ Y5 )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ( Y1 @ Y4 @ Y5 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= sconfl )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= symm )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] : ( d_unsorted_0 = Y0 ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) )
= rc )
& ( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) )
& ( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y2 @ Y4 )
| ~ ( Y0 @ Y3 @ Y4 ) ) ) ) )
| ~ ( Y2 @ Y1 ) ) ) ) )
= term )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( trc
= ( ^ [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 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
= so )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) )
| ( Y2 @ Y3 ) ) )
| ( Y2 @ Y1 ) ) ) ) )
= ind )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( innf
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
& ( trsc
= ( ^ [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 @ Y4 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ( Y4 = Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y7 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y3 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) )
& ( Y4 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y4 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y1 @ Y7 @ Y5 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y4 ) ) ) ) ) ) )
= cr )
& ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ( Y1 = Y2 ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y2 )
| ( Y3 @ Y5 @ Y2 )
| ( Y4 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y8 @ Y6 )
| ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ( ( Y5 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
& ( Y2 != Y1 ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y8 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) )
| ( Y7 @ Y2 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) )
= confl )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) )
= norm )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) ) ) )
= tc )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( Y0 @ Y1 @ Y3 @ Y2 )
| ( Y0 @ Y4 @ Y3 @ Y2 ) ) ) ) ) ) )
= mono )
& ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
& ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
& ( idem
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ Y1 )
= ( Y0 @ ( Y0 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
= asymm )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y3 @ Y5 )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ~ ( Y7 @ Y8 @ Y10 )
| ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y6 @ Y8 )
| ~ ( Y1 @ Y7 @ Y6 )
| ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ( Y1 @ Y4 @ Y5 )
| ( Y2 @ Y5 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= sconfl )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( ( total
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X1 = X2 )
| ( X0 @ X1 @ X2 ) ) ) )
& ( ( ^ [X3: $i > $i > $o,X4: $i,X5: $i] : ( X3 @ X5 @ X4 ) )
= inv )
& ( ( ^ [X6: $i > $i > $o] :
! [X7: $i,X8: $i,X9: $i,X10: $i > $i > $o,X11: $i > $i > $o] :
( ~ ! [X12: $i,X13: $i] :
( ~ ( X6 @ X12 @ X13 )
| ( X10 @ X12 @ X13 ) )
| ( X7 = X8 )
| ~ ! [X14: $i,X15: $i,X16: $i] :
( ~ ( X10 @ X16 @ X15 )
| ~ ( X10 @ X14 @ X16 )
| ( X10 @ X14 @ X15 ) )
| ( X10 @ X7 @ X8 )
| ( X11 @ X8 @ X7 )
| ~ ! [X17: $i,X18: $i,X19: $i] :
( ( X11 @ X18 @ X17 )
| ~ ( X11 @ X18 @ X19 )
| ~ ( X11 @ X19 @ X17 ) )
| ~ ! [X20: $i] :
( ~ ! [X21: $i > $i > $o] :
( ( X21 @ X7 @ X20 )
| ~ ! [X22: $i,X23: $i,X24: $i] :
( ~ ( X21 @ X22 @ X23 )
| ~ ( X21 @ X24 @ X22 )
| ( X21 @ X24 @ X23 ) )
| ~ ! [X25: $i,X26: $i] :
( ( X21 @ X26 @ X25 )
| ~ ( X6 @ X26 @ X25 ) ) )
| ~ ! [X27: $i > $i > $o] :
( ~ ! [X28: $i,X29: $i,X30: $i] :
( ( X27 @ X29 @ X28 )
| ~ ( X27 @ X30 @ X28 )
| ~ ( X27 @ X29 @ X30 ) )
| ~ ! [X31: $i,X32: $i] :
( ~ ( X6 @ X32 @ X31 )
| ( X27 @ X32 @ X31 ) )
| ( X27 @ X8 @ X20 ) ) )
| ~ ! [X33: $i,X34: $i] :
( ~ ( X6 @ X33 @ X34 )
| ( X11 @ X33 @ X34 ) )
| ( ~ ! [X35: $i > $i > $o] :
( ( X35 @ X9 @ X8 )
| ~ ! [X36: $i,X37: $i] :
( ~ ( X6 @ X36 @ X37 )
| ( X35 @ X36 @ X37 ) )
| ~ ! [X38: $i,X39: $i,X40: $i] :
( ~ ( X35 @ X39 @ X38 )
| ~ ( X35 @ X38 @ X40 )
| ( X35 @ X39 @ X40 ) ) )
& ( X8 != X9 ) )
| ~ ( X6 @ X9 @ X7 ) ) )
= sconfl )
& ( ( ^ [X41: $i > $i > $o] :
! [X42: $i,X43: $i] :
( ~ ( X41 @ X43 @ X42 )
| ~ ( X41 @ X42 @ X43 ) ) )
= asymm )
& ( idem
= ( ^ [X44: ( $i > $i > $o ) > $i > $i > $o] :
! [X45: $i > $i > $o] :
( ( X44 @ X45 )
= ( X44 @ ( X44 @ X45 ) ) ) ) )
& ( antisymm
= ( ^ [X46: $i > $i > $o] :
! [X47: $i,X48: $i] :
( ~ ( X46 @ X48 @ X47 )
| ~ ( X46 @ X47 @ X48 )
| ( X47 = X48 ) ) ) )
& ( ( ^ [X49: $i > $i > $o,X50: $i,X51: $i] :
~ ( ~ ! [X52: $i > $i > $o] :
( ( X52 @ X51 @ X50 )
| ~ ! [X53: $i,X54: $i] :
( ( X52 @ X54 @ X53 )
| ~ ( X49 @ X54 @ X53 ) )
| ~ ! [X55: $i,X56: $i,X57: $i] :
( ~ ( X52 @ X55 @ X56 )
| ( X52 @ X55 @ X57 )
| ~ ( X52 @ X56 @ X57 ) ) )
& ! [X58: $i] :
( ~ ! [X59: $i > $i > $o] :
( ( X59 @ X51 @ X58 )
| ~ ! [X60: $i,X61: $i,X62: $i] :
( ( X59 @ X62 @ X61 )
| ~ ( X59 @ X62 @ X60 )
| ~ ( X59 @ X60 @ X61 ) )
| ~ ! [X63: $i,X64: $i] :
( ~ ( X49 @ X63 @ X64 )
| ( X59 @ X63 @ X64 ) ) )
| ~ ! [X65: $i > $i > $o] :
( ~ ! [X66: $i,X67: $i] :
( ( X65 @ X67 @ X66 )
| ~ ( X49 @ X67 @ X66 ) )
| ~ ! [X68: $i,X69: $i,X70: $i] :
( ~ ( X65 @ X70 @ X68 )
| ( X65 @ X70 @ X69 )
| ~ ( X65 @ X68 @ X69 ) )
| ( X65 @ X50 @ X58 ) ) )
& ~ ! [X71: $i > $i > $o] :
( ( X71 @ X50 @ X51 )
| ~ ! [X72: $i,X73: $i] :
( ~ ( X49 @ X73 @ X72 )
| ( X71 @ X73 @ X72 ) )
| ~ ! [X74: $i,X75: $i,X76: $i] :
( ~ ( X71 @ X74 @ X76 )
| ~ ( X71 @ X75 @ X74 )
| ( X71 @ X75 @ X76 ) ) )
& ( X50 != X51 ) ) )
= join )
& ( ( ^ [X77: $i > $i > $o] :
! [X78: $i,X79: $i > $i > $o,X80: $i,X81: $i > $i > $o,X82: $i] :
( ~ ! [X83: $i] :
( ~ ! [X84: $i > $i > $o] :
( ~ ! [X85: $i,X86: $i,X87: $i] :
( ( X84 @ X85 @ X86 )
| ~ ( X84 @ X87 @ X86 )
| ~ ( X84 @ X85 @ X87 ) )
| ( X84 @ X82 @ X83 )
| ~ ! [X88: $i,X89: $i] :
( ~ ( X77 @ X89 @ X88 )
| ( X84 @ X89 @ X88 ) ) )
| ~ ! [X90: $i > $i > $o] :
( ~ ! [X91: $i,X92: $i,X93: $i] :
( ( X90 @ X92 @ X93 )
| ~ ( X90 @ X92 @ X91 )
| ~ ( X90 @ X91 @ X93 ) )
| ( X90 @ X80 @ X83 )
| ~ ! [X94: $i,X95: $i] :
( ( X90 @ X94 @ X95 )
| ~ ( X77 @ X94 @ X95 ) ) ) )
| ( X79 @ X82 @ X80 )
| ( X81 @ X80 @ X82 )
| ~ ! [X96: $i,X97: $i,X98: $i] :
( ~ ( X81 @ X98 @ X97 )
| ~ ( X81 @ X97 @ X96 )
| ( X81 @ X98 @ X96 ) )
| ~ ( X77 @ X78 @ X80 )
| ~ ! [X99: $i,X100: $i,X101: $i] :
( ~ ( X79 @ X99 @ X100 )
| ( X79 @ X101 @ X100 )
| ~ ( X79 @ X101 @ X99 ) )
| ~ ! [X102: $i,X103: $i] :
( ~ ( X77 @ X102 @ X103 )
| ( X79 @ X102 @ X103 ) )
| ~ ! [X104: $i,X105: $i] :
( ~ ( X77 @ X105 @ X104 )
| ( X81 @ X105 @ X104 ) )
| ~ ( X77 @ X78 @ X82 )
| ( X80 = X82 ) ) )
= lconfl )
& ( ( ^ [X106: ( $i > $i > $o ) > $i > $i > $o] :
! [X107: $i > $i > $o,X108: $i,X109: $i,X110: $i > $i > $o] :
( ( X106 @ X107 @ X108 @ X109 )
| ~ ( X106 @ X110 @ X108 @ X109 )
| ~ ! [X111: $i,X112: $i] :
( ~ ( X110 @ X111 @ X112 )
| ( X107 @ X111 @ X112 ) ) ) )
= mono )
& ( ( ^ [X113: $i > $i > $o,X114: $i,X115: $i] :
! [X116: $i > $i > $o] :
( ~ ! [X117: $i,X118: $i] :
( ~ ( X113 @ X118 @ X117 )
| ( X116 @ X118 @ X117 ) )
| ~ ! [X119: $i,X120: $i,X121: $i] :
( ~ ( X116 @ X119 @ X121 )
| ~ ( X116 @ X120 @ X119 )
| ( X116 @ X120 @ X121 ) )
| ( X116 @ X114 @ X115 ) ) )
= tc )
& ( ( ^ [X122: $i > $i > $o] :
! [X123: $i,X124: $i] :
( ~ ( X122 @ X123 @ X124 )
| ~ ! [X125: $i] :
( ~ ! [X126: $i > $i > $o] :
( ( X126 @ X123 @ X125 )
| ~ ! [X127: $i,X128: $i] :
( ~ ( X122 @ X128 @ X127 )
| ( X126 @ X128 @ X127 ) )
| ~ ! [X129: $i,X130: $i,X131: $i] :
( ( X126 @ X131 @ X129 )
| ~ ( X126 @ X131 @ X130 )
| ~ ( X126 @ X130 @ X129 ) ) )
| ~ ! [X132: $i] :
~ ( X122 @ X125 @ X132 ) ) ) )
= norm )
& ( ( ^ [X133: $i > $i > $o] :
! [X134: $i,X135: $i > $i > $o,X136: $i > $i > $o,X137: $i,X138: $i] :
( ~ ! [X139: $i,X140: $i] :
( ~ ( X133 @ X140 @ X139 )
| ( X136 @ X140 @ X139 ) )
| ~ ! [X141: $i,X142: $i] :
( ( X135 @ X142 @ X141 )
| ~ ( X133 @ X142 @ X141 ) )
| ~ ! [X143: $i] :
( ~ ! [X144: $i > $i > $o] :
( ~ ! [X145: $i,X146: $i,X147: $i] :
( ( X144 @ X147 @ X146 )
| ~ ( X144 @ X147 @ X145 )
| ~ ( X144 @ X145 @ X146 ) )
| ~ ! [X148: $i,X149: $i] :
( ( X144 @ X148 @ X149 )
| ~ ( X133 @ X148 @ X149 ) )
| ( X144 @ X134 @ X143 ) )
| ~ ! [X150: $i > $i > $o] :
( ~ ! [X151: $i,X152: $i] :
( ( X150 @ X152 @ X151 )
| ~ ( X133 @ X152 @ X151 ) )
| ( X150 @ X137 @ X143 )
| ~ ! [X153: $i,X154: $i,X155: $i] :
( ~ ( X150 @ X154 @ X153 )
| ~ ( X150 @ X155 @ X154 )
| ( X150 @ X155 @ X153 ) ) ) )
| ~ ! [X156: $i,X157: $i,X158: $i] :
( ( X135 @ X158 @ X157 )
| ~ ( X135 @ X156 @ X157 )
| ~ ( X135 @ X158 @ X156 ) )
| ( ( X137 != X138 )
& ~ ! [X159: $i > $i > $o] :
( ~ ! [X160: $i,X161: $i] :
( ( X159 @ X161 @ X160 )
| ~ ( X133 @ X161 @ X160 ) )
| ~ ! [X162: $i,X163: $i,X164: $i] :
( ( X159 @ X163 @ X164 )
| ~ ( X159 @ X163 @ X162 )
| ~ ( X159 @ X162 @ X164 ) )
| ( X159 @ X138 @ X137 ) ) )
| ( ~ ! [X165: $i > $i > $o] :
( ~ ! [X166: $i,X167: $i] :
( ( X165 @ X167 @ X166 )
| ~ ( X133 @ X167 @ X166 ) )
| ( X165 @ X138 @ X134 )
| ~ ! [X168: $i,X169: $i,X170: $i] :
( ~ ( X165 @ X169 @ X168 )
| ( X165 @ X170 @ X168 )
| ~ ( X165 @ X170 @ X169 ) ) )
& ( X134 != X138 ) )
| ~ ! [X171: $i,X172: $i,X173: $i] :
( ( X136 @ X172 @ X173 )
| ~ ( X136 @ X172 @ X171 )
| ~ ( X136 @ X171 @ X173 ) )
| ( X135 @ X137 @ X134 )
| ( X136 @ X134 @ X137 )
| ( X134 = X137 ) ) )
= confl )
& ( nfof
= ( ^ [X174: $i > $i > $o,X175: $i,X176: $i] :
( ( ( X175 = X176 )
| ! [X177: $i > $i > $o] :
( ~ ! [X178: $i,X179: $i,X180: $i] :
( ( X177 @ X180 @ X179 )
| ~ ( X177 @ X178 @ X179 )
| ~ ( X177 @ X180 @ X178 ) )
| ~ ! [X181: $i,X182: $i] :
( ~ ( X174 @ X181 @ X182 )
| ( X177 @ X181 @ X182 ) )
| ( X177 @ X176 @ X175 ) ) )
& ! [X183: $i] :
~ ( X174 @ X175 @ X183 ) ) ) )
& ( ( ^ [X184: $i > $i > $o] :
! [X185: $i,X186: $i > $i > $o,X187: $i,X188: $i > $i > $o] :
( ( X188 @ X187 @ X185 )
| ~ ! [X189: $i,X190: $i,X191: $i] :
( ~ ( X188 @ X191 @ X190 )
| ( X188 @ X189 @ X190 )
| ~ ( X188 @ X189 @ X191 ) )
| ( ~ ! [X192: $i > $i > $o] :
( ( X192 @ X185 @ X187 )
| ~ ! [X193: $i,X194: $i] :
( ~ ( X184 @ X193 @ X194 )
| ( X192 @ X193 @ X194 ) )
| ~ ! [X195: $i,X196: $i,X197: $i] :
( ~ ( X192 @ X197 @ X196 )
| ~ ( X192 @ X195 @ X197 )
| ( X192 @ X195 @ X196 ) ) )
& ( X185 != X187 )
& ~ ! [X198: $i > $i > $o] :
( ~ ! [X199: $i,X200: $i] :
( ( X198 @ X199 @ X200 )
| ~ ( X184 @ X199 @ X200 ) )
| ~ ! [X201: $i,X202: $i,X203: $i] :
( ~ ( X198 @ X203 @ X201 )
| ( X198 @ X202 @ X201 )
| ~ ( X198 @ X202 @ X203 ) )
| ( X198 @ X187 @ X185 ) ) )
| ~ ! [X204: $i] :
( ~ ! [X205: $i > $i > $o] :
( ~ ! [X206: $i,X207: $i] :
( ( X205 @ X206 @ X207 )
| ~ ( X184 @ X206 @ X207 ) )
| ~ ! [X208: $i,X209: $i,X210: $i] :
( ~ ( X205 @ X208 @ X209 )
| ~ ( X205 @ X209 @ X210 )
| ( X205 @ X208 @ X210 ) )
| ( X205 @ X187 @ X204 ) )
| ~ ! [X211: $i > $i > $o] :
( ( X211 @ X185 @ X204 )
| ~ ! [X212: $i,X213: $i] :
( ( X211 @ X213 @ X212 )
| ~ ( X184 @ X213 @ X212 ) )
| ~ ! [X214: $i,X215: $i,X216: $i] :
( ( X211 @ X214 @ X215 )
| ~ ( X211 @ X214 @ X216 )
| ~ ( X211 @ X216 @ X215 ) ) ) )
| ( X186 @ X185 @ X187 )
| ~ ! [X217: $i,X218: $i] :
( ~ ( X184 @ X217 @ X218 )
| ( X186 @ X217 @ X218 ) )
| ~ ! [X219: $i,X220: $i,X221: $i] :
( ~ ( X186 @ X220 @ X219 )
| ( X186 @ X221 @ X219 )
| ~ ( X186 @ X221 @ X220 ) )
| ( X185 = X187 )
| ~ ! [X222: $i,X223: $i] :
( ( X188 @ X222 @ X223 )
| ~ ( X184 @ X222 @ X223 ) ) ) )
= cr )
& ( trsc
= ( ^ [X224: $i > $i > $o,X225: $i,X226: $i] :
( ! [X227: $i > $i > $o] :
( ~ ! [X228: $i,X229: $i,X230: $i] :
( ~ ( X227 @ X229 @ X230 )
| ( X227 @ X229 @ X228 )
| ~ ( X227 @ X230 @ X228 ) )
| ~ ! [X231: $i,X232: $i] :
( ( X227 @ X231 @ X232 )
| ~ ( X224 @ X231 @ X232 ) )
| ( X227 @ X225 @ X226 ) )
| ! [X233: $i > $i > $o] :
( ~ ! [X234: $i,X235: $i] :
( ( X233 @ X234 @ X235 )
| ~ ( X224 @ X234 @ X235 ) )
| ( X233 @ X226 @ X225 )
| ~ ! [X236: $i,X237: $i,X238: $i] :
( ~ ( X233 @ X237 @ X236 )
| ~ ( X233 @ X238 @ X237 )
| ( X233 @ X238 @ X236 ) ) )
| ( X225 = X226 ) ) ) )
& ( infl
= ( ^ [X239: ( $i > $i > $o ) > $i > $i > $o] :
! [X240: $i,X241: $i,X242: $i > $i > $o] :
( ~ ( X242 @ X240 @ X241 )
| ( X239 @ X242 @ X240 @ X241 ) ) ) )
& ( innf
= ( ^ [X243: $i > $i > $o,X244: $i] :
! [X245: $i] :
~ ( X243 @ X244 @ X245 ) ) )
& ! [X246: d_unsorted,X247: d_unsorted] :
( ( ( d2unsorted @ X246 )
= ( d2unsorted @ X247 ) )
=> ( X246 = X247 ) )
& ( trans
= ( ^ [X248: $i > $i > $o] :
! [X249: $i,X250: $i,X251: $i] :
( ~ ( X248 @ X251 @ X249 )
| ( X248 @ X250 @ X249 )
| ~ ( X248 @ X250 @ X251 ) ) ) )
& ( ( ^ [X252: $i > $i > $o] :
! [X253: $i > $o,X254: $i] :
( ( X253 @ X254 )
| ~ ! [X255: $i] :
( ( X253 @ X255 )
| ~ ! [X256: $i] :
( ~ ! [X257: $i > $i > $o] :
( ~ ! [X258: $i,X259: $i,X260: $i] :
( ~ ( X257 @ X259 @ X260 )
| ~ ( X257 @ X260 @ X258 )
| ( X257 @ X259 @ X258 ) )
| ~ ! [X261: $i,X262: $i] :
( ( X257 @ X261 @ X262 )
| ~ ( X252 @ X261 @ X262 ) )
| ( X257 @ X255 @ X256 ) )
| ( X253 @ X256 ) ) ) ) )
= ind )
& ( ( ^ [X263: $i > $i > $o] :
( ! [X264: $i,X265: $i] :
( ~ ( X263 @ X265 @ X264 )
| ~ ( X263 @ X264 @ X265 ) )
& ! [X266: $i,X267: $i,X268: $i] :
( ( X263 @ X267 @ X268 )
| ~ ( X263 @ X267 @ X266 )
| ~ ( X263 @ X266 @ X268 ) ) ) )
= so )
& ( trc
= ( ^ [X269: $i > $i > $o,X270: $i,X271: $i] :
( ( X270 = X271 )
| ! [X272: $i > $i > $o] :
( ~ ! [X273: $i,X274: $i] :
( ( X272 @ X273 @ X274 )
| ~ ( X269 @ X273 @ X274 ) )
| ~ ! [X275: $i,X276: $i,X277: $i] :
( ~ ( X272 @ X275 @ X277 )
| ~ ( X272 @ X277 @ X276 )
| ( X272 @ X275 @ X276 ) )
| ( X272 @ X270 @ X271 ) ) ) ) )
& ( irrefl
= ( ^ [X278: $i > $i > $o] :
! [X279: $i] :
~ ( X278 @ X279 @ X279 ) ) )
& ( ( ^ [X280: $i > $i > $o] :
! [X281: $i > $o,X282: $i] :
( ~ ( X281 @ X282 )
| ~ ! [X283: $i] :
( ~ ! [X284: $i] :
( ~ ( X280 @ X283 @ X284 )
| ~ ( X281 @ X284 ) )
| ~ ( X281 @ X283 ) ) ) )
= term )
& ( sc
= ( ^ [X285: $i > $i > $o,X286: $i,X287: $i] :
( ( X285 @ X287 @ X286 )
| ( X285 @ X286 @ X287 ) ) ) )
& ! [X288: $i] :
? [X289: d_unsorted] :
( ( d2unsorted @ X289 )
= X288 )
& ( subrel
= ( ^ [X290: $i > $i > $o,X291: $i > $i > $o] :
! [X292: $i,X293: $i] :
( ( X291 @ X292 @ X293 )
| ~ ( X290 @ X292 @ X293 ) ) ) )
& ( refl
= ( ^ [X294: $i > $i > $o] :
! [X295: $i] : ( X294 @ X295 @ X295 ) ) )
& ( ( ^ [X296: $i > $i > $o,X297: $i,X298: $i] :
( ( X296 @ X297 @ X298 )
| ( X297 = X298 ) ) )
= rc )
& ( ( ^ [X299: $i > $i > $o] :
( ! [X300: $i,X301: $i,X302: $i] :
( ( X299 @ X300 @ X301 )
| ~ ( X299 @ X300 @ X302 )
| ~ ( X299 @ X302 @ X301 ) )
& ! [X303: $i] : ( X299 @ X303 @ X303 )
& ! [X304: $i,X305: $i] :
( ~ ( X299 @ X305 @ X304 )
| ( X304 = X305 )
| ~ ( X299 @ X304 @ X305 ) ) ) )
= po )
& ! [X306: d_unsorted] : ( d_unsorted_0 = X306 )
& ( ( ^ [X307: $i > $i > $o] :
! [X308: $i,X309: $i] :
( ~ ( X307 @ X309 @ X308 )
| ( X307 @ X308 @ X309 ) ) )
= symm ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( total
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ( X4 @ X7 @ X6 )
| ( X6 = X7 )
| ( X4 @ X6 @ X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] : ( X4 @ X7 @ X6 ) )
= inv )
& ( ( ^ [X4: $i > $i > $o] :
! [X11: $i,X7: $i,X6: $i,X31: $i > $i > $o,X30: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X31 @ X14 @ X15 ) )
| ( X7 = X11 )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X31 @ X13 @ X26 )
| ~ ( X31 @ X12 @ X13 )
| ( X31 @ X12 @ X26 ) )
| ( X31 @ X11 @ X7 )
| ( X30 @ X7 @ X11 )
| ~ ! [X25: $i,X12: $i,X13: $i] :
( ( X30 @ X12 @ X25 )
| ~ ( X30 @ X12 @ X13 )
| ~ ( X30 @ X13 @ X25 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X11 @ X27 )
| ~ ! [X13: $i,X26: $i,X12: $i] :
( ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X25: $i,X12: $i,X13: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 ) ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X30 @ X14 @ X15 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X7 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X32: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X32 )
| ( X5 @ X12 @ X32 ) ) )
& ( X6 != X7 ) )
| ~ ( X4 @ X6 @ X11 ) ) )
= sconfl )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) ) )
= asymm )
& ( 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] :
( ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 )
| ( X6 = X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
~ ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X25: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 ) ) )
& ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X27 )
| ~ ! [X13: $i,X25: $i,X12: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 ) )
| ~ ! [X14: $i,X15: $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 @ X12 @ X13 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 ) )
| ( X5 @ X6 @ X27 ) ) )
& ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X7 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 ) ) )
& ( X6 != X7 ) ) )
= join )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X29: $i > $i > $o,X7: $i,X28: $i > $i > $o,X11: $i] :
( ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X26: $i,X13: $i] :
( ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X11 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X12: $i,X25: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) )
| ( X29 @ X11 @ X7 )
| ( X28 @ X7 @ X11 )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X28 @ X12 @ X13 )
| ~ ( X28 @ X13 @ X25 )
| ( X28 @ X12 @ X25 ) )
| ~ ( X4 @ X6 @ X7 )
| ~ ! [X13: $i,X26: $i,X12: $i] :
( ~ ( X29 @ X13 @ X26 )
| ( X29 @ X12 @ X26 )
| ~ ( X29 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X29 @ X14 @ X15 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X28 @ X14 @ X15 ) )
| ~ ( X4 @ X6 @ X11 )
| ( X7 = X11 ) ) )
= lconfl )
& ( ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X5: $i > $i > $o,X9: $i,X10: $i,X4: $i > $i > $o] :
( ( X8 @ X5 @ X9 @ X10 )
| ~ ( X8 @ X4 @ X9 @ X10 )
| ~ ! [X6: $i,X7: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X5 @ X6 @ X7 ) ) ) )
= mono )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X11: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) )
| ( X5 @ X6 @ X7 ) ) )
= tc )
& ( ( ^ [X4: $i > $i > $o] :
! [X6: $i,X23: $i] :
( ~ ( X4 @ X6 @ X23 )
| ~ ! [X24: $i] :
( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X24 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X11: $i,X13: $i,X12: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) ) )
| ~ ! [X22: $i] :
~ ( X4 @ X24 @ X22 ) ) ) )
= norm )
& ( ( ^ [X4: $i > $i > $o] :
! [X11: $i,X33: $i > $i > $o,X34: $i > $i > $o,X7: $i,X6: $i] :
( ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X34 @ X14 @ X15 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X33 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X26: $i,X12: $i] :
( ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X11 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 ) ) ) )
| ~ ! [X13: $i,X25: $i,X12: $i] :
( ( X33 @ X12 @ X25 )
| ~ ( X33 @ X13 @ X25 )
| ~ ( X33 @ X12 @ X13 ) )
| ( ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X35: $i] :
( ( X5 @ X12 @ X35 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X35 ) )
| ( X5 @ X6 @ X7 ) ) )
| ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X11 )
| ~ ! [X26: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) ) )
& ( X6 != X11 ) )
| ~ ! [X13: $i,X12: $i,X26: $i] :
( ( X34 @ X12 @ X26 )
| ~ ( X34 @ X12 @ X13 )
| ~ ( X34 @ X13 @ X26 ) )
| ( X33 @ X7 @ X11 )
| ( X34 @ X11 @ X7 )
| ( X7 = X11 ) ) )
= confl )
& ( nfof
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( ( X6 = X7 )
| ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X11: $i,X12: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X6 ) ) )
& ! [X22: $i] :
~ ( X4 @ X6 @ X22 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X36: $i > $i > $o,X6: $i,X37: $i > $i > $o] :
( ( X37 @ X6 @ X7 )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X37 @ X13 @ X26 )
| ( X37 @ X12 @ X26 )
| ~ ( X37 @ X12 @ X13 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X11: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) ) )
& ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X6 @ X7 ) ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 ) )
| ( X5 @ X6 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X25: $i,X13: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X25 ) ) ) )
| ( X36 @ X7 @ X6 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X36 @ X14 @ X15 ) )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X36 @ X13 @ X25 )
| ( X36 @ X12 @ X25 )
| ~ ( X36 @ X12 @ X13 ) )
| ( X6 = X7 )
| ~ ! [X14: $i,X15: $i] :
( ( X37 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) )
= cr )
& ( trsc
= ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X16 @ X17 ) )
| ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X17 @ X16 )
| ~ ! [X11: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) ) )
| ( X16 = X17 ) ) ) )
& ( infl
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X6: $i,X7: $i,X4: $i > $i > $o] :
( ~ ( X4 @ X6 @ X7 )
| ( X8 @ X4 @ X6 @ X7 ) ) ) )
& ( innf
= ( ^ [X4: $i > $i > $o,X6: $i] :
! [X7: $i] :
~ ( X4 @ X6 @ X7 ) ) )
& ! [X2: d_unsorted,X3: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ( trans
= ( ^ [X4: $i > $i > $o] :
! [X11: $i,X6: $i,X7: $i] :
( ~ ( X4 @ X7 @ X11 )
| ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X20: $i > $o,X21: $i] :
( ( X20 @ X21 )
| ~ ! [X6: $i] :
( ( X20 @ X6 )
| ~ ! [X7: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 ) )
| ( X20 @ X7 ) ) ) ) )
= ind )
& ( ( ^ [X4: $i > $i > $o] :
( ! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) )
& ! [X7: $i,X6: $i,X11: $i] :
( ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X11 ) ) ) )
= so )
& ( trc
= ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ( X16 = X17 )
| ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X11: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ( X5 @ X16 @ X17 ) ) ) ) )
& ( irrefl
= ( ^ [X4: $i > $i > $o] :
! [X6: $i] :
~ ( X4 @ X6 @ X6 ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X18: $i > $o,X19: $i] :
( ~ ( X18 @ X19 )
| ~ ! [X6: $i] :
( ~ ! [X7: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X18 @ X7 ) )
| ~ ( X18 @ X6 ) ) ) )
= term )
& ( sc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X4 @ X7 @ X6 )
| ( X4 @ X6 @ X7 ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( ( d2unsorted @ X1 )
= X0 )
& ( subrel
= ( ^ [X4: $i > $i > $o,X5: $i > $i > $o] :
! [X6: $i,X7: $i] :
( ( X5 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( refl
= ( ^ [X4: $i > $i > $o] :
! [X6: $i] : ( X4 @ X6 @ X6 ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X4 @ X6 @ X7 )
| ( X6 = X7 ) ) )
= rc )
& ( ( ^ [X4: $i > $i > $o] :
( ! [X6: $i,X11: $i,X7: $i] :
( ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X11 ) )
& ! [X6: $i] : ( X4 @ X6 @ X6 )
& ! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X6 = X7 )
| ~ ( X4 @ X7 @ X6 ) ) ) )
= po )
& ! [X1: d_unsorted] : ( d_unsorted_0 = X1 )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X4 @ X7 @ X6 ) ) )
= symm ) ),
file('/export/starexec/sandbox/tmp/tmp.qqkWGq3eP8/DTF2THF_20128.p',sev441_1) ).
thf(f185,plain,
! [X1: $i] :
( ( d2unsorted @ ( sK3 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( d2unsorted @ ( sK3 @ X1 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f183]) ).
thf(f183,plain,
! [X1: $i] :
( ( ^ [Y0: d_unsorted] :
( ( d2unsorted @ Y0 )
= X1 )
@ ( sK3 @ X1 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
! [X1: $i] :
( ( ?? @ d_unsorted
@ ^ [Y0: d_unsorted] :
( ( d2unsorted @ Y0 )
= X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f177]) ).
thf(f177,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f2778,plain,
! [X1: $i > $i > $o] :
( ( ( lconfl @ X1 )
= $true )
| ( ( sK24 @ X1 )
!= ( sK22 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f2777]) ).
thf(f2777,plain,
! [X1: $i > $i > $o] :
( ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2775]) ).
thf(f2775,plain,
! [X1: $i > $i > $o] :
( ( ( lconfl @ X1 )
= $true )
| ( $false
= ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2773]) ).
thf(f2773,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( lconfl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2770]) ).
thf(f2770,plain,
! [X1: $i > $i > $o] :
( ( ( lconfl @ X1 )
= $true )
| ( $false
= ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK25 @ X1 @ Y1 @ Y0 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2767]) ).
thf(f2767,plain,
! [X1: $i > $i > $o] :
( ( ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK25 @ X1 @ Y1 @ Y0 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK25 @ X1 @ Y0 @ Y2 )
| ( sK25 @ X1 @ Y0 @ Y1 )
| ~ ( sK25 @ X1 @ Y2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2764]) ).
thf(f2764,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK25 @ X1 @ Y1 @ Y0 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK25 @ X1 @ Y0 @ Y2 )
| ( sK25 @ X1 @ Y0 @ Y1 )
| ~ ( sK25 @ X1 @ Y2 @ Y1 ) ) ) ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK24 @ X1 ) ) ) )
| ( ( lconfl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2762]) ).
thf(f2762,plain,
! [X1: $i > $i > $o] :
( ( ( lconfl @ X1 )
= $true )
| ( $false
= ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK25 @ X1 @ Y1 @ Y0 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK25 @ X1 @ Y0 @ Y2 )
| ( sK25 @ X1 @ Y0 @ Y1 )
| ~ ( sK25 @ X1 @ Y2 @ Y1 ) ) ) ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK23 @ X1 @ Y0 @ Y2 )
| ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2760]) ).
thf(f2760,plain,
! [X1: $i > $i > $o] :
( ( ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK25 @ X1 @ Y1 @ Y0 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK25 @ X1 @ Y0 @ Y2 )
| ( sK25 @ X1 @ Y0 @ Y1 )
| ~ ( sK25 @ X1 @ Y2 @ Y1 ) ) ) ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK23 @ X1 @ Y0 @ Y2 )
| ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y0 @ Y1 ) ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2758]) ).
thf(f2758,plain,
! [X1: $i > $i > $o] :
( ( ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK25 @ X1 @ Y1 @ Y0 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK25 @ X1 @ Y0 @ Y2 )
| ( sK25 @ X1 @ Y0 @ Y1 )
| ~ ( sK25 @ X1 @ Y2 @ Y1 ) ) ) ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK23 @ X1 @ Y0 @ Y2 )
| ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y0 @ Y1 ) ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) )
| ( sK25 @ X1 @ ( sK22 @ X1 ) @ ( sK24 @ X1 ) ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2756]) ).
thf(f2756,plain,
! [X1: $i > $i > $o] :
( ( ( lconfl @ X1 )
= $true )
| ( $false
= ( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK23 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK25 @ X1 @ Y1 @ Y0 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK25 @ X1 @ Y0 @ Y2 )
| ( sK25 @ X1 @ Y0 @ Y1 )
| ~ ( sK25 @ X1 @ Y2 @ Y1 ) ) ) ) )
| ~ ( X1 @ ( sK26 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK23 @ X1 @ Y0 @ Y2 )
| ~ ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( sK23 @ X1 @ Y0 @ Y1 ) ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) )
| ( sK25 @ X1 @ ( sK22 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK24 @ X1 ) @ 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] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ ( sK22 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2751]) ).
thf(f2751,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y0 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK25 @ X1 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK25 @ X1 @ Y1 @ Y3 )
| ( sK25 @ X1 @ Y1 @ Y2 )
| ~ ( sK25 @ X1 @ Y3 @ Y2 ) ) ) ) )
| ~ ( X1 @ Y0 @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK23 @ X1 @ Y1 @ Y3 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ~ ( sK23 @ X1 @ Y1 @ Y2 ) ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) )
| ( sK25 @ X1 @ ( sK22 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ ( sK24 @ X1 ) @ 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] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y3 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
@ ( sK26 @ X1 ) ) )
| ( ( lconfl @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f2747]) ).
thf(f2747,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y0 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK23 @ X1 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK25 @ X1 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK25 @ X1 @ Y1 @ Y3 )
| ( sK25 @ X1 @ Y1 @ Y2 )
| ~ ( sK25 @ X1 @ Y3 @ Y2 ) ) ) ) )
| ~ ( X1 @ Y0 @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK23 @ X1 @ Y1 @ Y3 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 )
| ~ ( sK23 @ X1 @ Y1 @ Y2 ) ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) )
| ( sK25 @ X1 @ ( sK22 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ ( sK24 @ X1 ) @ 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] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y3 @ Y4 )
| ( Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2744]) ).
thf(f2744,plain,
! [X1: $i > $i > $o] :
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y1 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK23 @ X1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y4 @ Y3 ) ) ) ) )
| ~ ( X1 @ Y1 @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK23 @ X1 @ Y2 @ Y4 )
| ~ ( sK23 @ X1 @ Y3 @ Y4 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 ) ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) )
| ( Y0 @ ( sK22 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ ( sK24 @ X1 ) @ 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] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ ( sK22 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ ( sK25 @ X1 ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f2730]) ).
thf(f2730,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK24 @ X1 )
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y1 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK23 @ X1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y4 @ Y3 ) ) ) ) )
| ~ ( X1 @ Y1 @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK23 @ X1 @ Y2 @ Y4 )
| ~ ( sK23 @ X1 @ Y3 @ Y4 )
| ~ ( sK23 @ X1 @ Y2 @ Y3 ) ) ) ) )
| ( sK23 @ X1 @ ( sK24 @ X1 ) @ ( sK22 @ X1 ) )
| ( Y0 @ ( sK22 @ X1 ) @ ( sK24 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ ( sK24 @ X1 ) @ 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] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ ( sK22 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( lconfl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2726]) ).
thf(f2726,plain,
! [X1: $i > $i > $o] :
( ( ( lconfl @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y2 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK23 @ X1 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y1 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y4 )
| ~ ( Y1 @ Y5 @ Y4 ) ) ) ) )
| ~ ( X1 @ Y2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK23 @ X1 @ Y3 @ Y5 )
| ~ ( sK23 @ X1 @ Y4 @ Y5 )
| ~ ( sK23 @ X1 @ Y3 @ Y4 ) ) ) ) )
| ( sK23 @ X1 @ Y0 @ ( sK22 @ X1 ) )
| ( Y1 @ ( sK22 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y0 @ 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] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ ( sK22 @ X1 ) @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
@ ( sK24 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f2711]) ).
thf(f2711,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y2 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK23 @ X1 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y1 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y4 )
| ~ ( Y1 @ Y5 @ Y4 ) ) ) ) )
| ~ ( X1 @ Y2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK23 @ X1 @ Y3 @ Y5 )
| ~ ( sK23 @ X1 @ Y4 @ Y5 )
| ~ ( sK23 @ X1 @ Y3 @ Y4 ) ) ) ) )
| ( sK23 @ X1 @ Y0 @ ( sK22 @ X1 ) )
| ( Y1 @ ( sK22 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y0 @ 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] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ ( sK22 @ X1 ) @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2706]) ).
thf(f2706,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y3 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y2 @ Y4 @ Y6 )
| ( Y2 @ Y4 @ Y5 )
| ~ ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ~ ( X1 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y4 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) )
| ( Y0 @ Y1 @ ( sK22 @ X1 ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( X1 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ ( sK22 @ X1 ) @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( sK23 @ X1 ) ) )
| ( ( lconfl @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f2681]) ).
thf(f2681,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1
= ( sK22 @ X1 ) )
| ~ ( X1 @ Y3 @ ( sK22 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y2 @ Y4 @ Y6 )
| ( Y2 @ Y4 @ Y5 )
| ~ ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ~ ( X1 @ Y3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y4 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) ) )
| ( Y0 @ Y1 @ ( sK22 @ X1 ) )
| ( Y2 @ ( sK22 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 )
| ( Y5 @ Y7 @ Y6 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( X1 @ Y6 @ Y7 ) ) ) )
| ( Y5 @ ( sK22 @ X1 ) @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y8 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( lconfl @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2676]) ).
thf(f2676,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 = Y0 )
| ~ ( X1 @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( X1 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ~ ( X1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y5 @ Y7 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y0 )
| ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( X1 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y0 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( sK22 @ X1 ) ) )
| ( ( lconfl @ X1 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f1523]) ).
thf(f1523,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] :
( ( Y2 = Y0 )
| ~ ( X1 @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( X1 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ~ ( X1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y5 @ Y7 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y0 )
| ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( X1 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y0 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( lconfl @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1521]) ).
thf(f1521,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] :
( ( Y2 = Y0 )
| ~ ( X1 @ Y4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( X1 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y3 @ Y5 @ Y7 )
| ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y7 @ Y6 ) ) ) ) )
| ~ ( X1 @ Y4 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y5 @ Y7 )
| ~ ( Y1 @ Y6 @ Y7 )
| ~ ( Y1 @ Y5 @ Y6 ) ) ) ) )
| ( Y1 @ Y2 @ Y0 )
| ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( X1 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y0 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y9 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( lconfl @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f1520]) ).
thf(f1520,plain,
! [X1: $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] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= ( lconfl @ X1 ) ),
inference(argument_congruence,[status(thm)],[f31]) ).
thf(f31,plain,
( lconfl
= ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ^ [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] :
( ( Y3 = Y1 )
| ~ ( Y0 @ Y5 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y2 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ( Y4 @ Y6 @ Y7 )
| ~ ( Y4 @ Y8 @ Y7 ) ) ) ) )
| ~ ( Y0 @ Y5 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y7 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 ) ) ) ) )
| ( Y2 @ Y3 @ Y1 )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y10 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= lconfl )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f131,plain,
( ( ( lconfl @ sK2 )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f129,definition,
( spl0_4
<=> ( ( lconfl @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1822,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[status(thm)],[f1821]) ).
thf(f1821,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f1777]) ).
thf(f1777,plain,
( ( $false = $true )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f1766,f717]) ).
thf(f717,plain,
( ( $false
= ( join @ sK2 @ sK15 @ sK13 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f716]) ).
thf(f716,plain,
( ( ( ( ( sK2 @ sK14 @ sK15 )
& ( sK2 @ sK14 @ sK13 ) )
=> ( join @ sK2 @ sK15 @ sK13 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f715]) ).
thf(f715,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK2 @ sK14 @ Y0 )
& ( sK2 @ sK14 @ sK13 ) )
=> ( join @ sK2 @ Y0 @ sK13 ) )
@ sK15 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f674]) ).
thf(f674,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK2 @ sK14 @ Y0 )
& ( sK2 @ sK14 @ sK13 ) )
=> ( join @ sK2 @ Y0 @ sK13 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f673]) ).
thf(f673,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK2 @ Y0 @ sK13 ) )
=> ( join @ sK2 @ Y1 @ sK13 ) ) )
@ sK14 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f636]) ).
thf(f636,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y0 @ Y1 )
& ( sK2 @ Y0 @ sK13 ) )
=> ( join @ sK2 @ Y1 @ sK13 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f635]) ).
thf(f635,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK2 @ Y1 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( join @ sK2 @ Y2 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK2 @ Y1 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( join @ sK2 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f133]) ).
thf(f133,definition,
( spl0_5
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK2 @ Y1 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( join @ sK2 @ Y2 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f1766,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( join @ X1 @ X2 @ X3 ) ),
inference(subsumption_resolution,[status(thm)],[f1765,f192]) ).
thf(f1765,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( X2 != X3 )
| ( $true
= ( join @ X1 @ X2 @ X3 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1764]) ).
thf(f1764,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( X2 = X3 )
= $false )
| ( $true
= ( join @ X1 @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1763]) ).
thf(f1763,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( $true
= ( join @ X1 @ X2 @ X3 ) )
| ( ( X2 != X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1761]) ).
thf(f1761,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( $true
= ( join @ X1 @ X2 @ X3 ) )
| ( ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X2 @ X3 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1758]) ).
thf(f1758,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X2 @ X3 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $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 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) ) ) ) )
= $true )
| ( $true
= ( join @ X1 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1756]) ).
thf(f1756,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( $true
= ( join @ X1 @ X2 @ X3 ) )
| ( $true
= ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X2 @ X3 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $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 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X3 @ X2 ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1755]) ).
thf(f1755,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( $true
= ( join @ X1 @ X2 @ X3 ) )
| ( $false
= ( ~ ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X2 @ X3 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $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 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X3 @ X2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1753]) ).
thf(f1753,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ~ ( ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X2 @ X3 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
| ~ ( !! @ ( $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 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
| ( Y1 @ X3 @ Y0 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y1 )
| ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ( Y0 @ X3 @ X2 ) ) ) ) )
= ( join @ X1 @ X2 @ X3 ) ),
inference(beta_eta_normalization,[status(thm)],[f1752]) ).
thf(f1752,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] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X2 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
| ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ Y0 @ X2 ) ) ) )
@ X3 )
= ( join @ X1 @ X2 @ X3 ) ),
inference(argument_congruence,[status(thm)],[f1423]) ).
thf(f1423,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( join @ X1 @ X2 )
= ( ^ [Y0: $i] :
~ ( ( X2 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X2 @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
| ~ ( !! @ ( $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 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y2 )
| ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ Y0 @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1422]) ).
thf(f1422,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] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 )
| ~ ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y1 @ Y0 ) ) ) )
@ X2 )
= ( join @ X1 @ X2 ) ),
inference(argument_congruence,[status(thm)],[f1134]) ).
thf(f1134,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i,Y1: $i] :
~ ( ( Y0 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 )
| ~ ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y0 @ Y1 ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y3 )
| ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y1 @ Y0 ) ) ) ) )
= ( join @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f1133]) ).
thf(f1133,plain,
! [X1: $i > $i > $o] :
( ( join @ X1 )
= ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f99]) ).
thf(f99,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] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( ^ [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 @ Y5 @ Y6 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y5 @ Y4 )
| ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 ) ) ) ) )
= join )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f136,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f127,f133,f129]) ).
thf(f127,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK2 @ Y1 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( join @ sK2 @ Y2 @ Y0 ) ) ) ) ) )
| ( ( lconfl @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
( ( lconfl @ sK2 )
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK2 @ Y1 @ Y2 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( join @ sK2 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f124]) ).
thf(f124,plain,
( ( lconfl @ sK2 )
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( join @ Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
( lconfl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( join @ Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( join @ Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( lconfl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( join @ Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( lconfl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( join @ Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( lconfl
!= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( join @ X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( lconfl
!= ( ^ [X4: $i > $i > $o] :
! [X11: $i,X6: $i,X7: $i] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X6 @ X11 ) )
=> ( join @ X4 @ X11 @ X7 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( lconfl
= ( ^ [X4: $i > $i > $o] :
! [X11: $i,X6: $i,X7: $i] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X6 @ X11 ) )
=> ( join @ X4 @ X11 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qqkWGq3eP8/DTF2THF_20128.p',locally_confluent) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n002.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 09:36:46 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.26/0.47 % Domain : Software Verification
% 0.26/0.47 % Problem : Benchmark: SEV441^1, Active target: locally_confluent
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English :
% 0.26/0.47
% 0.26/0.47 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.26/0.47 % Source : [Kon26]
% 0.26/0.47 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % Rating : ? v9.3.0
% 0.26/0.47 % Syntax : Number of formulae : 35 ( 1 unt; 33 typ; 0 def)
% 0.26/0.47 % Number of atoms : 82 ( 51 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 33 ( 41 avg)
% 0.26/0.47 % Number of connectives : 985 ( 227 ~; 218 |; 44 &; 494 @)
% 0.26/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 32 ( 17 avg)
% 0.26/0.47 % Number of types : 4 ( 2 usr)
% 0.26/0.47 % Number of type conns : 262 ( 262 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 32 ( 31 usr; 1 con; 0-3 aty)
% 0.26/0.47 % Number of variables : 314 ( 48 ^; 265 !; 1 ?; 314 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments :
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(unsorted_type,type,
% 0.26/0.47 unsorted: $tType ).
% 0.26/0.47
% 0.26/0.47 thf(subrel_decl,type,
% 0.26/0.47 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(inv_decl,type,
% 0.26/0.47 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(idem_decl,type,
% 0.26/0.47 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(infl_decl,type,
% 0.26/0.47 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(mono_decl,type,
% 0.26/0.47 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(refl_decl,type,
% 0.26/0.47 refl: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(irrefl_decl,type,
% 0.26/0.47 irrefl: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(rc_decl,type,
% 0.26/0.47 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(symm_decl,type,
% 0.26/0.47 symm: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(antisymm_decl,type,
% 0.26/0.47 antisymm: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(asymm_decl,type,
% 0.26/0.47 asymm: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(sc_decl,type,
% 0.26/0.47 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(trans_decl,type,
% 0.26/0.47 trans: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(tc_decl,type,
% 0.26/0.47 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(trc_decl,type,
% 0.26/0.47 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(trsc_decl,type,
% 0.26/0.47 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(po_decl,type,
% 0.26/0.47 po: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(so_decl,type,
% 0.26/0.47 so: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(total_decl,type,
% 0.26/0.47 total: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(term_decl,type,
% 0.26/0.47 term: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(ind_decl,type,
% 0.26/0.47 ind: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(innf_decl,type,
% 0.26/0.47 innf: ( $i > $i > $o ) > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(nfof_decl,type,
% 0.26/0.47 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(norm_decl,type,
% 0.26/0.47 norm: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(join_decl,type,
% 0.26/0.47 join: ( $i > $i > $o ) > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(lconfl_decl,type,
% 0.26/0.47 lconfl: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(sconfl_decl,type,
% 0.26/0.47 sconfl: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(confl_decl,type,
% 0.26/0.47 confl: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(cr_decl,type,
% 0.26/0.47 cr: ( $i > $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 %----Types of the domains
% 0.26/0.47 thf(d_unsorted_type,type,
% 0.26/0.47 d_unsorted: $tType ).
% 0.26/0.47
% 0.26/0.47 %----Types of the promotion functions
% 0.26/0.47 thf(d2unsorted_decl,type,
% 0.26/0.47 d2unsorted: d_unsorted > $i ).
% 0.26/0.47
% 0.26/0.47 %----Types of the domain elements
% 0.26/0.47 thf(d_unsorted_0_decl,type,
% 0.26/0.47 d_unsorted_0: d_unsorted ).
% 0.26/0.47
% 0.26/0.47 thf(sev441_1,axiom,
% 0.26/0.47 ( ! [U: $i] :
% 0.26/0.47 ? [DU: d_unsorted] :
% 0.26/0.47 ( U
% 0.26/0.47 = ( d2unsorted @ DU ) )
% 0.26/0.47 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 0.26/0.47 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 0.26/0.47 ( ( ( d2unsorted @ DU1 )
% 0.26/0.47 = ( d2unsorted @ DU2 ) )
% 0.26/0.47 => ( DU1 = DU2 ) )
% 0.26/0.47 & ( subrel
% 0.26/0.47 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ( S @ X @ Y ) ) ) )
% 0.26/0.47 & ( inv
% 0.26/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 0.26/0.47 & ( idem
% 0.26/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.26/0.47 ! [R: $i > $i > $o] :
% 0.26/0.47 ( ( F @ R )
% 0.26/0.47 = ( F @ ( F @ R ) ) ) ) )
% 0.26/0.47 & ( infl
% 0.26/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.26/0.47 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ( F @ R @ X @ Y ) ) ) )
% 0.26/0.47 & ( mono
% 0.26/0.47 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.26/0.47 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 0.26/0.47 ( ~ ! [X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ( S @ X @ Y ) )
% 0.26/0.47 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 0.26/0.47 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 0.26/0.47 & ( refl
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i] : ( R @ X @ X ) ) )
% 0.26/0.47 & ( irrefl
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i] :
% 0.26/0.47 ~ ( R @ X @ X ) ) )
% 0.26/0.47 & ( rc
% 0.26/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.26/0.47 ( ( X = Y )
% 0.26/0.47 | ( R @ X @ Y ) ) ) )
% 0.26/0.47 & ( symm
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ( R @ Y @ X ) ) ) )
% 0.26/0.47 & ( antisymm
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ~ ( R @ Y @ X )
% 0.26/0.47 | ( X = Y ) ) ) )
% 0.26/0.47 & ( asymm
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ~ ( R @ Y @ X ) ) ) )
% 0.26/0.47 & ( sc
% 0.26/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.26/0.47 ( ( R @ Y @ X )
% 0.26/0.47 | ( R @ X @ Y ) ) ) )
% 0.26/0.47 & ( trans
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i,Z: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ~ ( R @ Y @ Z )
% 0.26/0.47 | ( R @ X @ Z ) ) ) )
% 0.26/0.47 & ( tc
% 0.26/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.26/0.47 ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Y ) ) ) )
% 0.26/0.47 & ( trc
% 0.26/0.47 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.26/0.47 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.26/0.47 | ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.26/0.47 & ( trsc
% 0.26/0.47 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 0.26/0.47 ( ( Flatten_var_0 = Flatten_var_1 )
% 0.26/0.47 | ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 0.26/0.47 | ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 0.26/0.47 & ( po
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ( ! [X: $i] : ( R @ X @ X )
% 0.26/0.47 & ! [X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ~ ( R @ Y @ X )
% 0.26/0.47 | ( X = Y ) )
% 0.26/0.47 & ! [X: $i,Y: $i,Z: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ~ ( R @ Y @ Z )
% 0.26/0.47 | ( R @ X @ Z ) ) ) ) )
% 0.26/0.47 & ( so
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ( ! [X: $i,Y: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ~ ( R @ Y @ X ) )
% 0.26/0.47 & ! [X: $i,Y: $i,Z: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Y )
% 0.26/0.47 | ~ ( R @ Y @ Z )
% 0.26/0.47 | ( R @ X @ Z ) ) ) ) )
% 0.26/0.47 & ( total
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i] :
% 0.26/0.47 ( ( X = Y )
% 0.26/0.47 | ( R @ X @ Y )
% 0.26/0.47 | ( R @ Y @ X ) ) ) )
% 0.26/0.47 & ( term
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [A: $i > $o,Bound_variable_862: $i] :
% 0.26/0.47 ( ~ ( A @ Bound_variable_862 )
% 0.26/0.47 | ~ ! [X: $i] :
% 0.26/0.47 ( ~ ( A @ X )
% 0.26/0.47 | ~ ! [Y: $i] :
% 0.26/0.47 ( ~ ( A @ Y )
% 0.26/0.47 | ~ ( R @ X @ Y ) ) ) ) ) )
% 0.26/0.47 & ( ind
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [P: $i > $o,Bound_variable_917: $i] :
% 0.26/0.47 ( ~ ! [X: $i] :
% 0.26/0.47 ( ~ ! [Y: $i] :
% 0.26/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Y ) )
% 0.26/0.47 | ( P @ Y ) )
% 0.26/0.47 | ( P @ X ) )
% 0.26/0.47 | ( P @ Bound_variable_917 ) ) ) )
% 0.26/0.47 & ( innf
% 0.26/0.47 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.26/0.47 ! [Y: $i] :
% 0.26/0.47 ~ ( R @ X @ Y ) ) )
% 0.26/0.47 & ( nfof
% 0.26/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.26/0.47 ( ( ( X = Y )
% 0.26/0.47 | ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ X ) ) )
% 0.26/0.47 & ! [Bound_variable_985: $i] :
% 0.26/0.47 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 0.26/0.47 & ( norm
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Bound_variable_1075: $i] :
% 0.26/0.47 ( ~ ( R @ X @ Bound_variable_1075 )
% 0.26/0.47 | ~ ! [Bound_variable_1049: $i] :
% 0.26/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Bound_variable_1049 ) )
% 0.26/0.47 | ~ ! [Bound_variable_985: $i] :
% 0.26/0.47 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 0.26/0.47 & ( join
% 0.26/0.47 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.26/0.47 ~ ( ( X != Y )
% 0.26/0.47 & ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ X ) )
% 0.26/0.47 & ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Y ) )
% 0.26/0.47 & ! [Bound_variable_1218: $i] :
% 0.26/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.26/0.47 | ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 0.26/0.47 & ( lconfl
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 0.26/0.47 ( ~ ( R @ X @ Z )
% 0.26/0.47 | ~ ( R @ X @ Y )
% 0.26/0.47 | ( Y = Z )
% 0.26/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.26/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.26/0.47 | ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1293 @ Y @ Z )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 0.26/0.47 & ( sconfl
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 0.26/0.47 ( ~ ( R @ X @ Z )
% 0.26/0.47 | ( ( X != Y )
% 0.26/0.47 & ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Y ) ) )
% 0.26/0.47 | ( Y = Z )
% 0.26/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.26/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.26/0.47 | ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1371 @ Y @ Z )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 0.26/0.47 & ( confl
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 0.26/0.47 ( ( ( X != Z )
% 0.26/0.47 & ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Z ) ) )
% 0.26/0.47 | ( ( X != Y )
% 0.26/0.47 & ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Y ) ) )
% 0.26/0.47 | ( Y = Z )
% 0.26/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.26/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.26/0.47 | ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Z @ Bound_variable_1218 ) ) )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1444 @ Y @ Z )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 0.26/0.47 & ( cr
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 0.26/0.47 ( ( ( X != Y )
% 0.26/0.47 & ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ X ) )
% 0.26/0.47 & ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Z )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Z ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Y ) ) )
% 0.26/0.47 | ( X = Y )
% 0.26/0.47 | ~ ! [Bound_variable_1218: $i] :
% 0.26/0.47 ( ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ Y @ Bound_variable_1218 ) )
% 0.26/0.47 | ~ ! [S: $i > $i > $o] :
% 0.26/0.47 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( S @ X @ Bound_variable_1218 ) ) )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 0.26/0.47 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1522 @ Y @ X )
% 0.26/0.47 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 0.26/0.47 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 0.26/0.47 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 0.26/0.47 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 0.26/0.47 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 0.26/0.47 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 0.26/0.47 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 0.26/0.47 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(locally_confluent,conjecture,
% 0.26/0.47 ( lconfl
% 0.26/0.47 = ( ^ [R: $i > $i > $o] :
% 0.26/0.47 ! [X: $i,Y: $i,Z: $i] :
% 0.26/0.47 ( ( ( R @ X @ Z )
% 0.26/0.47 & ( R @ X @ Y ) )
% 0.26/0.47 => ( join @ R @ Z @ Y ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 ------------------------
% 1.84/1.39 ---- Embedded in THF ---
% 1.84/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.84/1.39 %%% Generated on Tue May 05 09:36:47 EDT 2026
% 1.84/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.84/1.39 %%% Logic specification used:
% 1.84/1.39 %%% thf(spec, logic, $$dhol).
% 1.84/1.39
% 1.84/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qqkWGq3eP8/DTF2DTF20128.p
% See solution above
% 1.84/1.39 ------------------------
% 2.05/1.41 ---- Cleaned THF ---
% 2.05/1.41 thf(unsorted_type,type,
% 2.05/1.41 unsorted: $tType ).
% 2.05/1.41
% 2.05/1.41 thf(subrel_decl,type,
% 2.05/1.41 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(inv_decl,type,
% 2.05/1.41 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(idem_decl,type,
% 2.05/1.41 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(infl_decl,type,
% 2.05/1.41 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_decl,type,
% 2.05/1.41 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(refl_decl,type,
% 2.05/1.41 refl: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(irrefl_decl,type,
% 2.05/1.41 irrefl: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(rc_decl,type,
% 2.05/1.41 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(symm_decl,type,
% 2.05/1.41 symm: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(antisymm_decl,type,
% 2.05/1.41 antisymm: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(asymm_decl,type,
% 2.05/1.41 asymm: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(sc_decl,type,
% 2.05/1.41 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(trans_decl,type,
% 2.05/1.41 trans: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(tc_decl,type,
% 2.05/1.41 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(trc_decl,type,
% 2.05/1.41 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(trsc_decl,type,
% 2.05/1.41 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(po_decl,type,
% 2.05/1.41 po: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(so_decl,type,
% 2.05/1.41 so: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(total_decl,type,
% 2.05/1.41 total: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(term_decl,type,
% 2.05/1.41 term: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(ind_decl,type,
% 2.05/1.41 ind: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(innf_decl,type,
% 2.05/1.41 innf: ( $i > $i > $o ) > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(nfof_decl,type,
% 2.05/1.41 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(norm_decl,type,
% 2.05/1.41 norm: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(join_decl,type,
% 2.05/1.41 join: ( $i > $i > $o ) > $i > $i > $o ).
% 2.05/1.41
% 2.05/1.41 thf(lconfl_decl,type,
% 2.05/1.41 lconfl: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(sconfl_decl,type,
% 2.05/1.41 sconfl: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(confl_decl,type,
% 2.05/1.41 confl: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(cr_decl,type,
% 2.05/1.41 cr: ( $i > $i > $o ) > $o ).
% 2.05/1.41
% 2.05/1.41 thf(d_unsorted_type,type,
% 2.05/1.41 d_unsorted: $tType ).
% 2.05/1.41
% 2.05/1.41 thf(d2unsorted_decl,type,
% 2.05/1.41 d2unsorted: d_unsorted > $i ).
% 2.05/1.41
% 2.05/1.41 thf(d_unsorted_0_decl,type,
% 2.05/1.41 d_unsorted_0: d_unsorted ).
% 2.05/1.41
% 2.05/1.41 thf(sev441_1,axiom,
% 2.05/1.41 ( ! [U: $i] :
% 2.05/1.41 ? [DU: d_unsorted] :
% 2.05/1.41 ( U
% 2.05/1.41 = ( d2unsorted @ DU ) )
% 2.05/1.41 & ! [DU: d_unsorted] : ( DU = d_unsorted_0 )
% 2.05/1.41 & ! [DU1: d_unsorted,DU2: d_unsorted] :
% 2.05/1.41 ( ( ( d2unsorted @ DU1 )
% 2.05/1.41 = ( d2unsorted @ DU2 ) )
% 2.05/1.41 => ( DU1 = DU2 ) )
% 2.05/1.41 & ( subrel
% 2.05/1.41 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ( S @ X @ Y ) ) ) )
% 2.05/1.41 & ( inv
% 2.05/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) )
% 2.05/1.41 & ( idem
% 2.05/1.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 2.05/1.41 ! [R: $i > $i > $o] :
% 2.05/1.41 ( ( F @ R )
% 2.05/1.41 = ( F @ ( F @ R ) ) ) ) )
% 2.05/1.41 & ( infl
% 2.05/1.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 2.05/1.41 ! [R: $i > $i > $o,X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ( F @ R @ X @ Y ) ) ) )
% 2.05/1.41 & ( mono
% 2.05/1.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 2.05/1.41 ! [R: $i > $i > $o,S: $i > $i > $o,Bound_variable_510: $i,Bound_variable_512: $i] :
% 2.05/1.41 ( ~ ! [X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ( S @ X @ Y ) )
% 2.05/1.41 | ~ ( F @ R @ Bound_variable_510 @ Bound_variable_512 )
% 2.05/1.41 | ( F @ S @ Bound_variable_510 @ Bound_variable_512 ) ) ) )
% 2.05/1.41 & ( refl
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i] : ( R @ X @ X ) ) )
% 2.05/1.41 & ( irrefl
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i] :
% 2.05/1.41 ~ ( R @ X @ X ) ) )
% 2.05/1.41 & ( rc
% 2.05/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.05/1.41 ( ( X = Y )
% 2.05/1.41 | ( R @ X @ Y ) ) ) )
% 2.05/1.41 & ( symm
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ( R @ Y @ X ) ) ) )
% 2.05/1.41 & ( antisymm
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ~ ( R @ Y @ X )
% 2.05/1.41 | ( X = Y ) ) ) )
% 2.05/1.41 & ( asymm
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ~ ( R @ Y @ X ) ) ) )
% 2.05/1.41 & ( sc
% 2.05/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.05/1.41 ( ( R @ Y @ X )
% 2.05/1.41 | ( R @ X @ Y ) ) ) )
% 2.05/1.41 & ( trans
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i,Z: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ~ ( R @ Y @ Z )
% 2.05/1.41 | ( R @ X @ Z ) ) ) )
% 2.05/1.41 & ( tc
% 2.05/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.05/1.41 ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Y ) ) ) )
% 2.05/1.41 & ( trc
% 2.05/1.41 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 2.05/1.41 ( ( Flatten_var_0 = Flatten_var_1 )
% 2.05/1.41 | ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 2.05/1.41 & ( trsc
% 2.05/1.41 = ( ^ [R: $i > $i > $o,Flatten_var_0: $i,Flatten_var_1: $i] :
% 2.05/1.41 ( ( Flatten_var_0 = Flatten_var_1 )
% 2.05/1.41 | ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Flatten_var_1 @ Flatten_var_0 ) )
% 2.05/1.41 | ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Flatten_var_0 @ Flatten_var_1 ) ) ) ) )
% 2.05/1.41 & ( po
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ( ! [X: $i] : ( R @ X @ X )
% 2.05/1.41 & ! [X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ~ ( R @ Y @ X )
% 2.05/1.41 | ( X = Y ) )
% 2.05/1.41 & ! [X: $i,Y: $i,Z: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ~ ( R @ Y @ Z )
% 2.05/1.41 | ( R @ X @ Z ) ) ) ) )
% 2.05/1.41 & ( so
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ( ! [X: $i,Y: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ~ ( R @ Y @ X ) )
% 2.05/1.41 & ! [X: $i,Y: $i,Z: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Y )
% 2.05/1.41 | ~ ( R @ Y @ Z )
% 2.05/1.41 | ( R @ X @ Z ) ) ) ) )
% 2.05/1.41 & ( total
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i] :
% 2.05/1.41 ( ( X = Y )
% 2.05/1.41 | ( R @ X @ Y )
% 2.05/1.41 | ( R @ Y @ X ) ) ) )
% 2.05/1.41 & ( term
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [A: $i > $o,Bound_variable_862: $i] :
% 2.05/1.41 ( ~ ( A @ Bound_variable_862 )
% 2.05/1.41 | ~ ! [X: $i] :
% 2.05/1.41 ( ~ ( A @ X )
% 2.05/1.41 | ~ ! [Y: $i] :
% 2.05/1.41 ( ~ ( A @ Y )
% 2.05/1.41 | ~ ( R @ X @ Y ) ) ) ) ) )
% 2.05/1.41 & ( ind
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [P: $i > $o,Bound_variable_917: $i] :
% 2.05/1.41 ( ~ ! [X: $i] :
% 2.05/1.41 ( ~ ! [Y: $i] :
% 2.05/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Y ) )
% 2.05/1.41 | ( P @ Y ) )
% 2.05/1.41 | ( P @ X ) )
% 2.05/1.41 | ( P @ Bound_variable_917 ) ) ) )
% 2.05/1.41 & ( innf
% 2.05/1.41 = ( ^ [R: $i > $i > $o,X: $i] :
% 2.05/1.41 ! [Y: $i] :
% 2.05/1.41 ~ ( R @ X @ Y ) ) )
% 2.05/1.41 & ( nfof
% 2.05/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.05/1.41 ( ( ( X = Y )
% 2.05/1.41 | ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ X ) ) )
% 2.05/1.41 & ! [Bound_variable_985: $i] :
% 2.05/1.41 ~ ( R @ X @ Bound_variable_985 ) ) ) )
% 2.05/1.41 & ( norm
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Bound_variable_1075: $i] :
% 2.05/1.41 ( ~ ( R @ X @ Bound_variable_1075 )
% 2.05/1.41 | ~ ! [Bound_variable_1049: $i] :
% 2.05/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Bound_variable_1049 ) )
% 2.05/1.41 | ~ ! [Bound_variable_985: $i] :
% 2.05/1.41 ~ ( R @ Bound_variable_1049 @ Bound_variable_985 ) ) ) ) )
% 2.05/1.41 & ( join
% 2.05/1.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 2.05/1.41 ~ ( ( X != Y )
% 2.05/1.41 & ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ X ) )
% 2.05/1.41 & ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Y ) )
% 2.05/1.41 & ! [Bound_variable_1218: $i] :
% 2.05/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.05/1.41 | ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Bound_variable_1218 ) ) ) ) ) )
% 2.05/1.41 & ( lconfl
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i,Z: $i,Bound_variable_1293: $i > $i > $o,Bound_variable_1309: $i > $i > $o] :
% 2.05/1.41 ( ~ ( R @ X @ Z )
% 2.05/1.41 | ~ ( R @ X @ Y )
% 2.05/1.41 | ( Y = Z )
% 2.05/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.05/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.05/1.41 | ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Z @ Bound_variable_1218 ) ) )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1293 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( Bound_variable_1293 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1293 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1293 @ Y @ Z )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1309 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( Bound_variable_1309 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1309 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1309 @ Z @ Y ) ) ) )
% 2.05/1.41 & ( sconfl
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i,Z: $i,Bound_variable_1371: $i > $i > $o,Bound_variable_1387: $i > $i > $o] :
% 2.05/1.41 ( ~ ( R @ X @ Z )
% 2.05/1.41 | ( ( X != Y )
% 2.05/1.41 & ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1347: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1347 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1347 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Y ) ) )
% 2.05/1.41 | ( Y = Z )
% 2.05/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.05/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.05/1.41 | ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Z @ Bound_variable_1218 ) ) )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1371 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( Bound_variable_1371 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1371 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1371 @ Y @ Z )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1387 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( Bound_variable_1387 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1387 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1387 @ Z @ Y ) ) ) )
% 2.05/1.41 & ( confl
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i,Z: $i,Bound_variable_1444: $i > $i > $o,Bound_variable_1460: $i > $i > $o] :
% 2.05/1.41 ( ( ( X != Z )
% 2.05/1.41 & ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Z ) ) )
% 2.05/1.41 | ( ( X != Y )
% 2.05/1.41 & ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1422: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1422 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1422 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Y ) ) )
% 2.05/1.41 | ( Y = Z )
% 2.05/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.05/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.05/1.41 | ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Z @ Bound_variable_1218 ) ) )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1444 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( Bound_variable_1444 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1444 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1444 @ Y @ Z )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1460 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( Bound_variable_1460 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1460 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1460 @ Z @ Y ) ) ) )
% 2.05/1.41 & ( cr
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i,Bound_variable_1522: $i > $i > $o,Bound_variable_1538: $i > $i > $o] :
% 2.05/1.41 ( ( ( X != Y )
% 2.05/1.41 & ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ X ) )
% 2.05/1.41 & ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Z: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Z )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Z ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Y ) ) )
% 2.05/1.41 | ( X = Y )
% 2.05/1.41 | ~ ! [Bound_variable_1218: $i] :
% 2.05/1.41 ( ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ Y @ Bound_variable_1218 ) )
% 2.05/1.41 | ~ ! [S: $i > $i > $o] :
% 2.05/1.41 ( ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( S @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( S @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( S @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( S @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( S @ X @ Bound_variable_1218 ) ) )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1125: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1522 @ Bound_variable_674 @ Bound_variable_1125 )
% 2.05/1.41 | ( Bound_variable_1522 @ Bound_variable_672 @ Bound_variable_1125 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1522 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1522 @ Y @ X )
% 2.05/1.41 | ~ ! [Bound_variable_672: $i,Bound_variable_674: $i,Bound_variable_1106: $i] :
% 2.05/1.41 ( ~ ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_674 )
% 2.05/1.41 | ~ ( Bound_variable_1538 @ Bound_variable_674 @ Bound_variable_1106 )
% 2.05/1.41 | ( Bound_variable_1538 @ Bound_variable_672 @ Bound_variable_1106 ) )
% 2.05/1.41 | ~ ! [Bound_variable_661: $i,Bound_variable_663: $i] :
% 2.05/1.41 ( ~ ( R @ Bound_variable_661 @ Bound_variable_663 )
% 2.05/1.41 | ( Bound_variable_1538 @ Bound_variable_661 @ Bound_variable_663 ) )
% 2.05/1.41 | ( Bound_variable_1538 @ X @ Y ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(locally_confluent,conjecture,
% 2.05/1.41 ( lconfl
% 2.05/1.41 = ( ^ [R: $i > $i > $o] :
% 2.05/1.41 ! [X: $i,Y: $i,Z: $i] :
% 2.05/1.41 ( ( ( R @ X @ Z )
% 2.05/1.41 & ( R @ X @ Y ) )
% 2.05/1.41 => ( join @ R @ Z @ Y ) ) ) ) ).
% 2.05/1.41 ------------------------
% 2.05/1.43 % (20228)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_20128 for (2999ds/4Mi)
% 2.05/1.43 % (20232)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_20128 for (2999ds/275Mi)
% 2.05/1.43 % (20228)Instruction limit reached!
% 2.05/1.43 % (20228)------------------------------
% 2.05/1.43 % (20228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.43 % (20228)Termination reason: Unknown
% 2.05/1.43 % (20228)Termination phase: shuffling
% 2.05/1.43
% 2.05/1.43 % (20228)Memory used [KB]: 1151
% 2.05/1.43 % (20228)Time elapsed: 0.003 s
% 2.05/1.43 % (20228)Instructions burned: 5 (million)
% 2.05/1.43 % (20228)------------------------------
% 2.05/1.43 % (20228)------------------------------
% 2.05/1.44 % (20227)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/183Mi)
% 2.05/1.44 % (20229)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_20128 for (2999ds/27Mi)
% 2.05/1.44 % (20230)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/2Mi)
% 2.05/1.44 % (20231)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_20128 for (2999ds/2Mi)
% 2.05/1.44 % (20233)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/18Mi)
% 2.05/1.44 % (20230)Instruction limit reached!
% 2.05/1.44 % (20230)------------------------------
% 2.05/1.44 % (20230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.44 % (20230)Termination reason: Unknown
% 2.05/1.44 % (20230)Termination phase: shuffling
% 2.05/1.44
% 2.05/1.44 % (20230)Memory used [KB]: 1023
% 2.05/1.44 % (20230)Time elapsed: 0.003 s
% 2.05/1.44 % (20230)Instructions burned: 2 (million)
% 2.05/1.44 % (20230)------------------------------
% 2.05/1.44 % (20230)------------------------------
% 2.05/1.44 % (20231)Instruction limit reached!
% 2.05/1.44 % (20231)------------------------------
% 2.05/1.44 % (20231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.44 % (20231)Termination reason: Unknown
% 2.05/1.44 % (20231)Termination phase: shuffling
% 2.05/1.44 % (20232)Refutation not found, incomplete strategy
% 2.05/1.44 % (20232)------------------------------
% 2.05/1.44 % (20232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.44 % (20232)Termination reason: Refutation not found, incomplete strategy
% 2.05/1.44
% 2.05/1.44
% 2.05/1.44 % (20232)Memory used [KB]: 6012
% 2.05/1.44 % (20232)Time elapsed: 0.010 s
% 2.05/1.44 % (20232)Instructions burned: 30 (million)
% 2.05/1.44 % (20232)------------------------------
% 2.05/1.44 % (20232)------------------------------
% 2.05/1.44
% 2.05/1.44 % (20231)Memory used [KB]: 1151
% 2.05/1.44 % (20231)Time elapsed: 0.004 s
% 2.05/1.44 % (20231)Instructions burned: 3 (million)
% 2.05/1.44 % (20231)------------------------------
% 2.05/1.44 % (20231)------------------------------
% 2.05/1.44 % (20234)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/3Mi)
% 2.05/1.44 % (20234)Instruction limit reached!
% 2.05/1.44 % (20234)------------------------------
% 2.05/1.44 % (20234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.44 % (20234)Termination reason: Unknown
% 2.05/1.44 % (20234)Termination phase: shuffling
% 2.05/1.44
% 2.05/1.44 % (20234)Memory used [KB]: 1151
% 2.05/1.44 % (20234)Time elapsed: 0.002 s
% 2.05/1.44 % (20234)Instructions burned: 3 (million)
% 2.05/1.44 % (20234)------------------------------
% 2.05/1.44 % (20234)------------------------------
% 2.05/1.45 % (20233)Instruction limit reached!
% 2.05/1.45 % (20233)------------------------------
% 2.05/1.45 % (20233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.45 % (20233)Termination reason: Unknown
% 2.05/1.45 % (20233)Termination phase: Property scanning
% 2.05/1.45
% 2.05/1.45 % (20233)Memory used [KB]: 1407
% 2.05/1.45 % (20233)Time elapsed: 0.012 s
% 2.05/1.45 % (20233)Instructions burned: 20 (million)
% 2.05/1.45 % (20233)------------------------------
% 2.05/1.45 % (20233)------------------------------
% 2.05/1.45 % (20237)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_20128 for (2999ds/3Mi)
% 2.05/1.45 % (20238)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_20128 for (2999ds/1041Mi)
% 2.05/1.45 % (20229)Instruction limit reached!
% 2.05/1.45 % (20229)------------------------------
% 2.05/1.45 % (20229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.45 % (20229)Termination reason: Unknown
% 2.05/1.45 % (20229)Termination phase: Preprocessing 3
% 2.05/1.45
% 2.05/1.45 % (20237)Instruction limit reached!
% 2.05/1.45 % (20237)------------------------------
% 2.05/1.45 % (20237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.45 % (20229)Memory used [KB]: 1535
% 2.05/1.45 % (20229)Time elapsed: 0.016 s
% 2.05/1.45 % (20229)Instructions burned: 28 (million)
% 2.05/1.45 % (20229)------------------------------
% 2.05/1.45 % (20229)------------------------------
% 2.05/1.45 % (20237)Termination reason: Unknown
% 2.05/1.45 % (20237)Termination phase: shuffling
% 2.05/1.45
% 2.05/1.45 % (20237)Memory used [KB]: 1151
% 2.05/1.45 % (20237)Time elapsed: 0.003 s
% 2.05/1.45 % (20237)Instructions burned: 4 (million)
% 2.05/1.45 % (20237)------------------------------
% 2.05/1.45 % (20237)------------------------------
% 2.05/1.46 % (20235)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_20128 for (2999ds/37Mi)
% 2.05/1.46 % (20236)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_20128 for (2999ds/15Mi)
% 2.05/1.46 % (20241)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_20128 for (2999ds/3Mi)
% 2.05/1.46 % (20241)Instruction limit reached!
% 2.05/1.46 % (20241)------------------------------
% 2.05/1.46 % (20241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.46 % (20241)Termination reason: Unknown
% 2.05/1.46 % (20241)Termination phase: shuffling
% 2.05/1.46
% 2.05/1.46 % (20241)Memory used [KB]: 1151
% 2.05/1.46 % (20241)Time elapsed: 0.002 s
% 2.05/1.46 % (20241)Instructions burned: 4 (million)
% 2.05/1.46 % (20241)------------------------------
% 2.05/1.46 % (20241)------------------------------
% 2.05/1.47 % (20236)Instruction limit reached!
% 2.05/1.47 % (20236)------------------------------
% 2.05/1.47 % (20236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.47 % (20236)Termination reason: Unknown
% 2.05/1.47 % (20236)Termination phase: shuffling
% 2.05/1.47
% 2.05/1.47 % (20236)Memory used [KB]: 1407
% 2.05/1.47 % (20236)Time elapsed: 0.010 s
% 2.05/1.47 % (20236)Instructions burned: 16 (million)
% 2.05/1.47 % (20236)------------------------------
% 2.05/1.47 % (20236)------------------------------
% 2.05/1.47 % (20239)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/7Mi)
% 2.05/1.47 % (20240)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/16Mi)
% 2.05/1.47 % (20239)Instruction limit reached!
% 2.05/1.47 % (20239)------------------------------
% 2.05/1.47 % (20239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.47 % (20239)Termination reason: Unknown
% 2.05/1.47 % (20239)Termination phase: shuffling
% 2.05/1.47
% 2.05/1.47 % (20239)Memory used [KB]: 1279
% 2.05/1.47 % (20239)Time elapsed: 0.006 s
% 2.05/1.47 % (20239)Instructions burned: 8 (million)
% 2.05/1.47 % (20239)------------------------------
% 2.05/1.47 % (20239)------------------------------
% 2.05/1.47 % (20242)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_20128 for (2999ds/3Mi)
% 2.05/1.48 % (20235)Instruction limit reached!
% 2.05/1.48 % (20235)------------------------------
% 2.05/1.48 % (20235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.48 % (20235)Termination reason: Unknown
% 2.05/1.48 % (20235)Termination phase: Saturation
% 2.05/1.48
% 2.05/1.48 % (20235)Memory used [KB]: 5884
% 2.05/1.48 % (20235)Time elapsed: 0.020 s
% 2.05/1.48 % (20235)Instructions burned: 37 (million)
% 2.05/1.48 % (20235)------------------------------
% 2.05/1.48 % (20235)------------------------------
% 2.05/1.48 % (20242)Instruction limit reached!
% 2.05/1.48 % (20242)------------------------------
% 2.05/1.48 % (20242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.48 % (20242)Termination reason: Unknown
% 2.05/1.48 % (20242)Termination phase: shuffling
% 2.05/1.48
% 2.05/1.48 % (20242)Memory used [KB]: 1151
% 2.05/1.48 % (20242)Time elapsed: 0.003 s
% 2.05/1.48 % (20242)Instructions burned: 4 (million)
% 2.05/1.48 % (20242)------------------------------
% 2.05/1.48 % (20242)------------------------------
% 2.05/1.48 % (20240)Instruction limit reached!
% 2.05/1.48 % (20240)------------------------------
% 2.05/1.48 % (20240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.48 % (20240)Termination reason: Unknown
% 2.05/1.48 % (20240)Termination phase: shuffling
% 2.05/1.48
% 2.05/1.48 % (20240)Memory used [KB]: 1407
% 2.05/1.48 % (20240)Time elapsed: 0.010 s
% 2.05/1.48 % (20240)Instructions burned: 16 (million)
% 2.05/1.48 % (20240)------------------------------
% 2.05/1.48 % (20240)------------------------------
% 2.05/1.48 % (20243)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/7Mi)
% 2.05/1.49 % (20245)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/4Mi)
% 2.05/1.49 % (20245)Instruction limit reached!
% 2.05/1.49 % (20245)------------------------------
% 2.05/1.49 % (20245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.49 % (20245)Termination reason: Unknown
% 2.05/1.49 % (20245)Termination phase: shuffling
% 2.05/1.49
% 2.05/1.49 % (20245)Memory used [KB]: 1151
% 2.05/1.49 % (20245)Time elapsed: 0.003 s
% 2.05/1.49 % (20245)Instructions burned: 4 (million)
% 2.05/1.49 % (20245)------------------------------
% 2.05/1.49 % (20245)------------------------------
% 2.05/1.49 % (20243)Instruction limit reached!
% 2.05/1.49 % (20243)------------------------------
% 2.05/1.49 % (20243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.49 % (20243)Termination reason: Unknown
% 2.05/1.49 % (20243)Termination phase: shuffling
% 2.05/1.49
% 2.05/1.49 % (20243)Memory used [KB]: 1279
% 2.05/1.49 % (20243)Time elapsed: 0.006 s
% 2.05/1.49 % (20243)Instructions burned: 8 (million)
% 2.05/1.49 % (20243)------------------------------
% 2.05/1.49 % (20243)------------------------------
% 2.05/1.49 % (20244)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/3Mi)
% 2.05/1.49 % (20244)Instruction limit reached!
% 2.05/1.49 % (20244)------------------------------
% 2.05/1.49 % (20244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.49 % (20244)Termination reason: Unknown
% 2.05/1.49 % (20244)Termination phase: shuffling
% 2.05/1.49
% 2.05/1.49 % (20244)Memory used [KB]: 1151
% 2.05/1.49 % (20244)Time elapsed: 0.004 s
% 2.05/1.49 % (20244)Instructions burned: 4 (million)
% 2.05/1.49 % (20244)------------------------------
% 2.05/1.49 % (20244)------------------------------
% 2.05/1.49 % (20246)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/18Mi)
% 2.05/1.49 % (20247)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/710Mi)
% 2.06/1.50 % (20248)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/6Mi)
% 2.06/1.50 % (20248)Instruction limit reached!
% 2.06/1.50 % (20248)------------------------------
% 2.06/1.50 % (20248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.50 % (20248)Termination reason: Unknown
% 2.06/1.50 % (20248)Termination phase: shuffling
% 2.06/1.50
% 2.06/1.50 % (20248)Memory used [KB]: 1279
% 2.06/1.50 % (20248)Time elapsed: 0.004 s
% 2.06/1.50 % (20248)Instructions burned: 7 (million)
% 2.06/1.50 % (20248)------------------------------
% 2.06/1.50 % (20248)------------------------------
% 2.06/1.50 % (20249)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_20128 for (2999ds/902Mi)
% 2.06/1.50 % (20246)Instruction limit reached!
% 2.06/1.50 % (20246)------------------------------
% 2.06/1.50 % (20246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.50 % (20246)Termination reason: Unknown
% 2.06/1.50 % (20246)Termination phase: Property scanning
% 2.06/1.50
% 2.06/1.50 % (20246)Memory used [KB]: 1407
% 2.06/1.50 % (20246)Time elapsed: 0.012 s
% 2.06/1.50 % (20246)Instructions burned: 19 (million)
% 2.06/1.50 % (20246)------------------------------
% 2.06/1.50 % (20246)------------------------------
% 2.06/1.51 % (20250)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_20128 for (2999ds/21Mi)
% 2.06/1.51 % (20251)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/5Mi)
% 2.06/1.51 % (20251)Instruction limit reached!
% 2.06/1.51 % (20251)------------------------------
% 2.06/1.51 % (20251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.51 % (20251)Termination reason: Unknown
% 2.06/1.51 % (20251)Termination phase: shuffling
% 2.06/1.51
% 2.06/1.51 % (20251)Memory used [KB]: 1279
% 2.06/1.51 % (20251)Time elapsed: 0.004 s
% 2.06/1.51 % (20251)Instructions burned: 8 (million)
% 2.06/1.51 % (20251)------------------------------
% 2.06/1.51 % (20251)------------------------------
% 2.06/1.52 % (20249)Refutation not found, incomplete strategy
% 2.06/1.52 % (20249)------------------------------
% 2.06/1.52 % (20249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.52 % (20249)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.52
% 2.06/1.52
% 2.06/1.52 % (20249)Memory used [KB]: 6012
% 2.06/1.52 % (20249)Time elapsed: 0.015 s
% 2.06/1.52 % (20249)Instructions burned: 48 (million)
% 2.06/1.52 % (20249)------------------------------
% 2.06/1.52 % (20249)------------------------------
% 2.06/1.52 % (20250)Instruction limit reached!
% 2.06/1.52 % (20250)------------------------------
% 2.06/1.52 % (20250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.52 % (20250)Termination reason: Unknown
% 2.06/1.52 % (20250)Termination phase: Property scanning
% 2.06/1.52
% 2.06/1.52 % (20250)Memory used [KB]: 1535
% 2.06/1.52 % (20250)Time elapsed: 0.012 s
% 2.06/1.52 % (20250)Instructions burned: 21 (million)
% 2.06/1.52 % (20250)------------------------------
% 2.06/1.52 % (20250)------------------------------
% 2.06/1.52 % (20227)Instruction limit reached!
% 2.06/1.52 % (20227)------------------------------
% 2.06/1.52 % (20227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.52 % (20227)Termination reason: Unknown
% 2.06/1.52 % (20227)Termination phase: Saturation
% 2.06/1.52
% 2.06/1.52 % (20227)Memory used [KB]: 6524
% 2.06/1.52 % (20227)Time elapsed: 0.083 s
% 2.06/1.52 % (20227)Instructions burned: 186 (million)
% 2.06/1.52 % (20227)------------------------------
% 2.06/1.52 % (20227)------------------------------
% 2.06/1.52 % (20252)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_20128 for (2999ds/6Mi)
% 2.06/1.52 % (20253)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/377Mi)
% 2.06/1.52 % (20252)Instruction limit reached!
% 2.06/1.52 % (20252)------------------------------
% 2.06/1.52 % (20252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.52 % (20252)Termination reason: Unknown
% 2.06/1.52 % (20252)Termination phase: shuffling
% 2.06/1.52
% 2.06/1.52 % (20252)Memory used [KB]: 1279
% 2.06/1.52 % (20252)Time elapsed: 0.006 s
% 2.06/1.53 % (20252)Instructions burned: 7 (million)
% 2.06/1.53 % (20252)------------------------------
% 2.06/1.53 % (20252)------------------------------
% 2.06/1.53 % (20254)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_20128 for (2999ds/779Mi)
% 2.06/1.53 % (20256)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/879Mi)
% 2.06/1.53 % (20255)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_20128 for (2999ds/19Mi)
% 2.06/1.54 % (20255)Instruction limit reached!
% 2.06/1.54 % (20255)------------------------------
% 2.06/1.54 % (20255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.54 % (20255)Termination reason: Unknown
% 2.06/1.54 % (20255)Termination phase: Property scanning
% 2.06/1.54
% 2.06/1.54 % (20255)Memory used [KB]: 1407
% 2.06/1.54 % (20255)Time elapsed: 0.008 s
% 2.06/1.54 % (20255)Instructions burned: 19 (million)
% 2.06/1.54 % (20255)------------------------------
% 2.06/1.54 % (20255)------------------------------
% 2.06/1.54 % (20257)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20128 for (2999ds/17Mi)
% 2.06/1.55 % (20257)Instruction limit reached!
% 2.06/1.55 % (20257)------------------------------
% 2.06/1.55 % (20257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.55 % (20257)Termination reason: Unknown
% 2.06/1.55 % (20257)Termination phase: Property scanning
% 2.06/1.55
% 2.06/1.55 % (20257)Memory used [KB]: 1535
% 2.06/1.55 % (20257)Time elapsed: 0.008 s
% 2.06/1.55 % (20257)Instructions burned: 19 (million)
% 2.06/1.55 % (20257)------------------------------
% 2.06/1.55 % (20257)------------------------------
% 2.06/1.55 % (20258)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20128 for (2998ds/3Mi)
% 2.06/1.55 % (20258)Instruction limit reached!
% 2.06/1.55 % (20258)------------------------------
% 2.06/1.55 % (20258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.55 % (20258)Termination reason: Unknown
% 2.06/1.55 % (20258)Termination phase: shuffling
% 2.06/1.55
% 2.06/1.55 % (20258)Memory used [KB]: 1151
% 2.06/1.55 % (20258)Time elapsed: 0.002 s
% 2.06/1.55 % (20258)Instructions burned: 3 (million)
% 2.06/1.55 % (20258)------------------------------
% 2.06/1.55 % (20258)------------------------------
% 2.06/1.56 % (20259)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20128 for (2998ds/30Mi)
% 2.06/1.56 % (20260)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20128 for (2998ds/127Mi)
% 2.06/1.57 % (20259)Instruction limit reached!
% 2.06/1.57 % (20259)------------------------------
% 2.06/1.57 % (20259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.57 % (20259)Termination reason: Unknown
% 2.06/1.57 % (20259)Termination phase: Property scanning
% 2.06/1.57
% 2.06/1.57 % (20259)Memory used [KB]: 1535
% 2.06/1.57 % (20259)Time elapsed: 0.010 s
% 2.06/1.57 % (20259)Instructions burned: 32 (million)
% 2.06/1.57 % (20259)------------------------------
% 2.06/1.57 % (20259)------------------------------
% 2.06/1.58 % (20261)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20128 for (2998ds/100Mi)
% 2.06/1.60 % (20260)Instruction limit reached!
% 2.06/1.60 % (20260)------------------------------
% 2.06/1.60 % (20260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.60 % (20260)Termination reason: Unknown
% 2.06/1.60 % (20260)Termination phase: Saturation
% 2.06/1.60
% 2.06/1.60 % (20260)Memory used [KB]: 6140
% 2.06/1.60 % (20260)Time elapsed: 0.037 s
% 2.06/1.60 % (20260)Instructions burned: 128 (million)
% 2.06/1.60 % (20260)------------------------------
% 2.06/1.60 % (20260)------------------------------
% 2.06/1.61 % (20261)Instruction limit reached!
% 2.06/1.61 % (20261)------------------------------
% 2.06/1.61 % (20261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.61 % (20261)Termination reason: Unknown
% 2.06/1.61 % (20261)Termination phase: Saturation
% 2.06/1.61
% 2.06/1.61 % (20261)Memory used [KB]: 6012
% 2.06/1.61 % (20261)Time elapsed: 0.028 s
% 2.06/1.61 % (20261)Instructions burned: 102 (million)
% 2.06/1.61 % (20261)------------------------------
% 2.06/1.61 % (20261)------------------------------
% 2.06/1.61 % (20262)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_20128 for (2998ds/3Mi)
% 2.06/1.61 % (20262)Instruction limit reached!
% 2.06/1.61 % (20262)------------------------------
% 2.06/1.61 % (20262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.61 % (20262)Termination reason: Unknown
% 2.06/1.61 % (20262)Termination phase: shuffling
% 2.06/1.61
% 2.06/1.61 % (20262)Memory used [KB]: 1279
% 2.06/1.61 % (20262)Time elapsed: 0.003 s
% 2.06/1.61 % (20262)Instructions burned: 6 (million)
% 2.06/1.61 % (20262)------------------------------
% 2.06/1.61 % (20262)------------------------------
% 2.06/1.62 % (20263)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_20128 for (2998ds/20Mi)
% 2.06/1.62 % (20264)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_20128 for (2998ds/86Mi)
% 2.06/1.62 % (20253)Instruction limit reached!
% 2.06/1.62 % (20253)------------------------------
% 2.06/1.62 % (20253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.62 % (20253)Termination reason: Unknown
% 2.06/1.62 % (20253)Termination phase: Saturation
% 2.06/1.62
% 2.06/1.62 % (20253)Memory used [KB]: 7291
% 2.06/1.62 % (20253)Time elapsed: 0.101 s
% 2.06/1.62 % (20253)Instructions burned: 379 (million)
% 2.06/1.62 % (20253)------------------------------
% 2.06/1.62 % (20253)------------------------------
% 2.06/1.62 % (20263)Instruction limit reached!
% 2.06/1.62 % (20263)------------------------------
% 2.06/1.62 % (20263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.62 % (20263)Termination reason: Unknown
% 2.06/1.62 % (20263)Termination phase: Property scanning
% 2.06/1.62
% 2.06/1.62 % (20263)Memory used [KB]: 1535
% 2.06/1.62 % (20263)Time elapsed: 0.007 s
% 2.06/1.62 % (20263)Instructions burned: 21 (million)
% 2.06/1.62 % (20263)------------------------------
% 2.06/1.62 % (20263)------------------------------
% 2.06/1.63 % (20265)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_20128 for (2998ds/107Mi)
% 2.06/1.63 % (20266)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_20128 for (2998ds/39Mi)
% 2.06/1.64 % (20264)Instruction limit reached!
% 2.06/1.64 % (20264)------------------------------
% 2.06/1.64 % (20264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.64 % (20264)Termination reason: Unknown
% 2.06/1.64 % (20264)Termination phase: Saturation
% 2.06/1.64
% 2.06/1.64 % (20264)Memory used [KB]: 6140
% 2.06/1.64 % (20264)Time elapsed: 0.026 s
% 2.06/1.64 % (20264)Instructions burned: 88 (million)
% 2.06/1.64 % (20264)------------------------------
% 2.06/1.64 % (20264)------------------------------
% 2.06/1.64 % (20266)Instruction limit reached!
% 2.06/1.64 % (20266)------------------------------
% 2.06/1.64 % (20266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.64 % (20266)Termination reason: Unknown
% 2.06/1.64 % (20266)Termination phase: Saturation
% 2.06/1.64
% 2.06/1.64 % (20266)Memory used [KB]: 6012
% 2.06/1.64 % (20266)Time elapsed: 0.012 s
% 2.06/1.64 % (20266)Instructions burned: 40 (million)
% 2.06/1.64 % (20266)------------------------------
% 2.06/1.64 % (20266)------------------------------
% 2.06/1.65 % (20267)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_20128 for (2997ds/448Mi)
% 2.06/1.65 % (20268)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_20128 for (2997ds/46Mi)
% 2.06/1.66 % (20265)Instruction limit reached!
% 2.06/1.66 % (20265)------------------------------
% 2.06/1.66 % (20265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.66 % (20265)Termination reason: Unknown
% 2.06/1.66 % (20265)Termination phase: Saturation
% 2.06/1.66
% 2.06/1.66 % (20265)Memory used [KB]: 6140
% 2.06/1.66 % (20265)Time elapsed: 0.028 s
% 2.06/1.66 % (20265)Instructions burned: 107 (million)
% 2.06/1.66 % (20265)------------------------------
% 2.06/1.66 % (20265)------------------------------
% 2.06/1.66 % (20267)Refutation not found, incomplete strategy
% 2.06/1.66 % (20267)------------------------------
% 2.06/1.66 % (20267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.66 % (20267)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.66
% 2.06/1.66
% 2.06/1.66 % (20267)Memory used [KB]: 6012
% 2.06/1.66 % (20267)Time elapsed: 0.012 s
% 2.06/1.66 % (20267)Instructions burned: 36 (million)
% 2.06/1.66 % (20267)------------------------------
% 2.06/1.66 % (20267)------------------------------
% 2.06/1.67 % (20268)Instruction limit reached!
% 2.06/1.67 % (20268)------------------------------
% 2.06/1.67 % (20268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.67 % (20268)Termination reason: Unknown
% 2.06/1.67 % (20268)Termination phase: Saturation
% 2.06/1.67
% 2.06/1.67 % (20268)Memory used [KB]: 6012
% 2.06/1.67 % (20268)Time elapsed: 0.014 s
% 2.06/1.67 % (20268)Instructions burned: 47 (million)
% 2.06/1.67 % (20268)------------------------------
% 2.06/1.67 % (20268)------------------------------
% 2.06/1.67 % (20269)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_20128 for (2997ds/98Mi)
% 2.06/1.67 % (20270)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_20128 for (2997ds/507Mi)
% 2.06/1.68 % (20271)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_20128 for (2997ds/149Mi)
% 2.06/1.69 % (20269)Instruction limit reached!
% 2.06/1.69 % (20269)------------------------------
% 2.06/1.69 % (20269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.69 % (20269)Termination reason: Unknown
% 2.06/1.69 % (20269)Termination phase: Saturation
% 2.06/1.69
% 2.06/1.69 % (20269)Memory used [KB]: 1535
% 2.06/1.69 % (20269)Time elapsed: 0.025 s
% 2.06/1.69 % (20269)Instructions burned: 100 (million)
% 2.06/1.69 % (20269)------------------------------
% 2.06/1.69 % (20269)------------------------------
% 2.06/1.70 % (20247)Instruction limit reached!
% 2.06/1.70 % (20247)------------------------------
% 2.06/1.70 % (20247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.70 % (20247)Termination reason: Unknown
% 2.06/1.70 % (20247)Termination phase: Saturation
% 2.06/1.70
% 2.06/1.70 % (20247)Memory used [KB]: 8059
% 2.06/1.70 % (20247)Time elapsed: 0.204 s
% 2.06/1.70 % (20247)Instructions burned: 711 (million)
% 2.06/1.70 % (20247)------------------------------
% 2.06/1.70 % (20247)------------------------------
% 2.06/1.70 % (20272)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20128 for (2997ds/39Mi)
% 2.06/1.71 % (20273)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_20128 for (2997ds/6Mi)
% 2.06/1.71 % (20273)Instruction limit reached!
% 2.06/1.71 % (20273)------------------------------
% 2.06/1.71 % (20273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.71 % (20273)Termination reason: Unknown
% 2.06/1.71 % (20273)Termination phase: shuffling
% 2.06/1.71
% 2.06/1.71 % (20273)Memory used [KB]: 1279
% 2.06/1.71 % (20273)Time elapsed: 0.003 s
% 2.06/1.71 % (20273)Instructions burned: 7 (million)
% 2.06/1.71 % (20273)------------------------------
% 2.06/1.71 % (20273)------------------------------
% 2.06/1.71 % (20272)Instruction limit reached!
% 2.06/1.71 % (20272)------------------------------
% 2.06/1.71 % (20272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.71 % (20272)Termination reason: Unknown
% 2.06/1.71 % (20272)Termination phase: Function definition elimination
% 2.06/1.71
% 2.06/1.71 % (20272)Memory used [KB]: 1535
% 2.06/1.71 % (20272)Time elapsed: 0.011 s
% 2.06/1.71 % (20272)Instructions burned: 39 (million)
% 2.06/1.71 % (20272)------------------------------
% 2.06/1.71 % (20272)------------------------------
% 2.06/1.72 % (20274)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_20128 for (2997ds/1087Mi)
% 2.06/1.72 % (20238)Instruction limit reached!
% 2.06/1.72 % (20238)------------------------------
% 2.06/1.72 % (20238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.72 % (20238)Termination reason: Unknown
% 2.06/1.72 % (20238)Termination phase: Saturation
% 2.06/1.72
% 2.06/1.72 % (20238)Memory used [KB]: 7036
% 2.06/1.72 % (20238)Time elapsed: 0.269 s
% 2.06/1.72 % (20238)Instructions burned: 1044 (million)
% 2.06/1.72 % (20238)------------------------------
% 2.06/1.72 % (20238)------------------------------
% 2.06/1.72 % (20275)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20128 for (2997ds/47Mi)
% 2.06/1.72 % (20271)Instruction limit reached!
% 2.06/1.72 % (20271)------------------------------
% 2.06/1.72 % (20271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.72 % (20271)Termination reason: Unknown
% 2.06/1.72 % (20271)Termination phase: Saturation
% 2.06/1.72
% 2.06/1.72 % (20271)Memory used [KB]: 6396
% 2.06/1.72 % (20271)Time elapsed: 0.047 s
% 2.06/1.72 % (20271)Instructions burned: 150 (million)
% 2.06/1.72 % (20271)------------------------------
% 2.06/1.72 % (20271)------------------------------
% 2.06/1.73 % (20276)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_20128 for (2997ds/44Mi)
% 2.06/1.73 % (20275)Instruction limit reached!
% 2.06/1.73 % (20275)------------------------------
% 2.06/1.73 % (20275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.73 % (20275)Termination reason: Unknown
% 2.06/1.73 % (20275)Termination phase: Saturation
% 2.06/1.73
% 2.06/1.73 % (20275)Memory used [KB]: 6012
% 2.06/1.73 % (20275)Time elapsed: 0.013 s
% 2.06/1.73 % (20275)Instructions burned: 47 (million)
% 2.06/1.73 % (20275)------------------------------
% 2.06/1.73 % (20275)------------------------------
% 2.06/1.73 % (20277)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_20128 for (2997ds/432Mi)
% 2.06/1.74 % (20276)Refutation not found, incomplete strategy
% 2.06/1.74 % (20276)------------------------------
% 2.06/1.74 % (20276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.74 % (20276)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.74
% 2.06/1.74
% 2.06/1.74 % (20276)Memory used [KB]: 1535
% 2.06/1.74 % (20276)Time elapsed: 0.010 s
% 2.06/1.74 % (20276)Instructions burned: 32 (million)
% 2.06/1.74 % (20276)------------------------------
% 2.06/1.74 % (20276)------------------------------
% 2.06/1.74 % (20278)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20128 for (2997ds/62Mi)
% 2.06/1.75 % (20279)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_20128 for (2996ds/31Mi)
% 2.06/1.76 % (20279)Instruction limit reached!
% 2.06/1.76 % (20279)------------------------------
% 2.06/1.76 % (20279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.76 % (20279)Termination reason: Unknown
% 2.06/1.76 % (20279)Termination phase: Property scanning
% 2.06/1.76
% 2.06/1.76 % (20279)Memory used [KB]: 1535
% 2.06/1.76 % (20279)Time elapsed: 0.010 s
% 2.06/1.76 % (20279)Instructions burned: 35 (million)
% 2.06/1.76 % (20279)------------------------------
% 2.06/1.76 % (20279)------------------------------
% 2.06/1.76 % (20278)Instruction limit reached!
% 2.06/1.76 % (20278)------------------------------
% 2.06/1.76 % (20278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.76 % (20278)Termination reason: Unknown
% 2.06/1.76 % (20278)Termination phase: Saturation
% 2.06/1.76
% 2.06/1.76 % (20278)Memory used [KB]: 6396
% 2.06/1.76 % (20278)Time elapsed: 0.038 s
% 2.06/1.76 % (20278)Instructions burned: 65 (million)
% 2.06/1.76 % (20278)------------------------------
% 2.06/1.76 % (20278)------------------------------
% 2.06/1.76 % (20254)Instruction limit reached!
% 2.06/1.76 % (20254)------------------------------
% 2.06/1.76 % (20254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.76 % (20254)Termination reason: Unknown
% 2.06/1.76 % (20254)Termination phase: Saturation
% 2.06/1.76
% 2.06/1.76 % (20254)Memory used [KB]: 7164
% 2.06/1.76 % (20254)Time elapsed: 0.234 s
% 2.06/1.76 % (20254)Instructions burned: 780 (million)
% 2.06/1.76 % (20254)------------------------------
% 2.06/1.76 % (20254)------------------------------
% 2.06/1.77 % (20280)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20128 for (2996ds/96Mi)
% 2.06/1.77 % (20281)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_20128 for (2996ds/453Mi)
% 2.06/1.77 % (20282)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_20128 for (2996ds/71Mi)
% 2.06/1.79 % (20256)Instruction limit reached!
% 2.06/1.79 % (20256)------------------------------
% 2.06/1.79 % (20256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.79 % (20256)Termination reason: Unknown
% 2.06/1.79 % (20256)Termination phase: Saturation
% 2.06/1.79
% 2.06/1.79 % (20256)Memory used [KB]: 9210
% 2.06/1.79 % (20256)Time elapsed: 0.257 s
% 2.06/1.79 % (20256)Instructions burned: 881 (million)
% 2.06/1.79 % (20256)------------------------------
% 2.06/1.79 % (20256)------------------------------
% 2.06/1.79 % (20282)Instruction limit reached!
% 2.06/1.79 % (20282)------------------------------
% 2.06/1.79 % (20282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.79 % (20282)Termination reason: Unknown
% 2.06/1.79 % (20282)Termination phase: Saturation
% 2.06/1.79
% 2.06/1.79 % (20282)Memory used [KB]: 6140
% 2.06/1.79 % (20282)Time elapsed: 0.045 s
% 2.06/1.79 % (20282)Instructions burned: 73 (million)
% 2.06/1.79 % (20282)------------------------------
% 2.06/1.79 % (20282)------------------------------
% 2.06/1.79 % (20280)Instruction limit reached!
% 2.06/1.79 % (20280)------------------------------
% 2.06/1.79 % (20280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.79 % (20280)Termination reason: Unknown
% 2.06/1.79 % (20280)Termination phase: Saturation
% 2.06/1.79
% 2.06/1.79 % (20280)Memory used [KB]: 6140
% 2.06/1.79 % (20280)Time elapsed: 0.026 s
% 2.06/1.79 % (20280)Instructions burned: 99 (million)
% 2.06/1.79 % (20280)------------------------------
% 2.06/1.79 % (20280)------------------------------
% 2.06/1.80 % (20283)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20128 for (2996ds/83Mi)
% 2.06/1.80 % (20284)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20128 for (2996ds/11Mi)
% 2.06/1.80 % (20285)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_20128 for (2996ds/41Mi)
% 2.06/1.80 % (20284)Instruction limit reached!
% 2.06/1.80 % (20284)------------------------------
% 2.06/1.80 % (20284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.80 % (20284)Termination reason: Unknown
% 2.06/1.80 % (20284)Termination phase: shuffling
% 2.06/1.80
% 2.06/1.80 % (20284)Memory used [KB]: 1279
% 2.06/1.80 % (20284)Time elapsed: 0.005 s
% 2.06/1.80 % (20284)Instructions burned: 11 (million)
% 2.06/1.80 % (20284)------------------------------
% 2.06/1.80 % (20284)------------------------------
% 2.06/1.81 % (20283)Refutation not found, incomplete strategy
% 2.06/1.81 % (20283)------------------------------
% 2.06/1.81 % (20283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.81 % (20283)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.81
% 2.06/1.81
% 2.06/1.81 % (20283)Memory used [KB]: 6012
% 2.06/1.81 % (20283)Time elapsed: 0.010 s
% 2.06/1.81 % (20283)Instructions burned: 31 (million)
% 2.06/1.81 % (20283)------------------------------
% 2.06/1.81 % (20283)------------------------------
% 2.06/1.81 % (20285)Instruction limit reached!
% 2.06/1.81 % (20285)------------------------------
% 2.06/1.81 % (20285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.81 % (20285)Termination reason: Unknown
% 2.06/1.81 % (20285)Termination phase: Saturation
% 2.06/1.81
% 2.06/1.81 % (20285)Memory used [KB]: 6012
% 2.06/1.81 % (20285)Time elapsed: 0.012 s
% 2.06/1.81 % (20285)Instructions burned: 44 (million)
% 2.06/1.81 % (20285)------------------------------
% 2.06/1.81 % (20285)------------------------------
% 2.06/1.81 % (20286)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20128 for (2996ds/6Mi)
% 2.06/1.82 % (20286)Instruction limit reached!
% 2.06/1.82 % (20286)------------------------------
% 2.06/1.82 % (20286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.82 % (20286)Termination reason: Unknown
% 2.06/1.82 % (20286)Termination phase: shuffling
% 2.06/1.82
% 2.06/1.82 % (20286)Memory used [KB]: 1279
% 2.06/1.82 % (20286)Time elapsed: 0.004 s
% 2.06/1.82 % (20286)Instructions burned: 7 (million)
% 2.06/1.82 % (20286)------------------------------
% 2.06/1.82 % (20286)------------------------------
% 2.06/1.82 % (20287)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20128 for (2996ds/150Mi)
% 2.06/1.82 % (20288)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20128 for (2996ds/343Mi)
% 2.06/1.83 % (20270)Instruction limit reached!
% 2.06/1.83 % (20270)------------------------------
% 2.06/1.83 % (20270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.83 % (20270)Termination reason: Unknown
% 2.06/1.83 % (20270)Termination phase: Saturation
% 2.06/1.83
% 2.06/1.83 % (20270)Memory used [KB]: 7036
% 2.06/1.83 % (20270)Time elapsed: 0.153 s
% 2.06/1.83 % (20270)Instructions burned: 508 (million)
% 2.06/1.83 % (20270)------------------------------
% 2.06/1.83 % (20270)------------------------------
% 2.06/1.83 % (20289)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_20128 for (2996ds/109Mi)
% 2.06/1.83 % (20288)Refutation not found, incomplete strategy
% 2.06/1.83 % (20288)------------------------------
% 2.06/1.83 % (20288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.83 % (20288)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.83
% 2.06/1.83
% 2.06/1.83 % (20288)Memory used [KB]: 6012
% 2.06/1.83 % (20288)Time elapsed: 0.009 s
% 2.06/1.83 % (20288)Instructions burned: 32 (million)
% 2.06/1.83 % (20288)------------------------------
% 2.06/1.83 % (20288)------------------------------
% 2.06/1.84 % (20287)Refutation not found, incomplete strategy
% 2.06/1.84 % (20287)------------------------------
% 2.06/1.84 % (20287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.84 % (20287)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.84
% 2.06/1.84
% 2.06/1.84 % (20287)Memory used [KB]: 6012
% 2.06/1.84 % (20287)Time elapsed: 0.019 s
% 2.06/1.84 % (20287)Instructions burned: 62 (million)
% 2.06/1.84 % (20287)------------------------------
% 2.06/1.84 % (20287)------------------------------
% 2.06/1.84 % (20290)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_20128 for (2995ds/253Mi)
% 2.06/1.84 % (20291)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20128 for (2995ds/140Mi)
% 2.06/1.85 % (20290)Refutation not found, incomplete strategy
% 2.06/1.85 % (20290)------------------------------
% 2.06/1.85 % (20290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.85 % (20292)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_20128 for (2995ds/614Mi)
% 2.06/1.85 % (20290)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.85
% 2.06/1.85
% 2.06/1.85 % (20290)Memory used [KB]: 6012
% 2.06/1.85 % (20290)Time elapsed: 0.010 s
% 2.06/1.85 % (20290)Instructions burned: 31 (million)
% 2.06/1.85 % (20290)------------------------------
% 2.06/1.85 % (20290)------------------------------
% 2.06/1.85 % (20277)Instruction limit reached!
% 2.06/1.85 % (20277)------------------------------
% 2.06/1.85 % (20277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.85 % (20277)Termination reason: Unknown
% 2.06/1.85 % (20277)Termination phase: Saturation
% 2.06/1.85
% 2.06/1.85 % (20277)Memory used [KB]: 1918
% 2.06/1.85 % (20277)Time elapsed: 0.141 s
% 2.06/1.85 % (20277)Instructions burned: 435 (million)
% 2.06/1.85 % (20277)------------------------------
% 2.06/1.85 % (20277)------------------------------
% 2.06/1.86 % (20291)Refutation not found, incomplete strategy
% 2.06/1.86 % (20291)------------------------------
% 2.06/1.86 % (20291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.86 % (20291)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.86
% 2.06/1.86
% 2.06/1.86 % (20291)Memory used [KB]: 6012
% 2.06/1.86 % (20291)Time elapsed: 0.015 s
% 2.06/1.86 % (20291)Instructions burned: 55 (million)
% 2.06/1.86 % (20291)------------------------------
% 2.06/1.86 % (20291)------------------------------
% 2.06/1.86 % (20293)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_20128 for (2995ds/202Mi)
% 2.06/1.86 % (20289)Instruction limit reached!
% 2.06/1.86 % (20289)------------------------------
% 2.06/1.86 % (20289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.86 % (20289)Termination reason: Unknown
% 2.06/1.86 % (20289)Termination phase: Saturation
% 2.06/1.86
% 2.06/1.86 % (20289)Memory used [KB]: 6268
% 2.06/1.86 % (20289)Time elapsed: 0.031 s
% 2.06/1.86 % (20289)Instructions burned: 110 (million)
% 2.06/1.86 % (20289)------------------------------
% 2.06/1.86 % (20289)------------------------------
% 2.06/1.86 % (20294)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_20128 for (2995ds/339Mi)
% 2.06/1.87 % (20295)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_20128 for (2995ds/283Mi)
% 2.06/1.87 % (20296)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20128 for (2995ds/134Mi)
% 2.06/1.87 % (20293)Refutation not found, incomplete strategy
% 2.06/1.87 % (20293)------------------------------
% 2.06/1.87 % (20293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.87 % (20293)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.87
% 2.06/1.87
% 2.06/1.87 % (20293)Memory used [KB]: 6012
% 2.06/1.87 % (20293)Time elapsed: 0.015 s
% 2.06/1.87 % (20293)Instructions burned: 50 (million)
% 2.06/1.87 % (20293)------------------------------
% 2.06/1.87 % (20293)------------------------------
% 2.06/1.88 % (20297)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20128 for (2995ds/298Mi)
% 2.06/1.89 % (20294)Refutation not found, incomplete strategy
% 2.06/1.89 % (20294)------------------------------
% 2.06/1.89 % (20294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.89 % (20294)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.89
% 2.06/1.89
% 2.06/1.89 % (20294)Memory used [KB]: 6012
% 2.06/1.89 % (20294)Time elapsed: 0.024 s
% 2.06/1.89 % (20294)Instructions burned: 54 (million)
% 2.06/1.89 % (20294)------------------------------
% 2.06/1.89 % (20294)------------------------------
% 2.06/1.89 % (20281)Instruction limit reached!
% 2.06/1.89 % (20281)------------------------------
% 2.06/1.89 % (20281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.89 % (20281)Termination reason: Unknown
% 2.06/1.89 % (20281)Termination phase: Saturation
% 2.06/1.89
% 2.06/1.89 % (20281)Memory used [KB]: 6524
% 2.06/1.89 % (20281)Time elapsed: 0.146 s
% 2.06/1.89 % (20281)Instructions burned: 456 (million)
% 2.06/1.89 % (20281)------------------------------
% 2.06/1.89 % (20281)------------------------------
% 2.06/1.90 % (20298)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20128 for (2995ds/192Mi)
% 2.06/1.90 % (20299)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_20128 for (2995ds/258Mi)
% 2.06/1.90 % (20296)Instruction limit reached!
% 2.06/1.90 % (20296)------------------------------
% 2.06/1.90 % (20296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.90 % (20296)Termination reason: Unknown
% 2.06/1.90 % (20296)Termination phase: Saturation
% 2.06/1.90
% 2.06/1.90 % (20296)Memory used [KB]: 6396
% 2.06/1.90 % (20296)Time elapsed: 0.036 s
% 2.06/1.90 % (20296)Instructions burned: 135 (million)
% 2.06/1.90 % (20296)------------------------------
% 2.06/1.90 % (20296)------------------------------
% 2.06/1.91 % (20300)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_20128 for (2995ds/90Mi)
% 2.06/1.94 % (20295)Instruction limit reached!
% 2.06/1.94 % (20295)------------------------------
% 2.06/1.94 % (20295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.94 % (20295)Termination reason: Unknown
% 2.06/1.94 % (20295)Termination phase: Saturation
% 2.06/1.94
% 2.06/1.94 % (20295)Memory used [KB]: 6652
% 2.06/1.94 % (20295)Time elapsed: 0.072 s
% 2.06/1.94 % (20295)Instructions burned: 285 (million)
% 2.06/1.94 % (20295)------------------------------
% 2.06/1.94 % (20295)------------------------------
% 2.06/1.94 % (20300)Instruction limit reached!
% 2.06/1.94 % (20300)------------------------------
% 2.06/1.94 % (20300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.94 % (20300)Termination reason: Unknown
% 2.06/1.94 % (20300)Termination phase: Saturation
% 2.06/1.94
% 2.06/1.94 % (20300)Memory used [KB]: 6140
% 2.06/1.94 % (20300)Time elapsed: 0.027 s
% 2.06/1.94 % (20300)Instructions burned: 91 (million)
% 2.06/1.94 % (20300)------------------------------
% 2.06/1.94 % (20300)------------------------------
% 2.06/1.95 % (20301)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_20128 for (2994ds/231Mi)
% 2.06/1.95 % (20302)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_20128 for (2994ds/458Mi)
% 2.06/1.95 % (20298)Instruction limit reached!
% 2.06/1.95 % (20298)------------------------------
% 2.06/1.95 % (20298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.95 % (20298)Termination reason: Unknown
% 2.06/1.95 % (20298)Termination phase: Saturation
% 2.06/1.95
% 2.06/1.95 % (20298)Memory used [KB]: 6396
% 2.06/1.95 % (20298)Time elapsed: 0.051 s
% 2.06/1.95 % (20298)Instructions burned: 195 (million)
% 2.06/1.95 % (20298)------------------------------
% 2.06/1.95 % (20298)------------------------------
% 2.06/1.96 % (20297)Instruction limit reached!
% 2.06/1.96 % (20297)------------------------------
% 2.06/1.96 % (20297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.96 % (20297)Termination reason: Unknown
% 2.06/1.96 % (20297)Termination phase: Saturation
% 2.06/1.96
% 2.06/1.96 % (20297)Memory used [KB]: 6396
% 2.06/1.96 % (20297)Time elapsed: 0.077 s
% 2.06/1.96 % (20297)Instructions burned: 298 (million)
% 2.06/1.96 % (20297)------------------------------
% 2.06/1.96 % (20297)------------------------------
% 2.06/1.96 % (20303)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_20128 for (2994ds/31Mi)
% 2.06/1.97 % (20303)Instruction limit reached!
% 2.06/1.97 % (20303)------------------------------
% 2.06/1.97 % (20303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.97 % (20303)Termination reason: Unknown
% 2.06/1.97 % (20303)Termination phase: Property scanning
% 2.06/1.97
% 2.06/1.97 % (20303)Memory used [KB]: 1535
% 2.06/1.97 % (20303)Time elapsed: 0.010 s
% 2.06/1.97 % (20303)Instructions burned: 34 (million)
% 2.06/1.97 % (20303)------------------------------
% 2.06/1.97 % (20303)------------------------------
% 2.06/1.97 % (20299)Instruction limit reached!
% 2.06/1.97 % (20299)------------------------------
% 2.06/1.97 % (20299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.97 % (20299)Termination reason: Unknown
% 2.06/1.97 % (20299)Termination phase: Saturation
% 2.06/1.97
% 2.06/1.97 % (20299)Memory used [KB]: 7036
% 2.06/1.97 % (20299)Time elapsed: 0.068 s
% 2.06/1.97 % (20299)Instructions burned: 261 (million)
% 2.06/1.97 % (20299)------------------------------
% 2.06/1.97 % (20299)------------------------------
% 2.06/1.97 % (20304)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_20128 for (2994ds/297Mi)
% 2.06/1.98 % (20305)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_20128 for (2994ds/987Mi)
% 2.06/1.98 % (20306)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_20128 for (2994ds/182Mi)
% 2.06/1.98 % (20304)Refutation not found, incomplete strategy
% 2.06/1.98 % (20304)------------------------------
% 2.06/1.98 % (20304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.98 % (20304)Termination reason: Refutation not found, incomplete strategy
% 2.06/1.98
% 2.06/1.98
% 2.06/1.98 % (20304)Memory used [KB]: 6012
% 2.06/1.98 % (20304)Time elapsed: 0.013 s
% 2.06/1.98 % (20304)Instructions burned: 43 (million)
% 2.06/1.98 % (20304)------------------------------
% 2.06/1.98 % (20304)------------------------------
% 2.06/1.99 % (20307)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_20128 for (2994ds/182Mi)
% 2.06/2.00 % (20301)Instruction limit reached!
% 2.06/2.00 % (20301)------------------------------
% 2.06/2.00 % (20301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/2.00 % (20301)Termination reason: Unknown
% 2.06/2.00 % (20301)Termination phase: Saturation
% 2.06/2.00
% 2.06/2.00 % (20301)Memory used [KB]: 6396
% 2.06/2.00 % (20301)Time elapsed: 0.055 s
% 2.06/2.00 % (20301)Instructions burned: 233 (million)
% 2.06/2.00 % (20301)------------------------------
% 2.06/2.00 % (20301)------------------------------
% 2.06/2.01 % (20292)Instruction limit reached!
% 2.06/2.01 % (20292)------------------------------
% 2.06/2.01 % (20292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/2.01 % (20292)Termination reason: Unknown
% 2.06/2.01 % (20292)Termination phase: Saturation
% 2.06/2.01
% 2.06/2.01 % (20292)Memory used [KB]: 8443
% 2.06/2.01 % (20292)Time elapsed: 0.161 s
% 2.06/2.01 % (20292)Instructions burned: 618 (million)
% 2.06/2.01 % (20292)------------------------------
% 2.06/2.01 % (20292)------------------------------
% 6.13/2.02 % (20309)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_20128 for (2994ds/79Mi)
% 6.13/2.02 % (20308)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_20128 for (2994ds/154Mi)
% 6.13/2.02 % (20306)Instruction limit reached!
% 6.13/2.02 % (20306)------------------------------
% 6.13/2.02 % (20306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.02 % (20306)Termination reason: Unknown
% 6.13/2.02 % (20306)Termination phase: Saturation
% 6.13/2.02
% 6.13/2.02 % (20306)Memory used [KB]: 6524
% 6.13/2.02 % (20306)Time elapsed: 0.049 s
% 6.13/2.02 % (20306)Instructions burned: 185 (million)
% 6.13/2.02 % (20306)------------------------------
% 6.13/2.02 % (20306)------------------------------
% 6.13/2.03 % (20274)Instruction limit reached!
% 6.13/2.03 % (20274)------------------------------
% 6.13/2.03 % (20274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.03 % (20274)Termination reason: Unknown
% 6.13/2.03 % (20274)Termination phase: Saturation
% 6.13/2.03
% 6.13/2.03 % (20274)Memory used [KB]: 9978
% 6.13/2.03 % (20274)Time elapsed: 0.308 s
% 6.13/2.03 % (20274)Instructions burned: 1089 (million)
% 6.13/2.03 % (20274)------------------------------
% 6.13/2.03 % (20274)------------------------------
% 6.13/2.03 % (20310)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_20128 for (2994ds/216Mi)
% 6.13/2.04 % (20311)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_20128 for (2994ds/114Mi)
% 6.13/2.04 % (20309)Instruction limit reached!
% 6.13/2.04 % (20309)------------------------------
% 6.13/2.04 % (20309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.04 % (20309)Termination reason: Unknown
% 6.13/2.04 % (20309)Termination phase: Saturation
% 6.13/2.04
% 6.13/2.04 % (20309)Memory used [KB]: 6140
% 6.13/2.04 % (20309)Time elapsed: 0.022 s
% 6.13/2.04 % (20309)Instructions burned: 81 (million)
% 6.13/2.04 % (20309)------------------------------
% 6.13/2.04 % (20309)------------------------------
% 6.13/2.04 % (20307)Instruction limit reached!
% 6.13/2.04 % (20307)------------------------------
% 6.13/2.04 % (20307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.04 % (20307)Termination reason: Unknown
% 6.13/2.04 % (20307)Termination phase: Saturation
% 6.13/2.04
% 6.13/2.04 % (20307)Memory used [KB]: 6652
% 6.13/2.04 % (20307)Time elapsed: 0.054 s
% 6.13/2.04 % (20307)Instructions burned: 184 (million)
% 6.13/2.04 % (20307)------------------------------
% 6.13/2.04 % (20307)------------------------------
% 6.13/2.04 % (20310)Refutation not found, incomplete strategy
% 6.13/2.04 % (20310)------------------------------
% 6.13/2.04 % (20310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.04 % (20310)Termination reason: Refutation not found, incomplete strategy
% 6.13/2.04
% 6.13/2.04
% 6.13/2.04 % (20310)Memory used [KB]: 6012
% 6.13/2.04 % (20310)Time elapsed: 0.011 s
% 6.13/2.04 % (20310)Instructions burned: 35 (million)
% 6.13/2.04 % (20310)------------------------------
% 6.13/2.04 % (20310)------------------------------
% 6.13/2.05 % (20308)Refutation not found, incomplete strategy
% 6.13/2.05 % (20308)------------------------------
% 6.13/2.05 % (20308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.05 % (20308)Termination reason: Refutation not found, incomplete strategy
% 6.13/2.05
% 6.13/2.05
% 6.13/2.05 % (20308)Memory used [KB]: 6524
% 6.13/2.05 % (20308)Time elapsed: 0.049 s
% 6.13/2.05 % (20308)Instructions burned: 87 (million)
% 6.13/2.05 % (20308)------------------------------
% 6.13/2.05 % (20308)------------------------------
% 6.13/2.05 % (20312)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_20128 for (2993ds/922Mi)
% 6.13/2.05 % (20311)Refutation not found, incomplete strategy
% 6.13/2.05 % (20311)------------------------------
% 6.13/2.05 % (20311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.05 % (20311)Termination reason: Refutation not found, incomplete strategy
% 6.13/2.05
% 6.13/2.05
% 6.13/2.05 % (20311)Memory used [KB]: 6012
% 6.13/2.05 % (20311)Time elapsed: 0.014 s
% 6.13/2.05 % (20311)Instructions burned: 50 (million)
% 6.13/2.05 % (20311)------------------------------
% 6.13/2.05 % (20311)------------------------------
% 6.13/2.05 % (20313)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_20128 for (2993ds/182Mi)
% 6.13/2.05 % (20314)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_20128 for (2993ds/164Mi)
% 6.13/2.06 % (20316)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_20128 for (2993ds/368Mi)
% 6.13/2.06 % (20315)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_20128 for (2993ds/50Mi)
% 6.13/2.06 % (20314)Refutation not found, incomplete strategy
% 6.13/2.06 % (20314)------------------------------
% 6.13/2.06 % (20314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.06 % (20314)Termination reason: Refutation not found, incomplete strategy
% 6.13/2.06
% 6.13/2.06
% 6.13/2.06 % (20314)Memory used [KB]: 1535
% 6.13/2.06 % (20314)Time elapsed: 0.010 s
% 6.13/2.06 % (20314)Instructions burned: 35 (million)
% 6.13/2.06 % (20314)------------------------------
% 6.13/2.06 % (20314)------------------------------
% 6.13/2.07 % (20302)Instruction limit reached!
% 6.13/2.07 % (20302)------------------------------
% 6.13/2.07 % (20302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.07 % (20302)Termination reason: Unknown
% 6.13/2.07 % (20302)Termination phase: Saturation
% 6.13/2.07
% 6.13/2.07 % (20302)Memory used [KB]: 7547
% 6.13/2.07 % (20302)Time elapsed: 0.121 s
% 6.13/2.07 % (20302)Instructions burned: 459 (million)
% 6.13/2.07 % (20302)------------------------------
% 6.13/2.07 % (20302)------------------------------
% 6.13/2.07 % (20317)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_20128 for (2993ds/1021Mi)
% 6.13/2.08 % (20318)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_20128 for (2993ds/267Mi)
% 6.13/2.08 % (20315)Instruction limit reached!
% 6.13/2.08 % (20315)------------------------------
% 6.13/2.08 % (20315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.08 % (20315)Termination reason: Unknown
% 6.13/2.08 % (20315)Termination phase: Saturation
% 6.13/2.08
% 6.13/2.08 % (20315)Memory used [KB]: 10490
% 6.13/2.08 % (20315)Time elapsed: 0.023 s
% 6.13/2.08 % (20315)Instructions burned: 53 (million)
% 6.13/2.08 % (20315)------------------------------
% 6.13/2.08 % (20315)------------------------------
% 6.13/2.09 % (20319)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_20128 for (2993ds/204Mi)
% 6.13/2.10 % (20313)Instruction limit reached!
% 6.13/2.10 % (20313)------------------------------
% 6.13/2.10 % (20313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.10 % (20313)Termination reason: Unknown
% 6.13/2.10 % (20313)Termination phase: Saturation
% 6.13/2.10
% 6.13/2.10 % (20313)Memory used [KB]: 6012
% 6.13/2.10 % (20313)Time elapsed: 0.045 s
% 6.13/2.10 % (20313)Instructions burned: 185 (million)
% 6.13/2.10 % (20313)------------------------------
% 6.13/2.10 % (20313)------------------------------
% 6.13/2.11 % (20320)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_20128 for (2993ds/26Mi)
% 6.13/2.11 % (20320)Instruction limit reached!
% 6.13/2.11 % (20320)------------------------------
% 6.13/2.11 % (20320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.13/2.11 % (20320)Termination reason: Unknown
% 6.13/2.11 % (20320)Termination phase: Property scanning
% 6.13/2.11
% 6.13/2.11 % (20320)Memory used [KB]: 1407
% 6.13/2.11 % (20320)Time elapsed: 0.008 s
% 6.13/2.11 % (20320)Instructions burned: 26 (million)
% 6.13/2.11 % (20320)------------------------------
% 6.13/2.11 % (20320)------------------------------
% 6.57/2.12 % (20321)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_20128 for (2993ds/53Mi)
% 6.57/2.14 % (20321)Instruction limit reached!
% 6.57/2.14 % (20321)------------------------------
% 6.57/2.14 % (20321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.14 % (20321)Termination reason: Unknown
% 6.57/2.14 % (20321)Termination phase: Saturation
% 6.57/2.14
% 6.57/2.14 % (20321)Memory used [KB]: 6012
% 6.57/2.14 % (20321)Time elapsed: 0.015 s
% 6.57/2.14 % (20321)Instructions burned: 55 (million)
% 6.57/2.14 % (20321)------------------------------
% 6.57/2.14 % (20321)------------------------------
% 6.57/2.14 % (20319)Instruction limit reached!
% 6.57/2.14 % (20319)------------------------------
% 6.57/2.14 % (20319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.14 % (20319)Termination reason: Unknown
% 6.57/2.14 % (20319)Termination phase: Saturation
% 6.57/2.14
% 6.57/2.14 % (20319)Memory used [KB]: 6524
% 6.57/2.14 % (20319)Time elapsed: 0.054 s
% 6.57/2.14 % (20319)Instructions burned: 205 (million)
% 6.57/2.14 % (20319)------------------------------
% 6.57/2.14 % (20319)------------------------------
% 6.57/2.15 % (20322)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_20128 for (2992ds/4436Mi)
% 6.57/2.15 % (20318)Instruction limit reached!
% 6.57/2.15 % (20318)------------------------------
% 6.57/2.15 % (20318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.15 % (20318)Termination reason: Unknown
% 6.57/2.15 % (20318)Termination phase: Saturation
% 6.57/2.15
% 6.57/2.15 % (20318)Memory used [KB]: 6524
% 6.57/2.15 % (20318)Time elapsed: 0.067 s
% 6.57/2.15 % (20318)Instructions burned: 270 (million)
% 6.57/2.15 % (20318)------------------------------
% 6.57/2.15 % (20318)------------------------------
% 6.57/2.15 % (20323)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_20128 for (2992ds/1539Mi)
% 6.57/2.15 % (20316)Instruction limit reached!
% 6.57/2.15 % (20316)------------------------------
% 6.57/2.15 % (20316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.15 % (20316)Termination reason: Unknown
% 6.57/2.15 % (20316)Termination phase: Saturation
% 6.57/2.15
% 6.57/2.15 % (20316)Memory used [KB]: 7547
% 6.57/2.15 % (20316)Time elapsed: 0.097 s
% 6.57/2.15 % (20316)Instructions burned: 368 (million)
% 6.57/2.15 % (20316)------------------------------
% 6.57/2.15 % (20316)------------------------------
% 6.57/2.16 % (20324)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_20128 for (2992ds/408Mi)
% 6.57/2.16 % (20325)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_20128 for (2992ds/5205Mi)
% 6.93/2.22 % (20305)Instruction limit reached!
% 6.93/2.22 % (20305)------------------------------
% 6.93/2.22 % (20305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.22 % (20305)Termination reason: Unknown
% 6.93/2.22 % (20305)Termination phase: Saturation
% 6.93/2.22
% 6.93/2.22 % (20305)Memory used [KB]: 6652
% 6.93/2.22 % (20305)Time elapsed: 0.246 s
% 6.93/2.22 % (20305)Instructions burned: 989 (million)
% 6.93/2.22 % (20305)------------------------------
% 6.93/2.22 % (20305)------------------------------
% 6.93/2.23 % (20326)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_20128 for (2991ds/1913Mi)
% 6.93/2.26 % (20324)Instruction limit reached!
% 6.93/2.26 % (20324)------------------------------
% 6.93/2.26 % (20324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.26 % (20324)Termination reason: Unknown
% 6.93/2.26 % (20324)Termination phase: Saturation
% 6.93/2.26
% 6.93/2.26 % (20324)Memory used [KB]: 6524
% 6.93/2.26 % (20324)Time elapsed: 0.108 s
% 6.93/2.26 % (20324)Instructions burned: 408 (million)
% 6.93/2.26 % (20324)------------------------------
% 6.93/2.26 % (20324)------------------------------
% 6.93/2.27 % (20327)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_20128 for (2991ds/4350Mi)
% 6.93/2.29 % (20312)Instruction limit reached!
% 6.93/2.29 % (20312)------------------------------
% 6.93/2.29 % (20312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.29 % (20312)Termination reason: Unknown
% 6.93/2.29 % (20312)Termination phase: Saturation
% 6.93/2.29
% 6.93/2.29 % (20312)Memory used [KB]: 9850
% 6.93/2.29 % (20312)Time elapsed: 0.248 s
% 6.93/2.29 % (20312)Instructions burned: 922 (million)
% 6.93/2.29 % (20312)------------------------------
% 6.93/2.29 % (20312)------------------------------
% 7.34/2.30 % (20328)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_20128 for (2991ds/68Mi)
% 7.34/2.32 % (20328)Instruction limit reached!
% 7.34/2.32 % (20328)------------------------------
% 7.34/2.32 % (20328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.32 % (20328)Termination reason: Unknown
% 7.34/2.32 % (20328)Termination phase: Saturation
% 7.34/2.32
% 7.34/2.32 % (20328)Memory used [KB]: 6140
% 7.34/2.32 % (20328)Time elapsed: 0.020 s
% 7.34/2.32 % (20328)Instructions burned: 69 (million)
% 7.34/2.32 % (20328)------------------------------
% 7.34/2.32 % (20328)------------------------------
% 7.34/2.33 % (20329)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_20128 for (2990ds/358Mi)
% 7.34/2.35 % (20317)Instruction limit reached!
% 7.34/2.35 % (20317)------------------------------
% 7.34/2.35 % (20317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.35 % (20317)Termination reason: Unknown
% 7.34/2.35 % (20317)Termination phase: Saturation
% 7.34/2.35
% 7.34/2.35 % (20317)Memory used [KB]: 9594
% 7.34/2.35 % (20317)Time elapsed: 0.277 s
% 7.34/2.35 % (20317)Instructions burned: 1021 (million)
% 7.34/2.35 % (20317)------------------------------
% 7.34/2.35 % (20317)------------------------------
% 7.34/2.36 % (20330)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_20128 for (2990ds/31Mi)
% 7.34/2.37 % (20330)Instruction limit reached!
% 7.34/2.37 % (20330)------------------------------
% 7.34/2.37 % (20330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.37 % (20330)Termination reason: Unknown
% 7.34/2.37 % (20330)Termination phase: Property scanning
% 7.34/2.37
% 7.34/2.37 % (20330)Memory used [KB]: 1535
% 7.34/2.37 % (20330)Time elapsed: 0.010 s
% 7.34/2.37 % (20330)Instructions burned: 34 (million)
% 7.34/2.37 % (20330)------------------------------
% 7.34/2.37 % (20330)------------------------------
% 7.34/2.38 % (20331)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_20128 for (2990ds/279Mi)
% 7.68/2.40 % (20331)Refutation not found, incomplete strategy
% 7.68/2.40 % (20331)------------------------------
% 7.68/2.40 % (20331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.40 % (20331)Termination reason: Refutation not found, incomplete strategy
% 7.68/2.40
% 7.68/2.40
% 7.68/2.40 % (20331)Memory used [KB]: 6524
% 7.68/2.40 % (20331)Time elapsed: 0.023 s
% 7.68/2.40 % (20331)Instructions burned: 83 (million)
% 7.68/2.40 % (20331)------------------------------
% 7.68/2.40 % (20331)------------------------------
% 7.68/2.41 % (20332)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_20128 for (2990ds/258Mi)
% 7.68/2.42 % (20329)Instruction limit reached!
% 7.68/2.42 % (20329)------------------------------
% 7.68/2.42 % (20329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.42 % (20329)Termination reason: Unknown
% 7.68/2.42 % (20329)Termination phase: Saturation
% 7.68/2.42
% 7.68/2.42 % (20329)Memory used [KB]: 7036
% 7.68/2.42 % (20329)Time elapsed: 0.094 s
% 7.68/2.42 % (20329)Instructions burned: 361 (million)
% 7.68/2.42 % (20329)------------------------------
% 7.68/2.42 % (20329)------------------------------
% 7.68/2.44 % (20333)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_20128 for (2989ds/26Mi)
% 7.68/2.44 % (20333)Instruction limit reached!
% 7.68/2.44 % (20333)------------------------------
% 7.68/2.44 % (20333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.44 % (20333)Termination reason: Unknown
% 7.68/2.44 % (20333)Termination phase: Property scanning
% 7.68/2.44
% 7.68/2.44 % (20333)Memory used [KB]: 1407
% 7.68/2.44 % (20333)Time elapsed: 0.009 s
% 7.68/2.44 % (20333)Instructions burned: 27 (million)
% 7.68/2.44 % (20333)------------------------------
% 7.68/2.44 % (20333)------------------------------
% 7.68/2.45 % (20334)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_20128 for (2989ds/995Mi)
% 7.68/2.48 % (20332)Instruction limit reached!
% 7.68/2.48 % (20332)------------------------------
% 7.68/2.48 % (20332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.48 % (20332)Termination reason: Unknown
% 7.68/2.48 % (20332)Termination phase: Saturation
% 7.68/2.48
% 7.68/2.48 % (20332)Memory used [KB]: 6780
% 7.68/2.48 % (20332)Time elapsed: 0.075 s
% 7.68/2.48 % (20332)Instructions burned: 258 (million)
% 7.68/2.48 % (20332)------------------------------
% 7.68/2.48 % (20332)------------------------------
% 7.68/2.49 % (20335)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_20128 for (2989ds/373Mi)
% 7.93/2.60 % (20335)Instruction limit reached!
% 7.93/2.60 % (20335)------------------------------
% 7.93/2.60 % (20335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.93/2.60 % (20335)Termination reason: Unknown
% 7.93/2.60 % (20335)Termination phase: Saturation
% 7.93/2.60
% 7.93/2.60 % (20335)Memory used [KB]: 7291
% 7.93/2.60 % (20335)Time elapsed: 0.103 s
% 7.93/2.60 % (20335)Instructions burned: 373 (million)
% 7.93/2.60 % (20335)------------------------------
% 7.93/2.60 % (20335)------------------------------
% 8.04/2.61 % (20336)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_20128 for (2988ds/253Mi)
% 8.04/2.67 % (20336)Instruction limit reached!
% 8.04/2.67 % (20336)------------------------------
% 8.04/2.67 % (20336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.67 % (20336)Termination reason: Unknown
% 8.04/2.67 % (20336)Termination phase: Saturation
% 8.04/2.67
% 8.04/2.67 % (20336)Memory used [KB]: 6140
% 8.04/2.67 % (20336)Time elapsed: 0.065 s
% 8.04/2.67 % (20336)Instructions burned: 254 (million)
% 8.04/2.67 % (20336)------------------------------
% 8.04/2.67 % (20336)------------------------------
% 8.04/2.68 % (20337)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_20128 for (2987ds/832Mi)
% 8.04/2.69 % (20337)Refutation not found, incomplete strategy
% 8.04/2.69 % (20337)------------------------------
% 8.04/2.69 % (20337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.69 % (20337)Termination reason: Refutation not found, incomplete strategy
% 8.04/2.69
% 8.04/2.69
% 8.04/2.69 % (20337)Memory used [KB]: 6012
% 8.04/2.69 % (20337)Time elapsed: 0.014 s
% 8.04/2.69 % (20337)Instructions burned: 46 (million)
% 8.04/2.69 % (20337)------------------------------
% 8.04/2.69 % (20337)------------------------------
% 8.13/2.70 % (20338)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_20128 for (2987ds/668Mi)
% 8.13/2.74 % (20334)Instruction limit reached!
% 8.13/2.74 % (20334)------------------------------
% 8.13/2.74 % (20334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.13/2.74 % (20334)Termination reason: Unknown
% 8.13/2.74 % (20334)Termination phase: Saturation
% 8.13/2.74
% 8.13/2.74 % (20334)Memory used [KB]: 7164
% 8.13/2.74 % (20334)Time elapsed: 0.289 s
% 8.13/2.74 % (20334)Instructions burned: 997 (million)
% 8.13/2.74 % (20334)------------------------------
% 8.13/2.74 % (20334)------------------------------
% 8.13/2.75 % (20339)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_20128 for (2986ds/40Mi)
% 8.13/2.76 % (20339)Instruction limit reached!
% 8.13/2.76 % (20339)------------------------------
% 8.13/2.76 % (20339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.13/2.76 % (20339)Termination reason: Unknown
% 8.13/2.76 % (20339)Termination phase: Saturation
% 8.13/2.76
% 8.13/2.76 % (20339)Memory used [KB]: 6012
% 8.13/2.76 % (20339)Time elapsed: 0.012 s
% 8.13/2.76 % (20339)Instructions burned: 40 (million)
% 8.13/2.76 % (20339)------------------------------
% 8.13/2.76 % (20339)------------------------------
% 8.13/2.77 % (20340)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_20128 for (2986ds/294Mi)
% 8.13/2.78 % (20326)Instruction limit reached!
% 8.13/2.78 % (20326)------------------------------
% 8.13/2.78 % (20326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.13/2.78 % (20326)Termination reason: Unknown
% 8.13/2.78 % (20326)Termination phase: Saturation
% 8.13/2.78
% 8.13/2.78 % (20326)Memory used [KB]: 7803
% 8.13/2.78 % (20326)Time elapsed: 0.547 s
% 8.13/2.78 % (20326)Instructions burned: 1913 (million)
% 8.13/2.78 % (20326)------------------------------
% 8.13/2.78 % (20326)------------------------------
% 8.13/2.79 % (20341)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_20128 for (2986ds/187Mi)
% 9.01/2.83 % (20323)Instruction limit reached!
% 9.01/2.83 % (20323)------------------------------
% 9.01/2.83 % (20323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.83 % (20323)Termination reason: Unknown
% 9.01/2.83 % (20323)Termination phase: Saturation
% 9.01/2.83
% 9.01/2.83 % (20323)Memory used [KB]: 11769
% 9.01/2.83 % (20323)Time elapsed: 0.674 s
% 9.01/2.83 % (20323)Instructions burned: 1539 (million)
% 9.01/2.83 % (20323)------------------------------
% 9.01/2.83 % (20323)------------------------------
% 9.01/2.84 % (20341)Instruction limit reached!
% 9.01/2.84 % (20341)------------------------------
% 9.01/2.84 % (20341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.84 % (20341)Termination reason: Unknown
% 9.01/2.84 % (20341)Termination phase: Saturation
% 9.01/2.84
% 9.01/2.84 % (20341)Memory used [KB]: 6524
% 9.01/2.84 % (20341)Time elapsed: 0.050 s
% 9.01/2.84 % (20341)Instructions burned: 187 (million)
% 9.01/2.84 % (20341)------------------------------
% 9.01/2.84 % (20341)------------------------------
% 9.01/2.84 % (20340)Instruction limit reached!
% 9.01/2.84 % (20340)------------------------------
% 9.01/2.84 % (20340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.84 % (20340)Termination reason: Unknown
% 9.01/2.84 % (20340)Termination phase: Saturation
% 9.01/2.84
% 9.01/2.84 % (20340)Memory used [KB]: 6396
% 9.01/2.84 % (20340)Time elapsed: 0.072 s
% 9.01/2.84 % (20340)Instructions burned: 294 (million)
% 9.01/2.84 % (20340)------------------------------
% 9.01/2.84 % (20340)------------------------------
% 9.01/2.84 % (20343)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_20128 for (2985ds/1827Mi)
% 9.01/2.85 % (20342)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_20128 for (2986ds/371Mi)
% 9.01/2.85 % (20344)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_20128 for (2985ds/70Mi)
% 9.01/2.86 % (20342)Refutation not found, incomplete strategy
% 9.01/2.86 % (20342)------------------------------
% 9.01/2.86 % (20342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.86 % (20342)Termination reason: Refutation not found, incomplete strategy
% 9.01/2.86
% 9.01/2.86
% 9.01/2.86 % (20342)Memory used [KB]: 6012
% 9.01/2.86 % (20342)Time elapsed: 0.018 s
% 9.01/2.86 % (20342)Instructions burned: 31 (million)
% 9.01/2.86 % (20342)------------------------------
% 9.01/2.86 % (20342)------------------------------
% 9.01/2.87 % (20344)Instruction limit reached!
% 9.01/2.87 % (20344)------------------------------
% 9.01/2.87 % (20344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.87 % (20344)Termination reason: Unknown
% 9.01/2.87 % (20344)Termination phase: Saturation
% 9.01/2.87
% 9.01/2.87 % (20344)Memory used [KB]: 1663
% 9.01/2.87 % (20344)Time elapsed: 0.019 s
% 9.01/2.87 % (20344)Instructions burned: 71 (million)
% 9.01/2.87 % (20344)------------------------------
% 9.01/2.87 % (20344)------------------------------
% 9.01/2.88 % (20345)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_20128 for (2985ds/316Mi)
% 9.01/2.88 % (20346)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_20128 for (2985ds/932Mi)
% 9.01/2.89 % (20338)Instruction limit reached!
% 9.01/2.89 % (20338)------------------------------
% 9.01/2.89 % (20338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.89 % (20338)Termination reason: Unknown
% 9.01/2.89 % (20338)Termination phase: Saturation
% 9.01/2.89
% 9.01/2.89 % (20338)Memory used [KB]: 11385
% 9.01/2.89 % (20338)Time elapsed: 0.185 s
% 9.01/2.89 % (20338)Instructions burned: 669 (million)
% 9.01/2.89 % (20338)------------------------------
% 9.01/2.89 % (20338)------------------------------
% 9.01/2.90 % (20347)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_20128 for (2985ds/4714Mi)
% 10.09/2.90 % (20345)Refutation not found, incomplete strategy
% 10.09/2.90 % (20345)------------------------------
% 10.09/2.90 % (20345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.90 % (20345)Termination reason: Refutation not found, incomplete strategy
% 10.09/2.90
% 10.09/2.90
% 10.09/2.90 % (20345)Memory used [KB]: 6268
% 10.09/2.90 % (20345)Time elapsed: 0.027 s
% 10.09/2.90 % (20345)Instructions burned: 86 (million)
% 10.09/2.90 % (20345)------------------------------
% 10.09/2.90 % (20345)------------------------------
% 10.09/2.91 % (20347)Refutation not found, incomplete strategy
% 10.09/2.91 % (20347)------------------------------
% 10.09/2.91 % (20347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.91 % (20347)Termination reason: Refutation not found, incomplete strategy
% 10.09/2.91
% 10.09/2.91
% 10.09/2.91 % (20347)Memory used [KB]: 6268
% 10.09/2.91 % (20347)Time elapsed: 0.018 s
% 10.09/2.91 % (20347)Instructions burned: 65 (million)
% 10.09/2.91 % (20347)------------------------------
% 10.09/2.91 % (20347)------------------------------
% 10.09/2.91 % (20348)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_20128 for (2985ds/8250Mi)
% 10.09/2.92 % (20349)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_20128 for (2985ds/770Mi)
% 10.09/2.93 % (20349)Refutation not found, incomplete strategy
% 10.09/2.93 % (20349)------------------------------
% 10.09/2.93 % (20349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.93 % (20349)Termination reason: Refutation not found, incomplete strategy
% 10.09/2.93
% 10.09/2.93
% 10.09/2.93 % (20349)Memory used [KB]: 6012
% 10.09/2.93 % (20349)Time elapsed: 0.009 s
% 10.09/2.93 % (20349)Instructions burned: 29 (million)
% 10.09/2.93 % (20349)------------------------------
% 10.09/2.93 % (20349)------------------------------
% 10.09/2.94 % (20350)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_20128 for (2985ds/794Mi)
% 10.09/2.96 % (20350)Refutation not found, incomplete strategy
% 10.09/2.96 % (20350)------------------------------
% 10.09/2.96 % (20350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.96 % (20350)Termination reason: Refutation not found, incomplete strategy
% 10.09/2.96
% 10.09/2.96
% 10.09/2.96 % (20350)Memory used [KB]: 1535
% 10.09/2.96 % (20350)Time elapsed: 0.014 s
% 10.09/2.96 % (20350)Instructions burned: 48 (million)
% 10.09/2.96 % (20350)------------------------------
% 10.09/2.96 % (20350)------------------------------
% 10.09/2.97 % (20351)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_20128 for (2984ds/464Mi)
% 13.11/3.09 % (20351)Instruction limit reached!
% 13.11/3.09 % (20351)------------------------------
% 13.11/3.09 % (20351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.09 % (20351)Termination reason: Unknown
% 13.11/3.09 % (20351)Termination phase: Saturation
% 13.11/3.09
% 13.11/3.09 % (20351)Memory used [KB]: 7291
% 13.11/3.09 % (20351)Time elapsed: 0.123 s
% 13.11/3.09 % (20351)Instructions burned: 467 (million)
% 13.11/3.09 % (20351)------------------------------
% 13.11/3.09 % (20351)------------------------------
% 13.11/3.10 % (20352)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_20128 for (2983ds/1376Mi)
% 13.11/3.10 % (20346)Instruction limit reached!
% 13.11/3.10 % (20346)------------------------------
% 13.11/3.10 % (20346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.10 % (20346)Termination reason: Unknown
% 13.11/3.10 % (20346)Termination phase: Saturation
% 13.11/3.10
% 13.11/3.10 % (20346)Memory used [KB]: 7164
% 13.11/3.10 % (20346)Time elapsed: 0.223 s
% 13.11/3.10 % (20346)Instructions burned: 932 (million)
% 13.11/3.10 % (20346)------------------------------
% 13.11/3.10 % (20346)------------------------------
% 13.11/3.11 % (20353)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_20128 for (2983ds/906Mi)
% 14.70/3.35 % (20353)Instruction limit reached!
% 14.70/3.35 % (20353)------------------------------
% 14.70/3.35 % (20353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.35 % (20353)Termination reason: Unknown
% 14.70/3.35 % (20353)Termination phase: Saturation
% 14.70/3.35
% 14.70/3.35 % (20353)Memory used [KB]: 9722
% 14.70/3.35 % (20353)Time elapsed: 0.246 s
% 14.70/3.35 % (20353)Instructions burned: 906 (million)
% 14.70/3.35 % (20353)------------------------------
% 14.70/3.35 % (20353)------------------------------
% 14.70/3.36 % (20343)Instruction limit reached!
% 14.70/3.36 % (20343)------------------------------
% 14.70/3.36 % (20343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.36 % (20343)Termination reason: Unknown
% 14.70/3.36 % (20343)Termination phase: Saturation
% 14.70/3.36
% 14.70/3.36 % (20343)Memory used [KB]: 13048
% 14.70/3.36 % (20343)Time elapsed: 0.514 s
% 14.70/3.36 % (20343)Instructions burned: 1829 (million)
% 14.70/3.36 % (20343)------------------------------
% 14.70/3.36 % (20343)------------------------------
% 14.70/3.37 % (20354)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_20128 for (2980ds/434Mi)
% 14.70/3.37 % (20355)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_20128 for (2980ds/865Mi)
% 14.70/3.37 % (20354)Refutation not found, incomplete strategy
% 14.70/3.37 % (20354)------------------------------
% 14.70/3.37 % (20354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.37 % (20354)Termination reason: Refutation not found, incomplete strategy
% 14.70/3.37
% 14.70/3.37
% 14.70/3.37 % (20354)Memory used [KB]: 6012
% 14.70/3.37 % (20354)Time elapsed: 0.010 s
% 14.70/3.37 % (20354)Instructions burned: 31 (million)
% 14.70/3.37 % (20354)------------------------------
% 14.70/3.37 % (20354)------------------------------
% 14.70/3.38 % (20352)Instruction limit reached!
% 14.70/3.38 % (20352)------------------------------
% 14.70/3.38 % (20352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.38 % (20352)Termination reason: Unknown
% 14.70/3.38 % (20352)Termination phase: Saturation
% 14.70/3.38
% 14.70/3.38 % (20352)Memory used [KB]: 6396
% 14.70/3.38 % (20352)Time elapsed: 0.282 s
% 14.70/3.38 % (20352)Instructions burned: 1381 (million)
% 14.70/3.38 % (20352)------------------------------
% 14.70/3.38 % (20352)------------------------------
% 14.70/3.38 % (20356)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_20128 for (2980ds/593Mi)
% 14.70/3.39 % (20357)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_20128 for (2980ds/443Mi)
% 15.74/3.40 % (20322)Instruction limit reached!
% 15.74/3.40 % (20322)------------------------------
% 15.74/3.40 % (20322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.74/3.40 % (20322)Termination reason: Unknown
% 15.74/3.40 % (20322)Termination phase: Saturation
% 15.74/3.40
% 15.74/3.40 % (20322)Memory used [KB]: 19317
% 15.74/3.40 % (20322)Time elapsed: 1.257 s
% 15.74/3.40 % (20322)Instructions burned: 4437 (million)
% 15.74/3.40 % (20322)------------------------------
% 15.74/3.40 % (20322)------------------------------
% 15.74/3.41 % (20358)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_20128 for (2980ds/594Mi)
% 16.06/3.50 % (20357)Instruction limit reached!
% 16.06/3.50 % (20357)------------------------------
% 16.06/3.50 % (20357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.50 % (20357)Termination reason: Unknown
% 16.06/3.50 % (20357)Termination phase: Saturation
% 16.06/3.50
% 16.06/3.50 % (20357)Memory used [KB]: 7419
% 16.06/3.50 % (20357)Time elapsed: 0.116 s
% 16.06/3.50 % (20357)Instructions burned: 446 (million)
% 16.06/3.50 % (20357)------------------------------
% 16.06/3.50 % (20357)------------------------------
% 16.06/3.51 % (20359)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_20128 for (2979ds/327Mi)
% 16.06/3.52 % (20327)Instruction limit reached!
% 16.06/3.52 % (20327)------------------------------
% 16.06/3.52 % (20327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.52 % (20327)Termination reason: Unknown
% 16.06/3.52 % (20327)Termination phase: Saturation
% 16.06/3.52
% 16.06/3.52 % (20327)Memory used [KB]: 20980
% 16.06/3.52 % (20327)Time elapsed: 1.246 s
% 16.06/3.52 % (20327)Instructions burned: 4352 (million)
% 16.06/3.52 % (20327)------------------------------
% 16.06/3.52 % (20327)------------------------------
% 16.06/3.53 % (20360)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_20128 for (2979ds/5411Mi)
% 16.06/3.54 % (20360)Refutation not found, incomplete strategy
% 16.06/3.54 % (20360)------------------------------
% 16.06/3.54 % (20360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.54 % (20360)Termination reason: Refutation not found, incomplete strategy
% 16.06/3.54
% 16.06/3.54
% 16.06/3.54 % (20360)Memory used [KB]: 6012
% 16.06/3.54 % (20360)Time elapsed: 0.009 s
% 16.06/3.54 % (20360)Instructions burned: 28 (million)
% 16.06/3.54 % (20360)------------------------------
% 16.06/3.54 % (20360)------------------------------
% 16.06/3.55 % (20356)Instruction limit reached!
% 16.06/3.55 % (20356)------------------------------
% 16.06/3.55 % (20356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.55 % (20356)Termination reason: Unknown
% 16.06/3.55 % (20356)Termination phase: Saturation
% 16.06/3.55
% 16.06/3.55 % (20356)Memory used [KB]: 6396
% 16.06/3.55 % (20356)Time elapsed: 0.163 s
% 16.06/3.55 % (20356)Instructions burned: 593 (million)
% 16.06/3.55 % (20356)------------------------------
% 16.06/3.55 % (20356)------------------------------
% 16.06/3.55 % (20361)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_20128 for (2978ds/1762Mi)
% 16.06/3.56 % (20362)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_20128 for (2978ds/96Mi)
% 16.06/3.57 % (20358)Instruction limit reached!
% 16.06/3.57 % (20358)------------------------------
% 16.06/3.57 % (20358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.57 % (20358)Termination reason: Unknown
% 16.06/3.57 % (20358)Termination phase: Saturation
% 16.06/3.57
% 16.06/3.57 % (20358)Memory used [KB]: 8571
% 16.06/3.57 % (20358)Time elapsed: 0.157 s
% 16.06/3.57 % (20358)Instructions burned: 596 (million)
% 16.06/3.57 % (20358)------------------------------
% 16.06/3.57 % (20358)------------------------------
% 16.06/3.58 % (20363)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_20128 for (2978ds/503Mi)
% 16.06/3.58 % (20362)Instruction limit reached!
% 16.06/3.58 % (20362)------------------------------
% 16.06/3.58 % (20362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.58 % (20362)Termination reason: Unknown
% 16.06/3.58 % (20362)Termination phase: Saturation
% 16.06/3.58
% 16.06/3.58 % (20362)Memory used [KB]: 6268
% 16.06/3.58 % (20362)Time elapsed: 0.028 s
% 16.06/3.58 % (20362)Instructions burned: 97 (million)
% 16.06/3.58 % (20362)------------------------------
% 16.06/3.58 % (20362)------------------------------
% 16.06/3.59 % (20363)Refutation not found, incomplete strategy
% 16.06/3.59 % (20363)------------------------------
% 16.06/3.59 % (20363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.59 % (20363)Termination reason: Refutation not found, incomplete strategy
% 16.06/3.59
% 16.06/3.59
% 16.06/3.59 % (20363)Memory used [KB]: 6012
% 16.06/3.59 % (20363)Time elapsed: 0.010 s
% 16.06/3.59 % (20363)Instructions burned: 31 (million)
% 16.06/3.59 % (20363)------------------------------
% 16.06/3.59 % (20363)------------------------------
% 16.06/3.59 % (20364)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_20128 for (2978ds/90Mi)
% 16.06/3.59 % (20355)Instruction limit reached!
% 16.06/3.59 % (20355)------------------------------
% 16.06/3.59 % (20355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.06/3.59 % (20355)Termination reason: Unknown
% 16.06/3.59 % (20355)Termination phase: Saturation
% 16.06/3.59
% 16.06/3.59 % (20355)Memory used [KB]: 7419
% 16.06/3.59 % (20355)Time elapsed: 0.228 s
% 16.06/3.59 % (20355)Instructions burned: 866 (million)
% 16.06/3.59 % (20355)------------------------------
% 16.06/3.59 % (20355)------------------------------
% 17.07/3.60 % (20365)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_20128 for (2978ds/593Mi)
% 17.07/3.60 % (20359)Instruction limit reached!
% 17.07/3.60 % (20359)------------------------------
% 17.07/3.60 % (20359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.60 % (20359)Termination reason: Unknown
% 17.07/3.60 % (20359)Termination phase: Saturation
% 17.07/3.60
% 17.07/3.60 % (20359)Memory used [KB]: 8315
% 17.07/3.60 % (20359)Time elapsed: 0.087 s
% 17.07/3.60 % (20359)Instructions burned: 328 (million)
% 17.07/3.60 % (20359)------------------------------
% 17.07/3.60 % (20359)------------------------------
% 17.07/3.60 % (20325)Instruction limit reached!
% 17.07/3.60 % (20325)------------------------------
% 17.07/3.60 % (20325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.60 % (20325)Termination reason: Unknown
% 17.07/3.60 % (20325)Termination phase: Saturation
% 17.07/3.60
% 17.07/3.60 % (20325)Memory used [KB]: 11897
% 17.07/3.60 % (20325)Time elapsed: 1.440 s
% 17.07/3.60 % (20325)Instructions burned: 5206 (million)
% 17.07/3.60 % (20325)------------------------------
% 17.07/3.60 % (20325)------------------------------
% 17.07/3.60 % (20366)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_20128 for (2978ds/1512Mi)
% 17.07/3.61 % (20367)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_20128 for (2978ds/569Mi)
% 17.07/3.61 % (20368)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_20128 for (2978ds/501Mi)
% 17.07/3.62 % (20364)Instruction limit reached!
% 17.07/3.62 % (20364)------------------------------
% 17.07/3.62 % (20364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.62 % (20364)Termination reason: Unknown
% 17.07/3.62 % (20364)Termination phase: Saturation
% 17.07/3.62
% 17.07/3.62 % (20364)Memory used [KB]: 6268
% 17.07/3.62 % (20364)Time elapsed: 0.027 s
% 17.07/3.62 % (20364)Instructions burned: 92 (million)
% 17.07/3.62 % (20364)------------------------------
% 17.07/3.62 % (20364)------------------------------
% 17.07/3.63 % (20366)Refutation not found, incomplete strategy
% 17.07/3.63 % (20366)------------------------------
% 17.07/3.63 % (20366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.63 % (20366)Termination reason: Refutation not found, incomplete strategy
% 17.07/3.63
% 17.07/3.63
% 17.07/3.63 % (20366)Memory used [KB]: 6140
% 17.07/3.63 % (20366)Time elapsed: 0.022 s
% 17.07/3.63 % (20366)Instructions burned: 75 (million)
% 17.07/3.63 % (20366)------------------------------
% 17.07/3.63 % (20366)------------------------------
% 17.07/3.63 % (20368)Refutation not found, incomplete strategy
% 17.07/3.63 % (20368)------------------------------
% 17.07/3.63 % (20368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.63 % (20368)Termination reason: Refutation not found, incomplete strategy
% 17.07/3.63
% 17.07/3.63
% 17.07/3.63 % (20368)Memory used [KB]: 6012
% 17.07/3.63 % (20368)Time elapsed: 0.014 s
% 17.07/3.63 % (20368)Instructions burned: 51 (million)
% 17.07/3.63 % (20368)------------------------------
% 17.07/3.63 % (20368)------------------------------
% 17.07/3.63 % (20369)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_20128 for (2978ds/562Mi)
% 17.07/3.64 % (20371)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_20128 for (2977ds/582Mi)
% 17.07/3.64 % (20370)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_20128 for (2977ds/406Mi)
% 17.07/3.66 % (20370)Refutation not found, incomplete strategy
% 17.07/3.66 % (20370)------------------------------
% 17.07/3.66 % (20370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.07/3.66 % (20370)Termination reason: Refutation not found, incomplete strategy
% 17.07/3.66
% 17.07/3.66
% 17.07/3.66 % (20370)Memory used [KB]: 6140
% 17.07/3.66 % (20370)Time elapsed: 0.025 s
% 17.07/3.66 % (20370)Instructions burned: 88 (million)
% 17.07/3.66 % (20370)------------------------------
% 17.07/3.66 % (20370)------------------------------
% 17.07/3.67 % (20372)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_20128 for (2977ds/456Mi)
% 17.40/3.75 % (20365)Instruction limit reached!
% 17.40/3.75 % (20365)------------------------------
% 17.40/3.75 % (20365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.75 % (20365)Termination reason: Unknown
% 17.40/3.75 % (20365)Termination phase: Saturation
% 17.40/3.75
% 17.40/3.75 % (20365)Memory used [KB]: 8059
% 17.40/3.75 % (20365)Time elapsed: 0.155 s
% 17.40/3.75 % (20365)Instructions burned: 595 (million)
% 17.40/3.75 % (20365)------------------------------
% 17.40/3.75 % (20365)------------------------------
% 17.40/3.76 % (20373)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_20128 for (2976ds/393Mi)
% 17.40/3.76 % (20367)Instruction limit reached!
% 17.40/3.76 % (20367)------------------------------
% 17.40/3.76 % (20367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.76 % (20367)Termination reason: Unknown
% 17.40/3.76 % (20367)Termination phase: Saturation
% 17.40/3.76
% 17.40/3.76 % (20367)Memory used [KB]: 6780
% 17.40/3.76 % (20367)Time elapsed: 0.158 s
% 17.40/3.76 % (20367)Instructions burned: 571 (million)
% 17.40/3.76 % (20367)------------------------------
% 17.40/3.76 % (20367)------------------------------
% 17.40/3.77 % (20374)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_20128 for (2976ds/1335Mi)
% 17.40/3.78 % (20369)Instruction limit reached!
% 17.40/3.78 % (20369)------------------------------
% 17.40/3.78 % (20369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.78 % (20369)Termination reason: Unknown
% 17.40/3.78 % (20369)Termination phase: Saturation
% 17.40/3.78
% 17.40/3.78 % (20369)Memory used [KB]: 7036
% 17.40/3.78 % (20369)Time elapsed: 0.150 s
% 17.40/3.78 % (20369)Instructions burned: 562 (million)
% 17.40/3.78 % (20369)------------------------------
% 17.40/3.78 % (20369)------------------------------
% 17.40/3.78 % (20374)Refutation not found, incomplete strategy
% 17.40/3.78 % (20374)------------------------------
% 17.40/3.78 % (20374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.78 % (20374)Termination reason: Refutation not found, incomplete strategy
% 17.40/3.78
% 17.40/3.78
% 17.40/3.78 % (20374)Memory used [KB]: 6012
% 17.40/3.78 % (20374)Time elapsed: 0.011 s
% 17.40/3.78 % (20374)Instructions burned: 35 (million)
% 17.40/3.78 % (20374)------------------------------
% 17.40/3.78 % (20374)------------------------------
% 17.40/3.79 % (20375)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_20128 for (2976ds/3373Mi)
% 17.40/3.79 % (20371)Instruction limit reached!
% 17.40/3.79 % (20371)------------------------------
% 17.40/3.79 % (20371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.79 % (20371)Termination reason: Unknown
% 17.40/3.79 % (20371)Termination phase: Saturation
% 17.40/3.79
% 17.40/3.79 % (20371)Memory used [KB]: 7931
% 17.40/3.79 % (20371)Time elapsed: 0.152 s
% 17.40/3.79 % (20371)Instructions burned: 582 (million)
% 17.40/3.79 % (20371)------------------------------
% 17.40/3.79 % (20371)------------------------------
% 17.40/3.79 % (20372)Instruction limit reached!
% 17.40/3.79 % (20372)------------------------------
% 17.40/3.79 % (20372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.79 % (20372)Termination reason: Unknown
% 17.40/3.79 % (20372)Termination phase: Saturation
% 17.40/3.79
% 17.40/3.79 % (20372)Memory used [KB]: 7547
% 17.40/3.79 % (20372)Time elapsed: 0.121 s
% 17.40/3.79 % (20372)Instructions burned: 458 (million)
% 17.40/3.79 % (20372)------------------------------
% 17.40/3.79 % (20372)------------------------------
% 17.40/3.79 % (20376)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_20128 for (2976ds/474Mi)
% 18.30/3.80 % (20377)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_20128 for (2976ds/157Mi)
% 18.30/3.80 % (20378)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_20128 for (2976ds/590Mi)
% 18.30/3.83 % (20377)Instruction limit reached!
% 18.30/3.83 % (20377)------------------------------
% 18.30/3.83 % (20377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.30/3.83 % (20377)Termination reason: Unknown
% 18.30/3.83 % (20377)Termination phase: Saturation
% 18.30/3.83
% 18.30/3.83 % (20377)Memory used [KB]: 6012
% 18.30/3.83 % (20377)Time elapsed: 0.039 s
% 18.30/3.83 % (20377)Instructions burned: 160 (million)
% 18.30/3.83 % (20377)------------------------------
% 18.30/3.83 % (20377)------------------------------
% 18.30/3.84 % (20379)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_20128 for (2975ds/104Mi)
% 18.30/3.85 % (20373)Instruction limit reached!
% 18.30/3.85 % (20373)------------------------------
% 18.30/3.85 % (20373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.30/3.85 % (20373)Termination reason: Unknown
% 18.30/3.85 % (20373)Termination phase: Saturation
% 18.30/3.85
% 18.30/3.85 % (20373)Memory used [KB]: 6140
% 18.30/3.85 % (20373)Time elapsed: 0.094 s
% 18.30/3.85 % (20373)Instructions burned: 393 (million)
% 18.30/3.85 % (20373)------------------------------
% 18.30/3.85 % (20373)------------------------------
% 18.30/3.86 % (20380)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_20128 for (2975ds/414Mi)
% 18.30/3.87 % (20379)Instruction limit reached!
% 18.30/3.87 % (20379)------------------------------
% 18.30/3.87 % (20379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.30/3.87 % (20379)Termination reason: Unknown
% 18.30/3.87 % (20379)Termination phase: Saturation
% 18.30/3.87
% 18.30/3.87 % (20379)Memory used [KB]: 6140
% 18.30/3.87 % (20379)Time elapsed: 0.028 s
% 18.30/3.87 % (20379)Instructions burned: 105 (million)
% 18.30/3.87 % (20379)------------------------------
% 18.30/3.87 % (20379)------------------------------
% 18.30/3.88 % (20381)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_20128 for (2975ds/715Mi)
% 18.58/3.91 % (20376)Instruction limit reached!
% 18.58/3.91 % (20376)------------------------------
% 18.58/3.91 % (20376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.58/3.91 % (20376)Termination reason: Unknown
% 18.58/3.91 % (20376)Termination phase: Saturation
% 18.58/3.91
% 18.58/3.91 % (20376)Memory used [KB]: 6524
% 18.58/3.91 % (20376)Time elapsed: 0.119 s
% 18.58/3.91 % (20376)Instructions burned: 474 (million)
% 18.58/3.91 % (20376)------------------------------
% 18.58/3.91 % (20376)------------------------------
% 18.58/3.92 % (20382)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_20128 for (2975ds/961Mi)
% 18.58/3.96 % (20378)Instruction limit reached!
% 18.58/3.96 % (20378)------------------------------
% 18.58/3.96 % (20378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.58/3.96 % (20378)Termination reason: Unknown
% 18.58/3.96 % (20378)Termination phase: Saturation
% 18.58/3.96
% 18.58/3.96 % (20378)Memory used [KB]: 7036
% 18.58/3.96 % (20378)Time elapsed: 0.158 s
% 18.58/3.96 % (20378)Instructions burned: 590 (million)
% 18.58/3.96 % (20378)------------------------------
% 18.58/3.96 % (20378)------------------------------
% 18.58/3.96 % (20361)Instruction limit reached!
% 18.58/3.96 % (20361)------------------------------
% 18.58/3.96 % (20361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.58/3.96 % (20361)Termination reason: Unknown
% 18.58/3.96 % (20361)Termination phase: Saturation
% 18.58/3.96
% 18.58/3.96 % (20361)Memory used [KB]: 8187
% 18.58/3.96 % (20361)Time elapsed: 0.418 s
% 18.58/3.96 % (20361)Instructions burned: 1765 (million)
% 18.58/3.96 % (20361)------------------------------
% 18.58/3.96 % (20361)------------------------------
% 18.58/3.97 % (20383)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_20128 for (2974ds/1213Mi)
% 18.58/3.97 % (20384)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_20128 for (2974ds/1979Mi)
% 18.58/3.98 % (20380)Instruction limit reached!
% 18.58/3.98 % (20380)------------------------------
% 18.58/3.98 % (20380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.58/3.98 % (20380)Termination reason: Unknown
% 18.58/3.98 % (20380)Termination phase: Saturation
% 18.58/3.98
% 18.58/3.98 % (20380)Memory used [KB]: 6524
% 18.58/3.98 % (20380)Time elapsed: 0.114 s
% 18.58/3.98 % (20380)Instructions burned: 414 (million)
% 18.58/3.98 % (20380)------------------------------
% 18.58/3.98 % (20380)------------------------------
% 18.58/3.99 % (20385)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_20128 for (2974ds/481Mi)
% 20.11/4.07 % (20381)Instruction limit reached!
% 20.11/4.07 % (20381)------------------------------
% 20.11/4.07 % (20381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.11/4.07 % (20381)Termination reason: Unknown
% 20.11/4.07 % (20381)Termination phase: Saturation
% 20.11/4.07
% 20.11/4.07 % (20381)Memory used [KB]: 3837
% 20.11/4.07 % (20381)Time elapsed: 0.189 s
% 20.11/4.07 % (20381)Instructions burned: 716 (million)
% 20.11/4.07 % (20381)------------------------------
% 20.11/4.07 % (20381)------------------------------
% 20.11/4.08 % (20386)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_20128 for (2973ds/783Mi)
% 20.11/4.10 % (20385)Instruction limit reached!
% 20.11/4.10 % (20385)------------------------------
% 20.11/4.10 % (20385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.11/4.10 % (20385)Termination reason: Unknown
% 20.11/4.10 % (20385)Termination phase: Saturation
% 20.11/4.10
% 20.11/4.10 % (20385)Memory used [KB]: 6396
% 20.11/4.10 % (20385)Time elapsed: 0.141 s
% 20.11/4.11 % (20385)Instructions burned: 481 (million)
% 20.11/4.11 % (20385)------------------------------
% 20.11/4.11 % (20385)------------------------------
% 20.11/4.12 % (20387)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_20128 for (2973ds/432Mi)
% 20.78/4.12 % (20387)Refutation not found, incomplete strategy
% 20.78/4.12 % (20387)------------------------------
% 20.78/4.12 % (20387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.78/4.12 % (20387)Termination reason: Refutation not found, incomplete strategy
% 20.78/4.12
% 20.78/4.12
% 20.78/4.12 % (20387)Memory used [KB]: 6012
% 20.78/4.12 % (20387)Time elapsed: 0.010 s
% 20.78/4.12 % (20387)Instructions burned: 30 (million)
% 20.78/4.12 % (20387)------------------------------
% 20.78/4.12 % (20387)------------------------------
% 20.78/4.13 % (20388)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_20128 for (2972ds/1670Mi)
% 20.78/4.18 % (20382)Instruction limit reached!
% 20.78/4.18 % (20382)------------------------------
% 20.78/4.18 % (20382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.78/4.18 % (20382)Termination reason: Unknown
% 20.78/4.18 % (20382)Termination phase: Saturation
% 20.78/4.18
% 20.78/4.18 % (20382)Memory used [KB]: 9594
% 20.78/4.18 % (20382)Time elapsed: 0.259 s
% 20.78/4.18 % (20382)Instructions burned: 963 (million)
% 20.78/4.18 % (20382)------------------------------
% 20.78/4.18 % (20382)------------------------------
% 20.78/4.19 % (20389)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_20128 for (2972ds/90Mi)
% 21.18/4.21 % (20389)Instruction limit reached!
% 21.18/4.21 % (20389)------------------------------
% 21.18/4.21 % (20389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.21 % (20389)Termination reason: Unknown
% 21.18/4.21 % (20389)Termination phase: Saturation
% 21.18/4.21
% 21.18/4.21 % (20389)Memory used [KB]: 6140
% 21.18/4.21 % (20389)Time elapsed: 0.025 s
% 21.18/4.21 % (20389)Instructions burned: 91 (million)
% 21.18/4.21 % (20389)------------------------------
% 21.18/4.21 % (20389)------------------------------
% 21.18/4.22 % (20390)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_20128 for (2972ds/346Mi)
% 21.61/4.31 % (20390)Instruction limit reached!
% 21.61/4.31 % (20390)------------------------------
% 21.61/4.31 % (20390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.61/4.31 % (20390)Termination reason: Unknown
% 21.61/4.31 % (20390)Termination phase: Saturation
% 21.61/4.31
% 21.61/4.31 % (20390)Memory used [KB]: 6396
% 21.61/4.31 % (20390)Time elapsed: 0.086 s
% 21.61/4.31 % (20390)Instructions burned: 346 (million)
% 21.61/4.31 % (20390)------------------------------
% 21.61/4.31 % (20390)------------------------------
% 21.61/4.31 % (20386)Instruction limit reached!
% 21.61/4.31 % (20386)------------------------------
% 21.61/4.31 % (20386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.61/4.31 % (20386)Termination reason: Unknown
% 21.61/4.31 % (20386)Termination phase: Saturation
% 21.61/4.31
% 21.61/4.31 % (20386)Memory used [KB]: 8699
% 21.61/4.31 % (20386)Time elapsed: 0.254 s
% 21.61/4.31 % (20386)Instructions burned: 784 (million)
% 21.61/4.31 % (20386)------------------------------
% 21.61/4.31 % (20386)------------------------------
% 21.61/4.32 % (20391)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_20128 for (2971ds/401Mi)
% 21.61/4.32 % (20392)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_20128 for (2971ds/6454Mi)
% 21.61/4.32 % (20383)Instruction limit reached!
% 21.61/4.32 % (20383)------------------------------
% 21.61/4.32 % (20383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.61/4.32 % (20383)Termination reason: Unknown
% 21.61/4.32 % (20383)Termination phase: Saturation
% 21.61/4.32
% 21.61/4.32 % (20383)Memory used [KB]: 7036
% 21.61/4.32 % (20383)Time elapsed: 0.359 s
% 21.61/4.32 % (20383)Instructions burned: 1215 (million)
% 21.61/4.32 % (20383)------------------------------
% 21.61/4.32 % (20383)------------------------------
% 21.61/4.33 % (20393)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_20128 for (2970ds/283Mi)
% 22.30/4.41 % (20393)Instruction limit reached!
% 22.30/4.41 % (20393)------------------------------
% 22.30/4.41 % (20393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.30/4.41 % (20393)Termination reason: Unknown
% 22.30/4.41 % (20393)Termination phase: Saturation
% 22.30/4.41
% 22.30/4.41 % (20393)Memory used [KB]: 6780
% 22.30/4.41 % (20393)Time elapsed: 0.076 s
% 22.30/4.41 % (20393)Instructions burned: 285 (million)
% 22.30/4.41 % (20393)------------------------------
% 22.30/4.41 % (20393)------------------------------
% 22.30/4.42 % (20394)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_20128 for (2970ds/865Mi)
% 22.30/4.43 % (20391)Instruction limit reached!
% 22.30/4.43 % (20391)------------------------------
% 22.30/4.43 % (20391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.30/4.43 % (20391)Termination reason: Unknown
% 22.30/4.43 % (20391)Termination phase: Saturation
% 22.30/4.43
% 22.30/4.43 % (20391)Memory used [KB]: 7036
% 22.30/4.43 % (20391)Time elapsed: 0.111 s
% 22.30/4.43 % (20391)Instructions burned: 404 (million)
% 22.30/4.43 % (20391)------------------------------
% 22.30/4.43 % (20391)------------------------------
% 22.30/4.44 % (20395)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_20128 for (2969ds/4528Mi)
% 22.30/4.45 % (20395)Refutation not found, incomplete strategy
% 22.30/4.45 % (20395)------------------------------
% 22.30/4.45 % (20395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.30/4.45 % (20395)Termination reason: Refutation not found, incomplete strategy
% 22.30/4.45
% 22.30/4.45
% 22.30/4.45 % (20395)Memory used [KB]: 1535
% 22.30/4.45 % (20395)Time elapsed: 0.009 s
% 22.30/4.45 % (20395)Instructions burned: 28 (million)
% 22.30/4.45 % (20395)------------------------------
% 22.30/4.45 % (20395)------------------------------
% 22.30/4.46 % (20396)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_20128 for (2969ds/1001Mi)
% 22.81/4.52 % (20384)Instruction limit reached!
% 22.81/4.52 % (20384)------------------------------
% 22.81/4.52 % (20384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.81/4.52 % (20384)Termination reason: Unknown
% 22.81/4.52 % (20384)Termination phase: Saturation
% 22.81/4.52
% 22.81/4.52 % (20384)Memory used [KB]: 13432
% 22.81/4.52 % (20384)Time elapsed: 0.544 s
% 22.81/4.52 % (20384)Instructions burned: 1980 (million)
% 22.81/4.52 % (20384)------------------------------
% 22.81/4.52 % (20384)------------------------------
% 22.81/4.53 % (20397)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_20128 for (2969ds/102Mi)
% 22.81/4.55 % (20397)Instruction limit reached!
% 22.81/4.55 % (20397)------------------------------
% 22.81/4.55 % (20397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.81/4.55 % (20397)Termination reason: Unknown
% 22.81/4.55 % (20397)Termination phase: Saturation
% 22.81/4.55
% 22.81/4.55 % (20397)Memory used [KB]: 6012
% 22.81/4.55 % (20397)Time elapsed: 0.027 s
% 22.81/4.55 % (20397)Instructions burned: 105 (million)
% 22.81/4.55 % (20397)------------------------------
% 22.81/4.55 % (20397)------------------------------
% 22.81/4.56 % (20398)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_20128 for (2968ds/952Mi)
% 22.81/4.59 % (20375)Instruction limit reached!
% 22.81/4.59 % (20375)------------------------------
% 22.81/4.59 % (20375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.81/4.59 % (20375)Termination reason: Unknown
% 22.81/4.59 % (20375)Termination phase: Saturation
% 22.81/4.59
% 22.81/4.59 % (20375)Memory used [KB]: 12537
% 22.81/4.59 % (20375)Time elapsed: 0.807 s
% 22.81/4.59 % (20375)Instructions burned: 3373 (million)
% 22.81/4.59 % (20375)------------------------------
% 22.81/4.59 % (20375)------------------------------
% 23.07/4.60 % (20399)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_20128 for (2968ds/578Mi)
% 23.07/4.62 % (20388)Instruction limit reached!
% 23.07/4.62 % (20388)------------------------------
% 23.07/4.62 % (20388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.07/4.62 % (20388)Termination reason: Unknown
% 23.07/4.62 % (20388)Termination phase: Saturation
% 23.07/4.62
% 23.07/4.62 % (20388)Memory used [KB]: 8059
% 23.07/4.62 % (20388)Time elapsed: 0.489 s
% 23.07/4.62 % (20388)Instructions burned: 1673 (million)
% 23.07/4.62 % (20388)------------------------------
% 23.07/4.62 % (20388)------------------------------
% 23.07/4.63 % (20400)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_20128 for (2968ds/643Mi)
% 23.07/4.65 % (20394)Instruction limit reached!
% 23.07/4.65 % (20394)------------------------------
% 23.07/4.65 % (20394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.07/4.65 % (20394)Termination reason: Unknown
% 23.07/4.65 % (20394)Termination phase: Saturation
% 23.07/4.65
% 23.07/4.65 % (20394)Memory used [KB]: 7675
% 23.07/4.65 % (20394)Time elapsed: 0.237 s
% 23.07/4.65 % (20394)Instructions burned: 867 (million)
% 23.07/4.65 % (20394)------------------------------
% 23.07/4.65 % (20394)------------------------------
% 23.07/4.67 % (20401)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_20128 for (2967ds/865Mi)
% 23.07/4.68 % (20401)Refutation not found, incomplete strategy
% 23.07/4.68 % (20401)------------------------------
% 23.07/4.68 % (20401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.07/4.68 % (20401)Termination reason: Refutation not found, incomplete strategy
% 23.07/4.68
% 23.07/4.68
% 23.07/4.68 % (20401)Memory used [KB]: 6012
% 23.07/4.68 % (20401)Time elapsed: 0.018 s
% 23.07/4.68 % (20401)Instructions burned: 59 (million)
% 23.07/4.68 % (20401)------------------------------
% 23.07/4.68 % (20401)------------------------------
% 23.07/4.69 % (20402)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_20128 for (2967ds/1174Mi)
% 23.95/4.72 % (20396)Instruction limit reached!
% 23.95/4.72 % (20396)------------------------------
% 23.95/4.72 % (20396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.95/4.73 % (20396)Termination reason: Unknown
% 23.95/4.73 % (20396)Termination phase: Saturation
% 23.95/4.73
% 23.95/4.73 % (20396)Memory used [KB]: 9722
% 23.95/4.73 % (20396)Time elapsed: 0.270 s
% 23.95/4.73 % (20396)Instructions burned: 1001 (million)
% 23.95/4.73 % (20396)------------------------------
% 23.95/4.73 % (20396)------------------------------
% 23.95/4.74 % (20403)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_20128 for (2966ds/644Mi)
% 23.95/4.75 % (20399)Instruction limit reached!
% 23.95/4.75 % (20399)------------------------------
% 23.95/4.75 % (20399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.95/4.75 % (20399)Termination reason: Unknown
% 23.95/4.75 % (20399)Termination phase: Saturation
% 23.95/4.75
% 23.95/4.75 % (20399)Memory used [KB]: 6780
% 23.95/4.75 % (20399)Time elapsed: 0.152 s
% 23.95/4.75 % (20399)Instructions burned: 579 (million)
% 23.95/4.75 % (20399)------------------------------
% 23.95/4.75 % (20399)------------------------------
% 23.95/4.76 % (20404)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_20128 for (2966ds/1201Mi)
% 24.50/4.81 % (20400)Instruction limit reached!
% 24.50/4.81 % (20400)------------------------------
% 24.50/4.81 % (20400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.50/4.81 % (20400)Termination reason: Unknown
% 24.50/4.81 % (20400)Termination phase: Saturation
% 24.50/4.81
% 24.50/4.81 % (20400)Memory used [KB]: 7164
% 24.50/4.81 % (20400)Time elapsed: 0.177 s
% 24.50/4.81 % (20400)Instructions burned: 643 (million)
% 24.50/4.81 % (20400)------------------------------
% 24.50/4.81 % (20400)------------------------------
% 24.50/4.82 % (20405)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_20128 for (2966ds/1046Mi)
% 24.50/4.82 % (20398)Instruction limit reached!
% 24.50/4.82 % (20398)------------------------------
% 24.50/4.82 % (20398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.50/4.82 % (20398)Termination reason: Unknown
% 24.50/4.82 % (20398)Termination phase: Saturation
% 24.50/4.82
% 24.50/4.82 % (20398)Memory used [KB]: 9466
% 24.50/4.82 % (20398)Time elapsed: 0.258 s
% 24.50/4.82 % (20398)Instructions burned: 954 (million)
% 24.50/4.82 % (20398)------------------------------
% 24.50/4.82 % (20398)------------------------------
% 24.50/4.83 % (20406)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_20128 for (2966ds/222Mi)
% 24.50/4.88 % (20406)Instruction limit reached!
% 24.50/4.88 % (20406)------------------------------
% 24.50/4.88 % (20406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.50/4.88 % (20406)Termination reason: Unknown
% 24.50/4.88 % (20406)Termination phase: Saturation
% 24.50/4.88
% 24.50/4.88 % (20406)Memory used [KB]: 6012
% 24.50/4.88 % (20406)Time elapsed: 0.055 s
% 24.50/4.88 % (20406)Instructions burned: 225 (million)
% 24.50/4.88 % (20406)------------------------------
% 24.50/4.88 % (20406)------------------------------
% 24.50/4.89 % (20407)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_20128 for (2965ds/68Mi)
% 25.10/4.91 % (20407)Instruction limit reached!
% 25.10/4.91 % (20407)------------------------------
% 25.10/4.91 % (20407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.10/4.91 % (20407)Termination reason: Unknown
% 25.10/4.91 % (20407)Termination phase: Saturation
% 25.10/4.91
% 25.10/4.91 % (20407)Memory used [KB]: 6140
% 25.10/4.91 % (20407)Time elapsed: 0.019 s
% 25.10/4.91 % (20407)Instructions burned: 68 (million)
% 25.10/4.91 % (20407)------------------------------
% 25.10/4.91 % (20407)------------------------------
% 25.10/4.91 % (20403)Instruction limit reached!
% 25.10/4.91 % (20403)------------------------------
% 25.10/4.91 % (20403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.10/4.91 % (20403)Termination reason: Unknown
% 25.10/4.91 % (20403)Termination phase: Saturation
% 25.10/4.91
% 25.10/4.91 % (20403)Memory used [KB]: 7803
% 25.10/4.91 % (20403)Time elapsed: 0.180 s
% 25.10/4.91 % (20403)Instructions burned: 645 (million)
% 25.10/4.91 % (20403)------------------------------
% 25.10/4.91 % (20403)------------------------------
% 25.10/4.92 % (20408)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_20128 for (2965ds/454Mi)
% 25.10/4.92 % (20409)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_20128 for (2965ds/360Mi)
% 25.10/5.01 % (20402)Instruction limit reached!
% 25.10/5.01 % (20402)------------------------------
% 25.10/5.01 % (20402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.10/5.01 % (20402)Termination reason: Unknown
% 25.10/5.01 % (20402)Termination phase: Saturation
% 25.10/5.01
% 25.10/5.01 % (20402)Memory used [KB]: 10106
% 25.10/5.01 % (20402)Time elapsed: 0.321 s
% 25.10/5.01 % (20402)Instructions burned: 1176 (million)
% 25.10/5.01 % (20402)------------------------------
% 25.10/5.01 % (20402)------------------------------
% 27.05/5.02 % (20409)Instruction limit reached!
% 27.05/5.02 % (20409)------------------------------
% 27.05/5.02 % (20409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.05/5.02 % (20409)Termination reason: Unknown
% 27.05/5.02 % (20409)Termination phase: Saturation
% 27.05/5.02
% 27.05/5.02 % (20409)Memory used [KB]: 6652
% 27.05/5.02 % (20409)Time elapsed: 0.096 s
% 27.05/5.02 % (20409)Instructions burned: 362 (million)
% 27.05/5.02 % (20409)------------------------------
% 27.05/5.02 % (20409)------------------------------
% 27.05/5.02 % (20410)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_20128 for (2964ds/157Mi)
% 27.05/5.03 % (20411)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_20128 for (2964ds/5061Mi)
% 27.05/5.04 % (20408)Instruction limit reached!
% 27.05/5.04 % (20408)------------------------------
% 27.05/5.04 % (20408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.05/5.04 % (20408)Termination reason: Unknown
% 27.05/5.04 % (20408)Termination phase: Saturation
% 27.05/5.04
% 27.05/5.04 % (20408)Memory used [KB]: 11001
% 27.05/5.04 % (20408)Time elapsed: 0.117 s
% 27.05/5.04 % (20408)Instructions burned: 455 (million)
% 27.05/5.04 % (20408)------------------------------
% 27.05/5.04 % (20408)------------------------------
% 27.05/5.05 % (20412)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_20128 for (2963ds/2401Mi)
% 27.05/5.06 % (20404)Instruction limit reached!
% 27.05/5.06 % (20404)------------------------------
% 27.05/5.06 % (20404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.05/5.06 % (20404)Termination reason: Unknown
% 27.05/5.06 % (20404)Termination phase: Saturation
% 27.05/5.06
% 27.05/5.06 % (20404)Memory used [KB]: 6652
% 27.05/5.06 % (20404)Time elapsed: 0.299 s
% 27.05/5.06 % (20404)Instructions burned: 1204 (million)
% 27.05/5.06 % (20404)------------------------------
% 27.05/5.06 % (20404)------------------------------
% 27.05/5.06 % (20410)Instruction limit reached!
% 27.05/5.06 % (20410)------------------------------
% 27.05/5.06 % (20410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.05/5.06 % (20410)Termination reason: Unknown
% 27.05/5.06 % (20410)Termination phase: Saturation
% 27.05/5.06
% 27.05/5.06 % (20410)Memory used [KB]: 6012
% 27.05/5.06 % (20410)Time elapsed: 0.044 s
% 27.05/5.06 % (20410)Instructions burned: 159 (million)
% 27.05/5.06 % (20410)------------------------------
% 27.05/5.06 % (20410)------------------------------
% 27.05/5.07 % (20413)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_20128 for (2963ds/5798Mi)
% 27.05/5.08 % (20414)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_20128 for (2963ds/346Mi)
% 27.52/5.13 % (20405)Instruction limit reached!
% 27.52/5.13 % (20405)------------------------------
% 27.52/5.13 % (20405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.13 % (20405)Termination reason: Unknown
% 27.52/5.13 % (20405)Termination phase: Saturation
% 27.52/5.13
% 27.52/5.13 % (20405)Memory used [KB]: 8571
% 27.52/5.13 % (20405)Time elapsed: 0.315 s
% 27.52/5.13 % (20405)Instructions burned: 1048 (million)
% 27.52/5.13 % (20405)------------------------------
% 27.52/5.13 % (20405)------------------------------
% 27.52/5.14 % (20415)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_20128 for (2962ds/1321Mi)
% 27.52/5.16 % (20415)Refutation not found, incomplete strategy
% 27.52/5.16 % (20415)------------------------------
% 27.52/5.16 % (20415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.16 % (20415)Termination reason: Refutation not found, incomplete strategy
% 27.52/5.16
% 27.52/5.16
% 27.52/5.16 % (20415)Memory used [KB]: 1535
% 27.52/5.16 % (20415)Time elapsed: 0.014 s
% 27.52/5.16 % (20415)Instructions burned: 46 (million)
% 27.52/5.16 % (20415)------------------------------
% 27.52/5.16 % (20415)------------------------------
% 27.52/5.17 % (20414)Instruction limit reached!
% 27.52/5.17 % (20414)------------------------------
% 27.52/5.17 % (20414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.17 % (20414)Termination reason: Unknown
% 27.52/5.17 % (20414)Termination phase: Saturation
% 27.52/5.17
% 27.52/5.17 % (20414)Memory used [KB]: 6396
% 27.52/5.17 % (20414)Time elapsed: 0.087 s
% 27.52/5.17 % (20414)Instructions burned: 348 (million)
% 27.52/5.17 % (20414)------------------------------
% 27.52/5.17 % (20414)------------------------------
% 27.52/5.17 % (20416)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_20128 for (2962ds/1312Mi)
% 27.52/5.18 % (20417)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_20128 for (2962ds/672Mi)
% 27.52/5.18 % (20417)Refutation not found, incomplete strategy
% 27.52/5.18 % (20417)------------------------------
% 27.52/5.18 % (20417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.18 % (20417)Termination reason: Refutation not found, incomplete strategy
% 27.52/5.18
% 27.52/5.18
% 27.52/5.18 % (20417)Memory used [KB]: 6012
% 27.52/5.18 % (20417)Time elapsed: 0.009 s
% 27.52/5.18 % (20417)Instructions burned: 28 (million)
% 27.52/5.18 % (20417)------------------------------
% 27.52/5.18 % (20417)------------------------------
% 27.52/5.19 % (20418)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_20128 for (2962ds/1897Mi)
% 27.87/5.20 % (20418)Refutation not found, incomplete strategy
% 27.87/5.20 % (20418)------------------------------
% 27.87/5.20 % (20418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.87/5.20 % (20418)Termination reason: Refutation not found, incomplete strategy
% 27.87/5.20
% 27.87/5.20
% 27.87/5.20 % (20418)Memory used [KB]: 6012
% 27.87/5.20 % (20418)Time elapsed: 0.010 s
% 27.87/5.20 % (20418)Instructions burned: 30 (million)
% 27.87/5.20 % (20418)------------------------------
% 27.87/5.20 % (20418)------------------------------
% 27.87/5.21 % (20419)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_20128 for (2962ds/1202Mi)
% 28.28/5.49 % (20348)Instruction limit reached!
% 28.28/5.49 % (20348)------------------------------
% 28.28/5.49 % (20348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.28/5.49 % (20348)Termination reason: Unknown
% 28.28/5.49 % (20348)Termination phase: Saturation
% 28.28/5.49
% 28.28/5.49 % (20348)Memory used [KB]: 33901
% 28.28/5.49 % (20348)Time elapsed: 2.576 s
% 28.28/5.49 % (20348)Instructions burned: 8251 (million)
% 28.28/5.49 % (20348)------------------------------
% 28.28/5.49 % (20348)------------------------------
% 28.28/5.49 % (20416)Instruction limit reached!
% 28.28/5.49 % (20416)------------------------------
% 28.28/5.49 % (20416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.28/5.49 % (20416)Termination reason: Unknown
% 28.28/5.49 % (20416)Termination phase: Saturation
% 28.28/5.49
% 28.28/5.49 % (20416)Memory used [KB]: 6780
% 28.28/5.49 % (20416)Time elapsed: 0.328 s
% 28.28/5.49 % (20416)Instructions burned: 1312 (million)
% 28.28/5.49 % (20416)------------------------------
% 28.28/5.49 % (20416)------------------------------
% 28.83/5.50 % (20420)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_20128 for (2959ds/1493Mi)
% 28.83/5.50 % (20421)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_20128 for (2959ds/7679Mi)
% 28.83/5.51 % (20420)Refutation not found, incomplete strategy
% 28.83/5.51 % (20420)------------------------------
% 28.83/5.51 % (20420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.51 % (20420)Termination reason: Refutation not found, incomplete strategy
% 28.83/5.51
% 28.83/5.51
% 28.83/5.51 % (20420)Memory used [KB]: 6012
% 28.83/5.51 % (20420)Time elapsed: 0.011 s
% 28.83/5.51 % (20420)Instructions burned: 35 (million)
% 28.83/5.51 % (20420)------------------------------
% 28.83/5.51 % (20420)------------------------------
% 28.83/5.51 % (20421)Refutation not found, incomplete strategy
% 28.83/5.51 % (20421)------------------------------
% 28.83/5.51 % (20421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.51 % (20421)Termination reason: Refutation not found, incomplete strategy
% 28.83/5.51
% 28.83/5.51
% 28.83/5.51 % (20421)Memory used [KB]: 1535
% 28.83/5.51 % (20421)Time elapsed: 0.010 s
% 28.83/5.51 % (20421)Instructions burned: 33 (million)
% 28.83/5.51 % (20421)------------------------------
% 28.83/5.51 % (20421)------------------------------
% 28.83/5.52 % (20422)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_20128 for (2959ds/340Mi)
% 28.83/5.52 % (20423)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_20128 for (2959ds/3672Mi)
% 28.83/5.54 % (20422)Refutation not found, incomplete strategy
% 28.83/5.54 % (20422)------------------------------
% 28.83/5.54 % (20422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.54 % (20422)Termination reason: Refutation not found, incomplete strategy
% 28.83/5.54
% 28.83/5.54
% 28.83/5.54 % (20422)Memory used [KB]: 6140
% 28.83/5.54 % (20422)Time elapsed: 0.022 s
% 28.83/5.54 % (20422)Instructions burned: 82 (million)
% 28.83/5.54 % (20422)------------------------------
% 28.83/5.54 % (20422)------------------------------
% 28.83/5.55 % (20424)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_20128 for (2958ds/1535Mi)
% 28.83/5.58 % (20419)Instruction limit reached!
% 28.83/5.58 % (20419)------------------------------
% 28.83/5.58 % (20419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.83/5.58 % (20419)Termination reason: Unknown
% 28.83/5.58 % (20419)Termination phase: Saturation
% 28.83/5.58
% 28.83/5.58 % (20419)Memory used [KB]: 2814
% 28.83/5.58 % (20419)Time elapsed: 0.368 s
% 28.83/5.58 % (20419)Instructions burned: 1202 (million)
% 28.83/5.58 % (20419)------------------------------
% 28.83/5.58 % (20419)------------------------------
% 28.83/5.59 % (20425)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_20128 for (2958ds/4637Mi)
% 29.47/5.72 % (20412)Instruction limit reached!
% 29.47/5.72 % (20412)------------------------------
% 29.47/5.72 % (20412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.47/5.72 % (20412)Termination reason: Unknown
% 29.47/5.72 % (20412)Termination phase: Saturation
% 29.47/5.72
% 29.47/5.72 % (20412)Memory used [KB]: 9978
% 29.47/5.72 % (20412)Time elapsed: 0.672 s
% 29.47/5.72 % (20412)Instructions burned: 2401 (million)
% 29.47/5.72 % (20412)------------------------------
% 29.47/5.72 % (20412)------------------------------
% 29.47/5.73 % (20426)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_20128 for (2957ds/3174Mi)
% 30.36/5.92 % (20424)Instruction limit reached!
% 30.36/5.92 % (20424)------------------------------
% 30.36/5.92 % (20424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.36/5.92 % (20424)Termination reason: Unknown
% 30.36/5.92 % (20424)Termination phase: Saturation
% 30.36/5.92
% 30.36/5.92 % (20424)Memory used [KB]: 8571
% 30.36/5.92 % (20424)Time elapsed: 0.387 s
% 30.36/5.92 % (20424)Instructions burned: 1537 (million)
% 30.36/5.92 % (20424)------------------------------
% 30.36/5.92 % (20424)------------------------------
% 30.36/5.93 % (20427)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_20128 for (2955ds/307Mi)
% 30.36/6.01 % (20427)Instruction limit reached!
% 30.36/6.01 % (20427)------------------------------
% 30.36/6.01 % (20427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.36/6.01 % (20427)Termination reason: Unknown
% 30.36/6.01 % (20427)Termination phase: Saturation
% 30.36/6.01
% 30.36/6.01 % (20427)Memory used [KB]: 6140
% 30.36/6.01 % (20427)Time elapsed: 0.080 s
% 30.36/6.01 % (20427)Instructions burned: 307 (million)
% 30.36/6.01 % (20427)------------------------------
% 30.36/6.01 % (20427)------------------------------
% 34.04/6.02 % (20428)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_20128 for (2954ds/3619Mi)
% 34.04/6.03 % (20428)Refutation not found, incomplete strategy
% 34.04/6.03 % (20428)------------------------------
% 34.04/6.03 % (20428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.04/6.03 % (20428)Termination reason: Refutation not found, incomplete strategy
% 34.04/6.03
% 34.04/6.03
% 34.04/6.03 % (20428)Memory used [KB]: 6012
% 34.04/6.03 % (20428)Time elapsed: 0.014 s
% 34.04/6.03 % (20428)Instructions burned: 48 (million)
% 34.04/6.03 % (20428)------------------------------
% 34.04/6.03 % (20428)------------------------------
% 34.04/6.04 % (20429)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_20128 for (2953ds/2325Mi)
% 34.66/6.15 % (20392)Instruction limit reached!
% 34.66/6.15 % (20392)------------------------------
% 34.66/6.15 % (20392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.66/6.15 % (20392)Termination reason: Unknown
% 34.66/6.15 % (20392)Termination phase: Saturation
% 34.66/6.15
% 34.66/6.15 % (20392)Memory used [KB]: 29167
% 34.66/6.15 % (20392)Time elapsed: 1.826 s
% 34.66/6.15 % (20392)Instructions burned: 6456 (million)
% 34.66/6.15 % (20392)------------------------------
% 34.66/6.15 % (20392)------------------------------
% 34.66/6.16 % (20430)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_20128 for (2952ds/2341Mi)
% 36.12/6.44 % (20411)Instruction limit reached!
% 36.12/6.44 % (20411)------------------------------
% 36.12/6.44 % (20411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.12/6.44 % (20411)Termination reason: Unknown
% 36.12/6.44 % (20411)Termination phase: Saturation
% 36.12/6.44
% 36.12/6.44 % (20411)Memory used [KB]: 8059
% 36.12/6.44 % (20411)Time elapsed: 1.415 s
% 36.12/6.44 % (20411)Instructions burned: 5061 (million)
% 36.12/6.44 % (20411)------------------------------
% 36.12/6.44 % (20411)------------------------------
% 36.12/6.45 % (20431)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_20128 for (2949ds/7257Mi)
% 36.12/6.46 % (20431)Refutation not found, incomplete strategy
% 36.12/6.46 % (20431)------------------------------
% 36.12/6.46 % (20431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.12/6.46 % (20431)Termination reason: Refutation not found, incomplete strategy
% 36.12/6.46
% 36.12/6.46
% 36.12/6.46 % (20431)Memory used [KB]: 6012
% 36.12/6.46 % (20431)Time elapsed: 0.010 s
% 36.12/6.46 % (20431)Instructions burned: 30 (million)
% 36.12/6.46 % (20431)------------------------------
% 36.12/6.46 % (20431)------------------------------
% 36.12/6.47 % (20432)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_20128 for (2949ds/3710Mi)
% 36.58/6.56 % (20423)Instruction limit reached!
% 36.58/6.56 % (20423)------------------------------
% 36.58/6.56 % (20423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.58/6.56 % (20423)Termination reason: Unknown
% 36.58/6.56 % (20423)Termination phase: Saturation
% 36.58/6.56
% 36.58/6.56 % (20423)Memory used [KB]: 18677
% 36.58/6.56 % (20423)Time elapsed: 1.042 s
% 36.58/6.56 % (20423)Instructions burned: 3675 (million)
% 36.58/6.56 % (20423)------------------------------
% 36.58/6.56 % (20423)------------------------------
% 36.58/6.58 % (20433)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_20128 for (2948ds/326Mi)
% 36.58/6.58 % (20433)Refutation not found, incomplete strategy
% 36.58/6.58 % (20433)------------------------------
% 36.58/6.58 % (20433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.58/6.58 % (20433)Termination reason: Refutation not found, incomplete strategy
% 36.58/6.58
% 36.58/6.58
% 36.58/6.58 % (20433)Memory used [KB]: 6012
% 36.58/6.58 % (20433)Time elapsed: 0.010 s
% 36.58/6.58 % (20433)Instructions burned: 30 (million)
% 36.58/6.58 % (20433)------------------------------
% 36.58/6.58 % (20433)------------------------------
% 36.58/6.59 % (20434)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_20128 for (2948ds/1100Mi)
% 37.00/6.60 % (20426)Instruction limit reached!
% 37.00/6.60 % (20426)------------------------------
% 37.00/6.60 % (20426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.60 % (20426)Termination reason: Unknown
% 37.00/6.60 % (20426)Termination phase: Saturation
% 37.00/6.60
% 37.00/6.60 % (20426)Memory used [KB]: 16119
% 37.00/6.60 % (20426)Time elapsed: 0.900 s
% 37.00/6.60 % (20426)Instructions burned: 3176 (million)
% 37.00/6.60 % (20426)------------------------------
% 37.00/6.60 % (20426)------------------------------
% 37.00/6.61 % (20434)Refutation not found, incomplete strategy
% 37.00/6.61 % (20434)------------------------------
% 37.00/6.61 % (20434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.61 % (20434)Termination reason: Refutation not found, incomplete strategy
% 37.00/6.61
% 37.00/6.61
% 37.00/6.61 % (20434)Memory used [KB]: 6140
% 37.00/6.61 % (20434)Time elapsed: 0.015 s
% 37.00/6.61 % (20434)Instructions burned: 51 (million)
% 37.00/6.61 % (20434)------------------------------
% 37.00/6.61 % (20434)------------------------------
% 37.00/6.62 % (20435)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_20128 for (2948ds/406Mi)
% 37.00/6.62 % (20436)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_20128 for (2948ds/1871Mi)
% 37.00/6.64 % (20435)Refutation not found, incomplete strategy
% 37.00/6.64 % (20435)------------------------------
% 37.00/6.64 % (20435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.64 % (20435)Termination reason: Refutation not found, incomplete strategy
% 37.00/6.64
% 37.00/6.64
% 37.00/6.64 % (20435)Memory used [KB]: 6140
% 37.00/6.64 % (20435)Time elapsed: 0.024 s
% 37.00/6.64 % (20435)Instructions burned: 85 (million)
% 37.00/6.64 % (20435)------------------------------
% 37.00/6.64 % (20435)------------------------------
% 37.00/6.65 % (20437)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_20128 for (2947ds/1194Mi)
% 37.00/6.69 % (20429)Instruction limit reached!
% 37.00/6.69 % (20429)------------------------------
% 37.00/6.69 % (20429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.69 % (20429)Termination reason: Unknown
% 37.00/6.69 % (20429)Termination phase: Saturation
% 37.00/6.69
% 37.00/6.69 % (20429)Memory used [KB]: 13816
% 37.00/6.69 % (20429)Time elapsed: 0.652 s
% 37.00/6.69 % (20429)Instructions burned: 2326 (million)
% 37.00/6.69 % (20429)------------------------------
% 37.00/6.69 % (20429)------------------------------
% 37.94/6.70 % (20438)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_20128 for (2947ds/474Mi)
% 37.94/6.70 % (20413)Instruction limit reached!
% 37.94/6.70 % (20413)------------------------------
% 37.94/6.70 % (20413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.94/6.70 % (20413)Termination reason: Unknown
% 37.94/6.70 % (20413)Termination phase: Saturation
% 37.94/6.70
% 37.94/6.70 % (20413)Memory used [KB]: 18038
% 37.94/6.70 % (20413)Time elapsed: 1.634 s
% 37.94/6.70 % (20413)Instructions burned: 5800 (million)
% 37.94/6.70 % (20413)------------------------------
% 37.94/6.70 % (20413)------------------------------
% 37.94/6.72 % (20439)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_20128 for (2947ds/3115Mi)
% 38.05/6.81 % (20430)Instruction limit reached!
% 38.05/6.81 % (20430)------------------------------
% 38.05/6.81 % (20430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.05/6.81 % (20430)Termination reason: Unknown
% 38.05/6.81 % (20430)Termination phase: Saturation
% 38.05/6.81
% 38.05/6.81 % (20430)Memory used [KB]: 14711
% 38.05/6.81 % (20430)Time elapsed: 0.653 s
% 38.05/6.81 % (20430)Instructions burned: 2342 (million)
% 38.05/6.81 % (20430)------------------------------
% 38.05/6.81 % (20430)------------------------------
% 38.05/6.82 % (20438)Instruction limit reached!
% 38.05/6.82 % (20438)------------------------------
% 38.05/6.82 % (20438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.05/6.82 % (20438)Termination reason: Unknown
% 38.05/6.82 % (20438)Termination phase: Saturation
% 38.05/6.82
% 38.05/6.82 % (20438)Memory used [KB]: 6524
% 38.05/6.82 % (20438)Time elapsed: 0.119 s
% 38.05/6.82 % (20438)Instructions burned: 477 (million)
% 38.05/6.82 % (20438)------------------------------
% 38.05/6.82 % (20438)------------------------------
% 38.05/6.82 % (20440)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_20128 for (2946ds/831Mi)
% 38.05/6.83 % (20441)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_20128 for (2946ds/1188Mi)
% 38.94/6.94 % (20425)Instruction limit reached!
% 38.94/6.94 % (20425)------------------------------
% 38.94/6.94 % (20425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.94/6.94 % (20425)Termination reason: Unknown
% 38.94/6.94 % (20425)Termination phase: Saturation
% 38.94/6.94
% 38.94/6.94 % (20425)Memory used [KB]: 24434
% 38.94/6.94 % (20425)Time elapsed: 1.360 s
% 38.94/6.94 % (20425)Instructions burned: 4638 (million)
% 38.94/6.94 % (20425)------------------------------
% 38.94/6.94 % (20425)------------------------------
% 38.94/6.96 % (20442)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_20128 for (2944ds/2868Mi)
% 38.94/6.97 % (20437)Instruction limit reached!
% 38.94/6.97 % (20437)------------------------------
% 38.94/6.97 % (20437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.94/6.97 % (20437)Termination reason: Unknown
% 38.94/6.97 % (20437)Termination phase: Saturation
% 38.94/6.97
% 38.94/6.97 % (20437)Memory used [KB]: 10106
% 38.94/6.97 % (20437)Time elapsed: 0.326 s
% 38.94/6.97 % (20437)Instructions burned: 1195 (million)
% 38.94/6.97 % (20437)------------------------------
% 38.94/6.97 % (20437)------------------------------
% 38.94/6.98 % (20442)Refutation not found, incomplete strategy
% 38.94/6.98 % (20442)------------------------------
% 38.94/6.98 % (20442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.94/6.98 % (20442)Termination reason: Refutation not found, incomplete strategy
% 38.94/6.98
% 38.94/6.98
% 38.94/6.98 % (20442)Memory used [KB]: 6396
% 38.94/6.98 % (20442)Time elapsed: 0.022 s
% 38.94/6.98 % (20442)Instructions burned: 72 (million)
% 38.94/6.98 % (20442)------------------------------
% 38.94/6.98 % (20442)------------------------------
% 38.94/6.98 % (20443)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_20128 for (2944ds/1516Mi)
% 38.94/6.99 % (20444)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_20128 for (2944ds/2321Mi)
% 38.94/6.99 % (20443)Refutation not found, incomplete strategy
% 38.94/6.99 % (20443)------------------------------
% 38.94/6.99 % (20443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.94/6.99 % (20443)Termination reason: Refutation not found, incomplete strategy
% 38.94/6.99
% 38.94/6.99
% 38.94/6.99 % (20443)Memory used [KB]: 6012
% 38.94/6.99 % (20443)Time elapsed: 0.010 s
% 38.94/6.99 % (20443)Instructions burned: 31 (million)
% 38.94/6.99 % (20443)------------------------------
% 38.94/6.99 % (20443)------------------------------
% 38.94/7.00 % (20445)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_20128 for (2944ds/2812Mi)
% 38.94/7.01 % (20444)Refutation not found, incomplete strategy
% 38.94/7.01 % (20444)------------------------------
% 38.94/7.01 % (20444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.94/7.01 % (20444)Termination reason: Refutation not found, incomplete strategy
% 38.94/7.01
% 38.94/7.01
% 38.94/7.01 % (20444)Memory used [KB]: 6396
% 38.94/7.01 % (20444)Time elapsed: 0.018 s
% 38.94/7.01 % (20444)Instructions burned: 60 (million)
% 38.94/7.01 % (20444)------------------------------
% 38.94/7.01 % (20444)------------------------------
% 41.03/7.02 % (20446)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_20128 for (2944ds/4604Mi)
% 41.03/7.04 % (20440)Instruction limit reached!
% 41.03/7.04 % (20440)------------------------------
% 41.03/7.04 % (20440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.03/7.04 % (20440)Termination reason: Unknown
% 41.03/7.04 % (20440)Termination phase: Saturation
% 41.03/7.04
% 41.03/7.04 % (20440)Memory used [KB]: 9083
% 41.03/7.04 % (20440)Time elapsed: 0.220 s
% 41.03/7.04 % (20440)Instructions burned: 831 (million)
% 41.03/7.04 % (20440)------------------------------
% 41.03/7.04 % (20440)------------------------------
% 41.03/7.05 % (20447)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_20128 for (2943ds/2678Mi)
% 41.56/7.11 % (20441)Instruction limit reached!
% 41.56/7.11 % (20441)------------------------------
% 41.56/7.11 % (20441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.56/7.11 % (20441)Termination reason: Unknown
% 41.56/7.11 % (20441)Termination phase: Saturation
% 41.56/7.11
% 41.56/7.11 % (20441)Memory used [KB]: 6652
% 41.56/7.11 % (20441)Time elapsed: 0.288 s
% 41.56/7.11 % (20441)Instructions burned: 1191 (million)
% 41.56/7.11 % (20441)------------------------------
% 41.56/7.11 % (20441)------------------------------
% 41.56/7.12 % (20448)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_20128 for (2943ds/643Mi)
% 41.56/7.15 % (20436)Instruction limit reached!
% 41.56/7.15 % (20436)------------------------------
% 41.56/7.15 % (20436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.56/7.15 % (20436)Termination reason: Unknown
% 41.56/7.15 % (20436)Termination phase: Saturation
% 41.56/7.15
% 41.56/7.15 % (20436)Memory used [KB]: 12920
% 41.56/7.15 % (20436)Time elapsed: 0.526 s
% 41.56/7.15 % (20436)Instructions burned: 1873 (million)
% 41.56/7.15 % (20436)------------------------------
% 41.56/7.15 % (20436)------------------------------
% 41.56/7.16 % (20449)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_20128 for (2942ds/458Mi)
% 41.88/7.28 % (20449)Instruction limit reached!
% 41.88/7.28 % (20449)------------------------------
% 41.88/7.28 % (20449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.88/7.28 % (20449)Termination reason: Unknown
% 41.88/7.28 % (20449)Termination phase: Saturation
% 41.88/7.28
% 41.88/7.28 % (20449)Memory used [KB]: 6652
% 41.88/7.28 % (20449)Time elapsed: 0.126 s
% 41.88/7.28 % (20449)Instructions burned: 458 (million)
% 41.88/7.28 % (20449)------------------------------
% 41.88/7.28 % (20449)------------------------------
% 41.88/7.29 % (20450)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_20128 for (2941ds/2546Mi)
% 41.88/7.29 % (20448)Instruction limit reached!
% 41.88/7.29 % (20448)------------------------------
% 41.88/7.29 % (20448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.88/7.29 % (20448)Termination reason: Unknown
% 41.88/7.29 % (20448)Termination phase: Saturation
% 41.88/7.29
% 41.88/7.29 % (20448)Memory used [KB]: 7036
% 41.88/7.29 % (20448)Time elapsed: 0.171 s
% 41.88/7.29 % (20448)Instructions burned: 644 (million)
% 41.88/7.29 % (20448)------------------------------
% 41.88/7.29 % (20448)------------------------------
% 42.48/7.30 % (20451)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_20128 for (2941ds/1432Mi)
% 42.48/7.37 % (20432)Instruction limit reached!
% 42.48/7.37 % (20432)------------------------------
% 42.48/7.37 % (20432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.48/7.37 % (20432)Termination reason: Unknown
% 42.48/7.37 % (20432)Termination phase: Saturation
% 42.48/7.37
% 42.48/7.37 % (20432)Memory used [KB]: 9338
% 42.48/7.37 % (20432)Time elapsed: 0.903 s
% 42.48/7.37 % (20432)Instructions burned: 3712 (million)
% 42.48/7.37 % (20432)------------------------------
% 42.48/7.37 % (20432)------------------------------
% 42.48/7.38 % (20452)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_20128 for (2940ds/386Mi)
% 42.76/7.47 % (20439)Instruction limit reached!
% 42.76/7.47 % (20439)------------------------------
% 42.76/7.47 % (20439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.76/7.47 % (20439)Termination reason: Unknown
% 42.76/7.47 % (20439)Termination phase: Saturation
% 42.76/7.47
% 42.76/7.47 % (20439)Memory used [KB]: 6908
% 42.76/7.47 % (20439)Time elapsed: 0.757 s
% 42.76/7.47 % (20439)Instructions burned: 3116 (million)
% 42.76/7.47 % (20439)------------------------------
% 42.76/7.47 % (20439)------------------------------
% 42.76/7.48 % (20453)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_20128 for (2939ds/360Mi)
% 42.76/7.49 % (20452)Instruction limit reached!
% 42.76/7.49 % (20452)------------------------------
% 42.76/7.49 % (20452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.76/7.49 % (20452)Termination reason: Unknown
% 42.76/7.49 % (20452)Termination phase: Saturation
% 42.76/7.49
% 42.76/7.49 % (20452)Memory used [KB]: 7036
% 42.76/7.49 % (20452)Time elapsed: 0.103 s
% 42.76/7.49 % (20452)Instructions burned: 388 (million)
% 42.76/7.49 % (20452)------------------------------
% 42.76/7.49 % (20452)------------------------------
% 42.76/7.50 % (20454)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_20128 for (2939ds/5446Mi)
% 43.06/7.57 % (20453)Instruction limit reached!
% 43.06/7.57 % (20453)------------------------------
% 43.06/7.57 % (20453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.06/7.57 % (20453)Termination reason: Unknown
% 43.06/7.57 % (20453)Termination phase: Saturation
% 43.06/7.57
% 43.06/7.57 % (20453)Memory used [KB]: 6652
% 43.06/7.57 % (20453)Time elapsed: 0.095 s
% 43.06/7.57 % (20453)Instructions burned: 362 (million)
% 43.06/7.57 % (20453)------------------------------
% 43.06/7.57 % (20453)------------------------------
% 43.06/7.58 % (20455)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_20128 for (2938ds/2573Mi)
% 43.28/7.60 % (20451)Instruction limit reached!
% 43.28/7.60 % (20451)------------------------------
% 43.28/7.60 % (20451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.28/7.60 % (20451)Termination reason: Unknown
% 43.28/7.60 % (20451)Termination phase: Saturation
% 43.28/7.60
% 43.28/7.60 % (20451)Memory used [KB]: 8315
% 43.28/7.60 % (20451)Time elapsed: 0.300 s
% 43.28/7.60 % (20451)Instructions burned: 1434 (million)
% 43.28/7.60 % (20451)------------------------------
% 43.28/7.60 % (20451)------------------------------
% 43.28/7.61 % (20456)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_20128 for (2938ds/2655Mi)
% 43.68/7.78 % (20447)Instruction limit reached!
% 43.68/7.78 % (20447)------------------------------
% 43.68/7.78 % (20447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.68/7.78 % (20447)Termination reason: Unknown
% 43.68/7.78 % (20447)Termination phase: Saturation
% 43.68/7.78
% 43.68/7.78 % (20447)Memory used [KB]: 12409
% 43.68/7.78 % (20447)Time elapsed: 0.733 s
% 43.68/7.78 % (20447)Instructions burned: 2680 (million)
% 43.68/7.78 % (20447)------------------------------
% 43.68/7.78 % (20447)------------------------------
% 43.68/7.79 % (20457)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_20128 for (2936ds/2781Mi)
% 43.68/7.79 % (20445)Instruction limit reached!
% 43.68/7.79 % (20445)------------------------------
% 43.68/7.79 % (20445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.68/7.79 % (20445)Termination reason: Unknown
% 43.68/7.79 % (20445)Termination phase: Saturation
% 43.68/7.79
% 43.68/7.79 % (20445)Memory used [KB]: 15735
% 43.68/7.79 % (20445)Time elapsed: 0.790 s
% 43.68/7.79 % (20445)Instructions burned: 2815 (million)
% 43.68/7.79 % (20445)------------------------------
% 43.68/7.79 % (20445)------------------------------
% 44.54/7.80 % (20458)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_20128 for (2936ds/307Mi)
% 44.54/7.88 % (20458)Instruction limit reached!
% 44.54/7.88 % (20458)------------------------------
% 44.54/7.88 % (20458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.54/7.88 % (20458)Termination reason: Unknown
% 44.54/7.88 % (20458)Termination phase: Saturation
% 44.54/7.88
% 44.54/7.88 % (20458)Memory used [KB]: 6140
% 44.54/7.88 % (20458)Time elapsed: 0.080 s
% 44.54/7.88 % (20458)Instructions burned: 309 (million)
% 44.54/7.88 % (20458)------------------------------
% 44.54/7.88 % (20458)------------------------------
% 44.54/7.89 % (20459)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_20128 for (2935ds/1548Mi)
% 44.62/7.90 % (20459)Refutation not found, incomplete strategy
% 44.62/7.90 % (20459)------------------------------
% 44.62/7.90 % (20459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.62/7.90 % (20459)Termination reason: Refutation not found, incomplete strategy
% 44.62/7.90
% 44.62/7.90
% 44.62/7.90 % (20459)Memory used [KB]: 6012
% 44.62/7.90 % (20459)Time elapsed: 0.010 s
% 44.62/7.90 % (20459)Instructions burned: 28 (million)
% 44.62/7.90 % (20459)------------------------------
% 44.62/7.90 % (20459)------------------------------
% 44.62/7.91 % (20460)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_20128 for (2935ds/5214Mi)
% 48.05/8.07 % (20450)Instruction limit reached!
% 48.05/8.07 % (20450)------------------------------
% 48.05/8.07 % (20450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.05/8.07 % (20450)Termination reason: Unknown
% 48.05/8.07 % (20450)Termination phase: Saturation
% 48.05/8.07
% 48.05/8.07 % (20450)Memory used [KB]: 9850
% 48.05/8.07 % (20450)Time elapsed: 0.777 s
% 48.05/8.07 % (20450)Instructions burned: 2546 (million)
% 48.05/8.07 % (20450)------------------------------
% 48.05/8.07 % (20450)------------------------------
% 48.05/8.08 % (20461)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_20128 for (2933ds/3201Mi)
% 49.16/8.22 % (20456)Instruction limit reached!
% 49.16/8.22 % (20456)------------------------------
% 49.16/8.22 % (20456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.16/8.22 % (20456)Termination reason: Unknown
% 49.16/8.22 % (20456)Termination phase: Saturation
% 49.16/8.22
% 49.16/8.22 % (20456)Memory used [KB]: 6524
% 49.16/8.22 % (20456)Time elapsed: 0.610 s
% 49.16/8.22 % (20456)Instructions burned: 2656 (million)
% 49.16/8.22 % (20456)------------------------------
% 49.16/8.22 % (20456)------------------------------
% 49.16/8.23 % (20462)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_20128 for (2932ds/454Mi)
% 49.16/8.23 % (20455)Instruction limit reached!
% 49.16/8.23 % (20455)------------------------------
% 49.16/8.23 % (20455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.16/8.23 % (20455)Termination reason: Unknown
% 49.16/8.23 % (20455)Termination phase: Saturation
% 49.16/8.23
% 49.16/8.23 % (20455)Memory used [KB]: 7291
% 49.16/8.23 % (20455)Time elapsed: 0.650 s
% 49.16/8.23 % (20455)Instructions burned: 2574 (million)
% 49.16/8.23 % (20455)------------------------------
% 49.16/8.23 % (20455)------------------------------
% 49.16/8.24 % (20463)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_20128 for (2932ds/3049Mi)
% 49.16/8.26 % (20463)Refutation not found, incomplete strategy
% 49.16/8.26 % (20463)------------------------------
% 49.16/8.26 % (20463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.16/8.26 % (20463)Termination reason: Refutation not found, incomplete strategy
% 49.16/8.26
% 49.16/8.26
% 49.16/8.26 % (20463)Memory used [KB]: 6012
% 49.16/8.26 % (20463)Time elapsed: 0.036 s
% 49.16/8.26 % (20463)Instructions burned: 48 (million)
% 49.16/8.26 % (20463)------------------------------
% 49.16/8.26 % (20463)------------------------------
% 49.16/8.27 % (20464)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_20128 for (2931ds/7311Mi)
% 49.16/8.27 % (20464)Refutation not found, incomplete strategy
% 49.16/8.27 % (20464)------------------------------
% 49.16/8.27 % (20464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.16/8.27 % (20464)Termination reason: Refutation not found, incomplete strategy
% 49.16/8.27
% 49.16/8.27
% 49.16/8.27 % (20464)Memory used [KB]: 6012
% 49.16/8.27 % (20464)Time elapsed: 0.031 s
% 49.16/8.27 % (20464)Instructions burned: 28 (million)
% 49.16/8.27 % (20464)------------------------------
% 49.16/8.27 % (20464)------------------------------
% 49.16/8.29 % (20465)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_20128 for (2931ds/6804Mi)
% 49.69/8.30 % (20465)Refutation not found, incomplete strategy
% 49.69/8.30 % (20465)------------------------------
% 49.69/8.30 % (20465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.30 % (20465)Termination reason: Refutation not found, incomplete strategy
% 49.69/8.30
% 49.69/8.30
% 49.69/8.30 % (20465)Memory used [KB]: 6012
% 49.69/8.30 % (20465)Time elapsed: 0.013 s
% 49.69/8.30 % (20465)Instructions burned: 45 (million)
% 49.69/8.30 % (20465)------------------------------
% 49.69/8.30 % (20465)------------------------------
% 49.69/8.31 % (20466)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_20128 for (2931ds/1683Mi)
% 49.69/8.35 % (20462)Instruction limit reached!
% 49.69/8.35 % (20462)------------------------------
% 49.69/8.35 % (20462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.35 % (20462)Termination reason: Unknown
% 49.69/8.35 % (20462)Termination phase: Saturation
% 49.69/8.35
% 49.69/8.35 % (20462)Memory used [KB]: 11257
% 49.69/8.35 % (20462)Time elapsed: 0.141 s
% 49.69/8.35 % (20462)Instructions burned: 454 (million)
% 49.69/8.35 % (20462)------------------------------
% 49.69/8.35 % (20462)------------------------------
% 49.69/8.36 % (20467)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_20128 for (2930ds/4688Mi)
% 49.69/8.38 % (20446)Instruction limit reached!
% 49.69/8.38 % (20446)------------------------------
% 49.69/8.38 % (20446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.38 % (20446)Termination reason: Unknown
% 49.69/8.38 % (20446)Termination phase: Saturation
% 49.69/8.38
% 49.69/8.38 % (20446)Memory used [KB]: 23794
% 49.69/8.38 % (20446)Time elapsed: 1.347 s
% 49.69/8.38 % (20446)Instructions burned: 4605 (million)
% 49.69/8.38 % (20446)------------------------------
% 49.69/8.38 % (20446)------------------------------
% 49.69/8.39 % (20468)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_20128 for (2930ds/2207Mi)
% 50.84/8.61 % (20457)Instruction limit reached!
% 50.84/8.61 % (20457)------------------------------
% 50.84/8.61 % (20457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.84/8.61 % (20457)Termination reason: Unknown
% 50.84/8.61 % (20457)Termination phase: Saturation
% 50.84/8.61
% 50.84/8.61 % (20457)Memory used [KB]: 2814
% 50.84/8.61 % (20457)Time elapsed: 0.823 s
% 50.84/8.61 % (20457)Instructions burned: 2783 (million)
% 50.84/8.61 % (20457)------------------------------
% 50.84/8.61 % (20457)------------------------------
% 50.84/8.62 % (20469)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_20128 for (2928ds/8216Mi)
% 51.06/8.78 % (20466)Instruction limit reached!
% 51.06/8.78 % (20466)------------------------------
% 51.06/8.78 % (20466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.06/8.78 % (20466)Termination reason: Unknown
% 51.06/8.78 % (20466)Termination phase: Saturation
% 51.06/8.78
% 51.06/8.78 % (20466)Memory used [KB]: 12792
% 51.06/8.78 % (20466)Time elapsed: 0.470 s
% 51.06/8.78 % (20466)Instructions burned: 1683 (million)
% 51.06/8.78 % (20466)------------------------------
% 51.06/8.78 % (20466)------------------------------
% 51.06/8.79 % (20470)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_20128 for (2926ds/430Mi)
% 51.94/8.90 % (20470)Instruction limit reached!
% 51.94/8.90 % (20470)------------------------------
% 51.94/8.90 % (20470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.94/8.90 % (20470)Termination reason: Unknown
% 51.94/8.90 % (20470)Termination phase: Saturation
% 51.94/8.90
% 51.94/8.90 % (20470)Memory used [KB]: 6524
% 51.94/8.90 % (20470)Time elapsed: 0.116 s
% 51.94/8.90 % (20470)Instructions burned: 431 (million)
% 51.94/8.90 % (20470)------------------------------
% 51.94/8.90 % (20470)------------------------------
% 51.94/8.91 % (20471)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_20128 for (2925ds/2012Mi)
% 51.94/8.97 % (20461)Instruction limit reached!
% 51.94/8.97 % (20461)------------------------------
% 51.94/8.97 % (20461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.94/8.97 % (20461)Termination reason: Unknown
% 51.94/8.97 % (20461)Termination phase: Saturation
% 51.94/8.97
% 51.94/8.97 % (20461)Memory used [KB]: 16119
% 51.94/8.97 % (20461)Time elapsed: 0.896 s
% 51.94/8.97 % (20461)Instructions burned: 3201 (million)
% 51.94/8.97 % (20461)------------------------------
% 51.94/8.97 % (20461)------------------------------
% 51.94/8.99 % (20472)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_20128 for (2924ds/631Mi)
% 54.97/9.02 % (20454)Instruction limit reached!
% 54.97/9.02 % (20454)------------------------------
% 54.97/9.02 % (20454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.97/9.02 % (20454)Termination reason: Unknown
% 54.97/9.02 % (20454)Termination phase: Saturation
% 54.97/9.02
% 54.97/9.02 % (20454)Memory used [KB]: 25969
% 54.97/9.02 % (20454)Time elapsed: 1.529 s
% 54.97/9.02 % (20454)Instructions burned: 5448 (million)
% 54.97/9.02 % (20454)------------------------------
% 54.97/9.02 % (20454)------------------------------
% 54.97/9.03 % (20468)Instruction limit reached!
% 54.97/9.03 % (20468)------------------------------
% 54.97/9.03 % (20468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.97/9.03 % (20468)Termination reason: Unknown
% 54.97/9.03 % (20468)Termination phase: Saturation
% 54.97/9.03
% 54.97/9.03 % (20468)Memory used [KB]: 14328
% 54.97/9.03 % (20468)Time elapsed: 0.626 s
% 54.97/9.03 % (20468)Instructions burned: 2210 (million)
% 54.97/9.03 % (20468)------------------------------
% 54.97/9.03 % (20468)------------------------------
% 54.97/9.03 % (20473)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_20128 for (2923ds/8785Mi)
% 54.97/9.04 % (20474)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_20128 for (2923ds/739Mi)
% 55.53/9.17 % (20472)Instruction limit reached!
% 55.53/9.17 % (20472)------------------------------
% 55.53/9.17 % (20472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.53/9.17 % (20472)Termination reason: Unknown
% 55.53/9.17 % (20472)Termination phase: Saturation
% 55.53/9.17
% 55.53/9.17 % (20472)Memory used [KB]: 7803
% 55.53/9.17 % (20472)Time elapsed: 0.181 s
% 55.53/9.17 % (20472)Instructions burned: 634 (million)
% 55.53/9.17 % (20472)------------------------------
% 55.53/9.17 % (20472)------------------------------
% 55.53/9.18 % (20475)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_20128 for (2922ds/5473Mi)
% 55.92/9.27 % (20474)Instruction limit reached!
% 55.92/9.27 % (20474)------------------------------
% 55.92/9.27 % (20474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.92/9.27 % (20474)Termination reason: Unknown
% 55.92/9.27 % (20474)Termination phase: Saturation
% 55.92/9.27
% 55.92/9.27 % (20474)Memory used [KB]: 6908
% 55.92/9.27 % (20474)Time elapsed: 0.233 s
% 55.92/9.27 % (20474)Instructions burned: 740 (million)
% 55.92/9.27 % (20474)------------------------------
% 55.92/9.27 % (20474)------------------------------
% 55.92/9.28 % (20476)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_20128 for (2921ds/43570Mi)
% 55.92/9.29 % (20476)Refutation not found, incomplete strategy
% 55.92/9.29 % (20476)------------------------------
% 55.92/9.29 % (20476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.92/9.29 % (20476)Termination reason: Refutation not found, incomplete strategy
% 55.92/9.29
% 55.92/9.29
% 55.92/9.29 % (20476)Memory used [KB]: 6012
% 55.92/9.29 % (20476)Time elapsed: 0.010 s
% 55.92/9.29 % (20476)Instructions burned: 28 (million)
% 55.92/9.29 % (20476)------------------------------
% 55.92/9.29 % (20476)------------------------------
% 56.58/9.30 % (20477)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_20128 for (2921ds/8382Mi)
% 56.58/9.38 % (20460)Instruction limit reached!
% 56.58/9.38 % (20460)------------------------------
% 56.58/9.38 % (20460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.58/9.38 % (20460)Termination reason: Unknown
% 56.58/9.38 % (20460)Termination phase: Saturation
% 56.58/9.38
% 56.58/9.38 % (20460)Memory used [KB]: 25330
% 56.58/9.38 % (20460)Time elapsed: 1.467 s
% 56.58/9.38 % (20460)Instructions burned: 5215 (million)
% 56.58/9.38 % (20460)------------------------------
% 56.58/9.38 % (20460)------------------------------
% 56.58/9.39 % (20478)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_20128 for (2920ds/407Mi)
% 56.96/9.45 % (20471)Instruction limit reached!
% 56.96/9.45 % (20471)------------------------------
% 56.96/9.45 % (20471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.96/9.45 % (20471)Termination reason: Unknown
% 56.96/9.45 % (20471)Termination phase: Saturation
% 56.96/9.45
% 56.96/9.45 % (20471)Memory used [KB]: 19317
% 56.96/9.45 % (20471)Time elapsed: 0.536 s
% 56.96/9.45 % (20471)Instructions burned: 2012 (million)
% 56.96/9.45 % (20471)------------------------------
% 56.96/9.45 % (20471)------------------------------
% 56.96/9.46 % (20479)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_20128 for (2919ds/2971Mi)
% 56.96/9.48 % (20479)Refutation not found, incomplete strategy
% 56.96/9.48 % (20479)------------------------------
% 56.96/9.48 % (20479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.96/9.48 % (20479)Termination reason: Refutation not found, incomplete strategy
% 56.96/9.48
% 56.96/9.48
% 56.96/9.48 % (20479)Memory used [KB]: 6524
% 56.96/9.48 % (20479)Time elapsed: 0.020 s
% 56.96/9.48 % (20479)Instructions burned: 68 (million)
% 56.96/9.48 % (20479)------------------------------
% 56.96/9.48 % (20479)------------------------------
% 56.96/9.49 % (20480)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_20128 for (2919ds/9822Mi)
% 56.96/9.50 % (20478)Instruction limit reached!
% 56.96/9.50 % (20478)------------------------------
% 56.96/9.50 % (20478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.96/9.50 % (20478)Termination reason: Unknown
% 56.96/9.50 % (20478)Termination phase: Saturation
% 56.96/9.50
% 56.96/9.50 % (20478)Memory used [KB]: 7675
% 56.96/9.50 % (20478)Time elapsed: 0.109 s
% 56.96/9.50 % (20478)Instructions burned: 410 (million)
% 56.96/9.50 % (20478)------------------------------
% 56.96/9.50 % (20478)------------------------------
% 57.37/9.50 % (20480)Refutation not found, incomplete strategy
% 57.37/9.50 % (20480)------------------------------
% 57.37/9.50 % (20480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.37/9.50 % (20480)Termination reason: Refutation not found, incomplete strategy
% 57.37/9.50
% 57.37/9.50
% 57.37/9.50 % (20480)Memory used [KB]: 6012
% 57.37/9.50 % (20480)Time elapsed: 0.015 s
% 57.37/9.50 % (20480)Instructions burned: 51 (million)
% 57.37/9.50 % (20480)------------------------------
% 57.37/9.50 % (20480)------------------------------
% 57.37/9.51 % (20481)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_20128 for (2919ds/8425Mi)
% 57.37/9.51 % (20482)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_20128 for (2919ds/3107Mi)
% 57.79/9.70 % (20467)Instruction limit reached!
% 57.79/9.70 % (20467)------------------------------
% 57.79/9.70 % (20467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.79/9.70 % (20467)Termination reason: Unknown
% 57.79/9.70 % (20467)Termination phase: Saturation
% 57.79/9.70
% 57.79/9.70 % (20467)Memory used [KB]: 9722
% 57.79/9.70 % (20467)Time elapsed: 1.343 s
% 57.79/9.70 % (20467)Instructions burned: 4690 (million)
% 57.79/9.70 % (20467)------------------------------
% 57.79/9.70 % (20467)------------------------------
% 57.79/9.71 % (20483)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_20128 for (2917ds/7967Mi)
% 57.79/9.73 % (20483)Refutation not found, incomplete strategy
% 57.79/9.73 % (20483)------------------------------
% 57.79/9.73 % (20483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.79/9.73 % (20483)Termination reason: Refutation not found, incomplete strategy
% 57.79/9.73
% 57.79/9.73
% 57.79/9.73 % (20483)Memory used [KB]: 6268
% 57.79/9.73 % (20483)Time elapsed: 0.017 s
% 57.79/9.73 % (20483)Instructions burned: 62 (million)
% 57.79/9.73 % (20483)------------------------------
% 57.79/9.73 % (20483)------------------------------
% 57.79/9.74 % (20484)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_20128 for (2916ds/3629Mi)
% 64.62/10.41 % (20482)Instruction limit reached!
% 64.62/10.41 % (20482)------------------------------
% 64.62/10.41 % (20482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.62/10.41 % (20482)Termination reason: Unknown
% 64.62/10.41 % (20482)Termination phase: Saturation
% 64.62/10.41
% 64.62/10.41 % (20482)Memory used [KB]: 11513
% 64.62/10.41 % (20482)Time elapsed: 0.885 s
% 64.62/10.41 % (20482)Instructions burned: 3108 (million)
% 64.62/10.41 % (20482)------------------------------
% 64.62/10.41 % (20482)------------------------------
% 64.62/10.42 % (20485)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_20128 for (2910ds/939Mi)
% 66.44/10.71 % (20475)Instruction limit reached!
% 66.44/10.71 % (20475)------------------------------
% 66.44/10.71 % (20475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.44/10.71 % (20475)Termination reason: Unknown
% 66.44/10.71 % (20475)Termination phase: Saturation
% 66.44/10.71
% 66.44/10.71 % (20475)Memory used [KB]: 25458
% 66.44/10.71 % (20475)Time elapsed: 1.532 s
% 66.44/10.71 % (20475)Instructions burned: 5476 (million)
% 66.44/10.71 % (20475)------------------------------
% 66.44/10.71 % (20475)------------------------------
% 66.44/10.71 % (20485)Instruction limit reached!
% 66.44/10.71 % (20485)------------------------------
% 66.44/10.71 % (20485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.44/10.71 % (20485)Termination reason: Unknown
% 66.44/10.71 % (20485)Termination phase: Saturation
% 66.44/10.71
% 66.44/10.71 % (20485)Memory used [KB]: 6268
% 66.44/10.71 % (20485)Time elapsed: 0.292 s
% 66.44/10.71 % (20485)Instructions burned: 939 (million)
% 66.44/10.71 % (20485)------------------------------
% 66.44/10.71 % (20485)------------------------------
% 66.44/10.72 % (20486)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_20128 for (2907ds/1188Mi)
% 66.44/10.72 % (20487)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_20128 for (2907ds/3205Mi)
% 67.26/10.82 % (20484)Instruction limit reached!
% 67.26/10.82 % (20484)------------------------------
% 67.26/10.82 % (20484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.26/10.82 % (20484)Termination reason: Unknown
% 67.26/10.82 % (20484)Termination phase: Saturation
% 67.26/10.82
% 67.26/10.82 % (20484)Memory used [KB]: 12409
% 67.26/10.82 % (20484)Time elapsed: 1.085 s
% 67.26/10.82 % (20484)Instructions burned: 3631 (million)
% 67.26/10.82 % (20484)------------------------------
% 67.26/10.82 % (20484)------------------------------
% 67.26/10.83 % (20488)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_20128 for (2906ds/865Mi)
% 67.26/10.85 % (20488)Refutation not found, incomplete strategy
% 67.26/10.85 % (20488)------------------------------
% 67.26/10.85 % (20488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.26/10.85 % (20488)Termination reason: Refutation not found, incomplete strategy
% 67.26/10.85
% 67.26/10.85
% 67.26/10.85 % (20488)Memory used [KB]: 6012
% 67.26/10.85 % (20488)Time elapsed: 0.018 s
% 67.26/10.85 % (20488)Instructions burned: 60 (million)
% 67.26/10.85 % (20488)------------------------------
% 67.26/10.85 % (20488)------------------------------
% 67.26/10.86 % (20489)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_20128 for (2905ds/7469Mi)
% 67.72/11.01 % (20469)Instruction limit reached!
% 67.72/11.01 % (20469)------------------------------
% 67.72/11.01 % (20469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.72/11.01 % (20469)Termination reason: Unknown
% 67.72/11.01 % (20469)Termination phase: Saturation
% 67.72/11.01
% 67.72/11.01 % (20469)Memory used [KB]: 14583
% 67.72/11.01 % (20469)Time elapsed: 2.384 s
% 67.72/11.01 % (20469)Instructions burned: 8216 (million)
% 67.72/11.01 % (20469)------------------------------
% 67.72/11.01 % (20469)------------------------------
% 67.72/11.01 % (20486)Instruction limit reached!
% 67.72/11.01 % (20486)------------------------------
% 67.72/11.01 % (20486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.72/11.01 % (20486)Termination reason: Unknown
% 67.72/11.01 % (20486)Termination phase: Saturation
% 67.72/11.01
% 67.72/11.01 % (20486)Memory used [KB]: 6652
% 67.72/11.01 % (20486)Time elapsed: 0.294 s
% 67.72/11.01 % (20486)Instructions burned: 1189 (million)
% 67.72/11.01 % (20486)------------------------------
% 67.72/11.01 % (20486)------------------------------
% 68.94/11.02 % (20490)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_20128 for (2904ds/4165Mi)
% 68.94/11.02 % (20491)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_20128 for (2904ds/13468Mi)
% 68.94/11.03 % (20491)Refutation not found, incomplete strategy
% 68.94/11.03 % (20491)------------------------------
% 68.94/11.03 % (20491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.94/11.03 % (20491)Termination reason: Refutation not found, incomplete strategy
% 68.94/11.03
% 68.94/11.03
% 68.94/11.03 % (20491)Memory used [KB]: 6012
% 68.94/11.03 % (20491)Time elapsed: 0.010 s
% 68.94/11.03 % (20491)Instructions burned: 33 (million)
% 68.94/11.03 % (20491)------------------------------
% 68.94/11.03 % (20491)------------------------------
% 68.94/11.04 % (20492)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_20128 for (2904ds/2635Mi)
% 69.45/11.16 % (20489)First to succeed.
% 69.45/11.19 % (20489)Refutation found. Thanks to Tanya!
% 69.45/11.19 % SZS status Theorem for DTF2THF_20128
% 69.45/11.19 % SZS output start Proof for DTF2THF_20128
% 69.45/11.19 thf(type_def_6, type, d_unsorted: $tType).
% 69.45/11.19 thf(func_def_0, type, unsorted: $tType).
% 69.45/11.19 thf(func_def_1, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 69.45/11.19 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 69.45/11.19 thf(func_def_30, type, d_unsorted: $tType).
% 69.45/11.19 thf(func_def_31, type, d2unsorted: d_unsorted > $i).
% 69.45/11.19 thf(func_def_32, type, d_unsorted_0: d_unsorted).
% 69.45/11.19 thf(func_def_54, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 69.45/11.19 thf(func_def_56, type, ph1: !>[X0: $tType]:(X0)).
% 69.45/11.19 thf(func_def_57, type, sK2: $i > $i > $o).
% 69.45/11.19 thf(func_def_58, type, sK3: $i > d_unsorted).
% 69.45/11.19 thf(func_def_59, type, sK4: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_60, type, sK5: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_61, type, sK6: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_62, type, sK7: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_63, type, sK8: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_64, type, sK9: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_65, type, sK10: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_66, type, sK11: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_67, type, sK12: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_71, type, sK16: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_72, type, sK17: (($i > $i > $o) > $i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_73, type, sK18: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_74, type, sK19: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_76, type, sK21: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_77, type, sK22: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_78, type, sK23: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_79, type, sK24: ($i > $i > $o) > $i).
% 69.45/11.19 thf(func_def_80, type, sK25: ($i > $i > $o) > $i > $i > $o).
% 69.45/11.19 thf(func_def_81, type, sK26: ($i > $i > $o) > $i).
% 69.45/11.19 thf(f2789,plain,(
% 69.45/11.19 $false),
% 69.45/11.19 inference(avatar_sat_refutation,[status(thm)],[f136,f1822,f2788])).
% 69.45/11.19 thf(f2788,plain,(
% 69.45/11.19 ~spl0_4),
% 69.45/11.19 inference(avatar_contradiction_clause,[status(thm)],[f2787])).
% 69.45/11.19 thf(f2787,plain,(
% 69.45/11.19 $false | ~spl0_4),
% 69.45/11.19 inference(trivial_inequality_removal,[status(thm)],[f2782])).
% 69.45/11.19 thf(f2782,plain,(
% 69.45/11.19 ($false = $true) | ~spl0_4),
% 69.45/11.19 inference(superposition,[status(thm)],[f131,f2779])).
% 69.45/11.19 thf(f2779,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(subsumption_resolution,[status(thm)],[f2778,f192])).
% 69.45/11.19 thf(f192,plain,(
% 69.45/11.19 ( ! [X2 : $i,X1 : $i] : ((X1 = X2)) )),
% 69.45/11.19 inference(superposition,[status(thm)],[f187,f187])).
% 69.45/11.19 thf(f187,plain,(
% 69.45/11.19 ( ! [X0 : $i,X1 : d_unsorted] : (((d2unsorted @ X1) = X0)) )),
% 69.45/11.19 inference(superposition,[status(thm)],[f185,f121])).
% 69.45/11.19 thf(f121,plain,(
% 69.45/11.19 ( ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1)) )),
% 69.45/11.19 inference(superposition,[status(thm)],[f107,f107])).
% 69.45/11.19 thf(f107,plain,(
% 69.45/11.19 ( ! [X1 : d_unsorted] : ((d_unsorted_0 = X1)) )),
% 69.45/11.19 inference(equality_proxy_clausification,[status(thm)],[f106])).
% 69.45/11.19 thf(f106,plain,(
% 69.45/11.19 ( ! [X1 : d_unsorted] : (((d_unsorted_0 = X1) = $true)) )),
% 69.45/11.19 inference(pi_clausification,[status(thm)],[f86])).
% 69.45/11.19 thf(f86,plain,(
% 69.45/11.19 ((!! @ d_unsorted @ (= @ d_unsorted_0)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 69.45/11.19 thf(f85,plain,(
% 69.45/11.19 ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 69.45/11.19 thf(f82,plain,(
% 69.45/11.19 ($true = ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 69.45/11.19 thf(f79,plain,(
% 69.45/11.19 ((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 69.45/11.19 thf(f77,plain,(
% 69.45/11.19 (((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 69.45/11.19 thf(f75,plain,(
% 69.45/11.19 ((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 69.45/11.19 thf(f73,plain,(
% 69.45/11.19 (((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 69.45/11.19 thf(f71,plain,(
% 69.45/11.19 ((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 69.45/11.19 thf(f69,plain,(
% 69.45/11.19 ($true = ((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 69.45/11.19 thf(f66,plain,(
% 69.45/11.19 ((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 69.45/11.19 thf(f63,plain,(
% 69.45/11.19 ($true = ((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 69.45/11.19 thf(f60,plain,(
% 69.45/11.19 ((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 69.45/11.19 thf(f57,plain,(
% 69.45/11.19 (((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 69.45/11.19 thf(f55,plain,(
% 69.45/11.19 ((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 69.45/11.19 thf(f53,plain,(
% 69.45/11.19 ($true = ((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 69.45/11.19 thf(f51,plain,(
% 69.45/11.19 ($true = (((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 69.45/11.19 thf(f48,plain,(
% 69.45/11.19 (((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 69.45/11.19 thf(f46,plain,(
% 69.45/11.19 ((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 69.45/11.19 thf(f44,plain,(
% 69.45/11.19 ($true = ((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 69.45/11.19 thf(f41,plain,(
% 69.45/11.19 ((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 69.45/11.19 thf(f38,plain,(
% 69.45/11.19 (((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 69.45/11.19 thf(f36,plain,(
% 69.45/11.19 ($true = (((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 69.45/11.19 thf(f33,plain,(
% 69.45/11.19 ($true = ((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 69.45/11.19 thf(f30,plain,(
% 69.45/11.19 ((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 69.45/11.19 thf(f28,plain,(
% 69.45/11.19 (((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 69.45/11.19 thf(f26,plain,(
% 69.45/11.19 ((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 69.45/11.19 thf(f24,plain,(
% 69.45/11.19 (((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 69.45/11.19 thf(f22,plain,(
% 69.45/11.19 ($true = (((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 69.45/11.19 thf(f20,plain,(
% 69.45/11.19 (((((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 69.45/11.19 thf(f18,plain,(
% 69.45/11.19 ((((((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y3 @ Y5)) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y3 @ Y4))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y9 @ Y10))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y7 @ Y8)))))))))) | (Y1 @ Y4 @ Y5)) | (Y2 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y8 @ Y7) | (~ (Y2 @ Y8 @ Y6))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))) = sconfl)) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 69.45/11.19 thf(f16,plain,(
% 69.45/11.19 ($true = ((((((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y3 @ Y5)) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y3 @ Y4))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y9 @ Y10))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y7 @ Y8)))))))))) | (Y1 @ Y4 @ Y5)) | (Y2 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y8 @ Y7) | (~ (Y2 @ Y8 @ Y6))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))) = sconfl)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)))),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 69.45/11.19 thf(f12,plain,(
% 69.45/11.19 ((((((((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (= @ d_unsorted_0))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y3 @ Y5)) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y3 @ Y4))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y9 @ Y10))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y7 @ Y8)))))))))) | (Y1 @ Y4 @ Y5)) | (Y2 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y8 @ Y7) | (~ (Y2 @ Y8 @ Y6))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))) = sconfl)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2))))))))) = $true)),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f11])).
% 69.45/11.19 thf(f11,plain,(
% 69.45/11.19 ((((((((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (d_unsorted_0 = Y0)))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y3 @ Y5)) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y3 @ Y4))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y9 @ Y10))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y7 @ Y8)))))))))) | (Y1 @ Y4 @ Y5)) | (Y2 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y8 @ Y7) | (~ (Y2 @ Y8 @ Y6))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))) = sconfl)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2))))))))) = $true)),
% 69.45/11.19 inference(cnf_transformation,[status(thm)],[f6])).
% 69.45/11.19 thf(f6,plain,(
% 69.45/11.19 ((((((((((((((((((((((((((((((((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2)))))))) = symm) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (d_unsorted_0 = Y0)))) & ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y3 @ Y1))) | (Y0 @ Y3 @ Y2)))))))))) = po)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) = rc)) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))))))) & (!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y2 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))))))) | (~ (Y2 @ Y1)))))))) = term)) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1))))))) & (trc = (^[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 @ Y6 @ Y5) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))) | (Y1 = Y2))))))))) & ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) = so)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) | (~ (Y5 @ Y6 @ Y8))) | (~ (Y5 @ Y7 @ Y6)))))))))))))))))) | (Y2 @ Y3))))) | (Y2 @ Y1))))))) = ind)) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y1 @ Y3)))))))))))) & (!! @ d_unsorted @ (^[Y0 : d_unsorted]: (!! @ d_unsorted @ (^[Y1 : d_unsorted]: (((d2unsorted @ Y1) = (d2unsorted @ Y0)) => (Y1 = Y0))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y2)))))))))))) & (trsc = (^[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 @ Y4 @ Y6) | (~ (Y3 @ Y4 @ Y5))) | (~ (Y3 @ Y5 @ Y6)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4))))))))))))))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y1 @ Y6 @ Y5))))))) | (Y4 = Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y7)) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (~ (Y6 @ Y9 @ Y7))) | (Y6 @ Y9 @ Y8))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y2 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y9 @ Y7) | (~ (Y6 @ Y8 @ Y7))) | (~ (Y6 @ Y9 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y2 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))))))) & (~ (Y4 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y8 @ Y7) | (~ (Y5 @ Y8 @ Y6))) | (~ (Y5 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y5 @ Y4 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y1 @ Y7 @ Y5)) | (Y1 @ Y7 @ Y6)) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y4))))))))))) = cr)) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))))) | (Y1 = Y2)))))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y5 = Y2) | (Y3 @ Y5 @ Y2)) | (Y4 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y7 @ Y8))) | (Y3 @ Y7 @ Y6)))))))))) | ((~ (Y5 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))) | (Y6 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (~ (Y4 @ Y8 @ Y7))) | (Y4 @ Y6 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10)))))))))) | (Y7 @ Y2 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y9)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y8 @ Y9)))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))))))))))))))) = confl)) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y5 @ Y7))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6))))))))) | (Y4 @ Y2 @ Y3))))))))) | (~ (Y0 @ Y2 @ Y1)))))))) = norm)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))))))))))) = tc)) & ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y1 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y1 @ Y3 @ Y2))) | (Y0 @ Y4 @ Y3 @ Y2))))))))))) = mono)) & ((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl)) & ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join)) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y2 @ Y1))) | (~ (Y0 @ Y1 @ Y2)))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1)))))))) & ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))) = asymm)) & ((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y3 @ Y5)) | ((~ (Y4 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (Y6 @ Y3 @ Y4))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y4 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (~ (Y7 @ Y8 @ Y10))) | (Y7 @ Y9 @ Y10))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y10 @ Y9))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y6 @ Y8)) | (~ (Y1 @ Y7 @ Y6))) | (Y1 @ Y7 @ Y8)))))))))) | (Y1 @ Y4 @ Y5)) | (Y2 @ Y5 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y8 @ Y7) | (~ (Y2 @ Y8 @ Y6))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y5 = Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))))))))))))))) = sconfl)) & ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) = inv)) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2))))))))) = $true)),
% 69.45/11.19 inference(fool_elimination,[status(thm)],[f5])).
% 69.45/11.19 thf(f5,plain,(
% 69.45/11.19 (total = (^[X0 : $i > $i > $o] : (! [X1 : $i,X2 : $i] : ((X0 @ X2 @ X1) | (X1 = X2) | (X0 @ X1 @ X2))))) & ((^[X3 : $i > $i > $o, X4 : $i, X5 : $i] : (X3 @ X5 @ X4)) = inv) & ((^[X6 : $i > $i > $o] : (! [X7 : $i,X8 : $i,X9 : $i,X10 : $i > $i > $o,X11 : $i > $i > $o] : (~! [X12 : $i,X13 : $i] : (~(X6 @ X12 @ X13) | (X10 @ X12 @ X13)) | (X7 = X8) | ~! [X14 : $i,X15 : $i,X16 : $i] : (~(X10 @ X16 @ X15) | ~(X10 @ X14 @ X16) | (X10 @ X14 @ X15)) | (X10 @ X7 @ X8) | (X11 @ X8 @ X7) | ~! [X17 : $i,X18 : $i,X19 : $i] : ((X11 @ X18 @ X17) | ~(X11 @ X18 @ X19) | ~(X11 @ X19 @ X17)) | ~! [X20 : $i] : (~! [X21 : $i > $i > $o] : ((X21 @ X7 @ X20) | ~! [X22 : $i,X23 : $i,X24 : $i] : (~(X21 @ X22 @ X23) | ~(X21 @ X24 @ X22) | (X21 @ X24 @ X23)) | ~! [X25 : $i,X26 : $i] : ((X21 @ X26 @ X25) | ~(X6 @ X26 @ X25))) | ~! [X27 : $i > $i > $o] : (~! [X28 : $i,X29 : $i,X30 : $i] : ((X27 @ X29 @ X28) | ~(X27 @ X30 @ X28) | ~(X27 @ X29 @ X30)) | ~! [X31 : $i,X32 : $i] : (~(X6 @ X32 @ X31) | (X27 @ X32 @ X31)) | (X27 @ X8 @ X20))) | ~! [X33 : $i,X34 : $i] : (~(X6 @ X33 @ X34) | (X11 @ X33 @ X34)) | (~! [X35 : $i > $i > $o] : ((X35 @ X9 @ X8) | ~! [X36 : $i,X37 : $i] : (~(X6 @ X36 @ X37) | (X35 @ X36 @ X37)) | ~! [X38 : $i,X39 : $i,X40 : $i] : (~(X35 @ X39 @ X38) | ~(X35 @ X38 @ X40) | (X35 @ X39 @ X40))) & (X8 != X9)) | ~(X6 @ X9 @ X7)))) = sconfl) & ((^[X41 : $i > $i > $o] : (! [X42 : $i,X43 : $i] : (~(X41 @ X43 @ X42) | ~(X41 @ X42 @ X43)))) = asymm) & (idem = (^[X44 : ($i > $i > $o) > $i > $i > $o] : (! [X45 : $i > $i > $o] : ((X44 @ X45) = (X44 @ (X44 @ X45)))))) & (antisymm = (^[X46 : $i > $i > $o] : (! [X47 : $i,X48 : $i] : (~(X46 @ X48 @ X47) | ~(X46 @ X47 @ X48) | (X47 = X48))))) & ((^[X49 : $i > $i > $o, X50 : $i, X51 : $i] : (~(~! [X52 : $i > $i > $o] : ((X52 @ X51 @ X50) | ~! [X53 : $i,X54 : $i] : ((X52 @ X54 @ X53) | ~(X49 @ X54 @ X53)) | ~! [X55 : $i,X56 : $i,X57 : $i] : (~(X52 @ X55 @ X56) | (X52 @ X55 @ X57) | ~(X52 @ X56 @ X57))) & ! [X58 : $i] : (~! [X59 : $i > $i > $o] : ((X59 @ X51 @ X58) | ~! [X60 : $i,X61 : $i,X62 : $i] : ((X59 @ X62 @ X61) | ~(X59 @ X62 @ X60) | ~(X59 @ X60 @ X61)) | ~! [X63 : $i,X64 : $i] : (~(X49 @ X63 @ X64) | (X59 @ X63 @ X64))) | ~! [X65 : $i > $i > $o] : (~! [X66 : $i,X67 : $i] : ((X65 @ X67 @ X66) | ~(X49 @ X67 @ X66)) | ~! [X68 : $i,X69 : $i,X70 : $i] : (~(X65 @ X70 @ X68) | (X65 @ X70 @ X69) | ~(X65 @ X68 @ X69)) | (X65 @ X50 @ X58))) & ~! [X71 : $i > $i > $o] : ((X71 @ X50 @ X51) | ~! [X72 : $i,X73 : $i] : (~(X49 @ X73 @ X72) | (X71 @ X73 @ X72)) | ~! [X74 : $i,X75 : $i,X76 : $i] : (~(X71 @ X74 @ X76) | ~(X71 @ X75 @ X74) | (X71 @ X75 @ X76))) & (X50 != X51)))) = join) & ((^[X77 : $i > $i > $o] : (! [X78 : $i,X79 : $i > $i > $o,X80 : $i,X81 : $i > $i > $o,X82 : $i] : (~! [X83 : $i] : (~! [X84 : $i > $i > $o] : (~! [X85 : $i,X86 : $i,X87 : $i] : ((X84 @ X85 @ X86) | ~(X84 @ X87 @ X86) | ~(X84 @ X85 @ X87)) | (X84 @ X82 @ X83) | ~! [X88 : $i,X89 : $i] : (~(X77 @ X89 @ X88) | (X84 @ X89 @ X88))) | ~! [X90 : $i > $i > $o] : (~! [X91 : $i,X92 : $i,X93 : $i] : ((X90 @ X92 @ X93) | ~(X90 @ X92 @ X91) | ~(X90 @ X91 @ X93)) | (X90 @ X80 @ X83) | ~! [X94 : $i,X95 : $i] : ((X90 @ X94 @ X95) | ~(X77 @ X94 @ X95)))) | (X79 @ X82 @ X80) | (X81 @ X80 @ X82) | ~! [X96 : $i,X97 : $i,X98 : $i] : (~(X81 @ X98 @ X97) | ~(X81 @ X97 @ X96) | (X81 @ X98 @ X96)) | ~(X77 @ X78 @ X80) | ~! [X99 : $i,X100 : $i,X101 : $i] : (~(X79 @ X99 @ X100) | (X79 @ X101 @ X100) | ~(X79 @ X101 @ X99)) | ~! [X102 : $i,X103 : $i] : (~(X77 @ X102 @ X103) | (X79 @ X102 @ X103)) | ~! [X104 : $i,X105 : $i] : (~(X77 @ X105 @ X104) | (X81 @ X105 @ X104)) | ~(X77 @ X78 @ X82) | (X80 = X82)))) = lconfl) & ((^[X106 : ($i > $i > $o) > $i > $i > $o] : (! [X107 : $i > $i > $o,X108 : $i,X109 : $i,X110 : $i > $i > $o] : ((X106 @ X107 @ X108 @ X109) | ~(X106 @ X110 @ X108 @ X109) | ~! [X111 : $i,X112 : $i] : (~(X110 @ X111 @ X112) | (X107 @ X111 @ X112))))) = mono) & ((^[X113 : $i > $i > $o, X114 : $i, X115 : $i] : (! [X116 : $i > $i > $o] : (~! [X117 : $i,X118 : $i] : (~(X113 @ X118 @ X117) | (X116 @ X118 @ X117)) | ~! [X119 : $i,X120 : $i,X121 : $i] : (~(X116 @ X119 @ X121) | ~(X116 @ X120 @ X119) | (X116 @ X120 @ X121)) | (X116 @ X114 @ X115)))) = tc) & ((^[X122 : $i > $i > $o] : (! [X123 : $i,X124 : $i] : (~(X122 @ X123 @ X124) | ~! [X125 : $i] : (~! [X126 : $i > $i > $o] : ((X126 @ X123 @ X125) | ~! [X127 : $i,X128 : $i] : (~(X122 @ X128 @ X127) | (X126 @ X128 @ X127)) | ~! [X129 : $i,X130 : $i,X131 : $i] : ((X126 @ X131 @ X129) | ~(X126 @ X131 @ X130) | ~(X126 @ X130 @ X129))) | ~! [X132 : $i] : ~(X122 @ X125 @ X132))))) = norm) & ((^[X133 : $i > $i > $o] : (! [X134 : $i,X135 : $i > $i > $o,X136 : $i > $i > $o,X137 : $i,X138 : $i] : (~! [X139 : $i,X140 : $i] : (~(X133 @ X140 @ X139) | (X136 @ X140 @ X139)) | ~! [X141 : $i,X142 : $i] : ((X135 @ X142 @ X141) | ~(X133 @ X142 @ X141)) | ~! [X143 : $i] : (~! [X144 : $i > $i > $o] : (~! [X145 : $i,X146 : $i,X147 : $i] : ((X144 @ X147 @ X146) | ~(X144 @ X147 @ X145) | ~(X144 @ X145 @ X146)) | ~! [X148 : $i,X149 : $i] : ((X144 @ X148 @ X149) | ~(X133 @ X148 @ X149)) | (X144 @ X134 @ X143)) | ~! [X150 : $i > $i > $o] : (~! [X151 : $i,X152 : $i] : ((X150 @ X152 @ X151) | ~(X133 @ X152 @ X151)) | (X150 @ X137 @ X143) | ~! [X153 : $i,X154 : $i,X155 : $i] : (~(X150 @ X154 @ X153) | ~(X150 @ X155 @ X154) | (X150 @ X155 @ X153)))) | ~! [X156 : $i,X157 : $i,X158 : $i] : ((X135 @ X158 @ X157) | ~(X135 @ X156 @ X157) | ~(X135 @ X158 @ X156)) | ((X137 != X138) & ~! [X159 : $i > $i > $o] : (~! [X160 : $i,X161 : $i] : ((X159 @ X161 @ X160) | ~(X133 @ X161 @ X160)) | ~! [X162 : $i,X163 : $i,X164 : $i] : ((X159 @ X163 @ X164) | ~(X159 @ X163 @ X162) | ~(X159 @ X162 @ X164)) | (X159 @ X138 @ X137))) | (~! [X165 : $i > $i > $o] : (~! [X166 : $i,X167 : $i] : ((X165 @ X167 @ X166) | ~(X133 @ X167 @ X166)) | (X165 @ X138 @ X134) | ~! [X168 : $i,X169 : $i,X170 : $i] : (~(X165 @ X169 @ X168) | (X165 @ X170 @ X168) | ~(X165 @ X170 @ X169))) & (X134 != X138)) | ~! [X171 : $i,X172 : $i,X173 : $i] : ((X136 @ X172 @ X173) | ~(X136 @ X172 @ X171) | ~(X136 @ X171 @ X173)) | (X135 @ X137 @ X134) | (X136 @ X134 @ X137) | (X134 = X137)))) = confl) & (nfof = (^[X174 : $i > $i > $o, X175 : $i, X176 : $i] : (((X175 = X176) | ! [X177 : $i > $i > $o] : (~! [X178 : $i,X179 : $i,X180 : $i] : ((X177 @ X180 @ X179) | ~(X177 @ X178 @ X179) | ~(X177 @ X180 @ X178)) | ~! [X181 : $i,X182 : $i] : (~(X174 @ X181 @ X182) | (X177 @ X181 @ X182)) | (X177 @ X176 @ X175))) & ! [X183 : $i] : ~(X174 @ X175 @ X183)))) & ((^[X184 : $i > $i > $o] : (! [X185 : $i,X186 : $i > $i > $o,X187 : $i,X188 : $i > $i > $o] : ((X188 @ X187 @ X185) | ~! [X189 : $i,X190 : $i,X191 : $i] : (~(X188 @ X191 @ X190) | (X188 @ X189 @ X190) | ~(X188 @ X189 @ X191)) | (~! [X192 : $i > $i > $o] : ((X192 @ X185 @ X187) | ~! [X193 : $i,X194 : $i] : (~(X184 @ X193 @ X194) | (X192 @ X193 @ X194)) | ~! [X195 : $i,X196 : $i,X197 : $i] : (~(X192 @ X197 @ X196) | ~(X192 @ X195 @ X197) | (X192 @ X195 @ X196))) & (X185 != X187) & ~! [X198 : $i > $i > $o] : (~! [X199 : $i,X200 : $i] : ((X198 @ X199 @ X200) | ~(X184 @ X199 @ X200)) | ~! [X201 : $i,X202 : $i,X203 : $i] : (~(X198 @ X203 @ X201) | (X198 @ X202 @ X201) | ~(X198 @ X202 @ X203)) | (X198 @ X187 @ X185))) | ~! [X204 : $i] : (~! [X205 : $i > $i > $o] : (~! [X206 : $i,X207 : $i] : ((X205 @ X206 @ X207) | ~(X184 @ X206 @ X207)) | ~! [X208 : $i,X209 : $i,X210 : $i] : (~(X205 @ X208 @ X209) | ~(X205 @ X209 @ X210) | (X205 @ X208 @ X210)) | (X205 @ X187 @ X204)) | ~! [X211 : $i > $i > $o] : ((X211 @ X185 @ X204) | ~! [X212 : $i,X213 : $i] : ((X211 @ X213 @ X212) | ~(X184 @ X213 @ X212)) | ~! [X214 : $i,X215 : $i,X216 : $i] : ((X211 @ X214 @ X215) | ~(X211 @ X214 @ X216) | ~(X211 @ X216 @ X215)))) | (X186 @ X185 @ X187) | ~! [X217 : $i,X218 : $i] : (~(X184 @ X217 @ X218) | (X186 @ X217 @ X218)) | ~! [X219 : $i,X220 : $i,X221 : $i] : (~(X186 @ X220 @ X219) | (X186 @ X221 @ X219) | ~(X186 @ X221 @ X220)) | (X185 = X187) | ~! [X222 : $i,X223 : $i] : ((X188 @ X222 @ X223) | ~(X184 @ X222 @ X223))))) = cr) & (trsc = (^[X224 : $i > $i > $o, X225 : $i, X226 : $i] : (! [X227 : $i > $i > $o] : (~! [X228 : $i,X229 : $i,X230 : $i] : (~(X227 @ X229 @ X230) | (X227 @ X229 @ X228) | ~(X227 @ X230 @ X228)) | ~! [X231 : $i,X232 : $i] : ((X227 @ X231 @ X232) | ~(X224 @ X231 @ X232)) | (X227 @ X225 @ X226)) | ! [X233 : $i > $i > $o] : (~! [X234 : $i,X235 : $i] : ((X233 @ X234 @ X235) | ~(X224 @ X234 @ X235)) | (X233 @ X226 @ X225) | ~! [X236 : $i,X237 : $i,X238 : $i] : (~(X233 @ X237 @ X236) | ~(X233 @ X238 @ X237) | (X233 @ X238 @ X236))) | (X225 = X226)))) & (infl = (^[X239 : ($i > $i > $o) > $i > $i > $o] : (! [X240 : $i,X241 : $i,X242 : $i > $i > $o] : (~(X242 @ X240 @ X241) | (X239 @ X242 @ X240 @ X241))))) & (innf = (^[X243 : $i > $i > $o, X244 : $i] : (! [X245 : $i] : ~(X243 @ X244 @ X245)))) & ! [X246 : d_unsorted,X247 : d_unsorted] : (((d2unsorted @ X246) = (d2unsorted @ X247)) => (X246 = X247)) & (trans = (^[X248 : $i > $i > $o] : (! [X249 : $i,X250 : $i,X251 : $i] : (~(X248 @ X251 @ X249) | (X248 @ X250 @ X249) | ~(X248 @ X250 @ X251))))) & ((^[X252 : $i > $i > $o] : (! [X253 : $i > $o,X254 : $i] : ((X253 @ X254) | ~! [X255 : $i] : ((X253 @ X255) | ~! [X256 : $i] : (~! [X257 : $i > $i > $o] : (~! [X258 : $i,X259 : $i,X260 : $i] : (~(X257 @ X259 @ X260) | ~(X257 @ X260 @ X258) | (X257 @ X259 @ X258)) | ~! [X261 : $i,X262 : $i] : ((X257 @ X261 @ X262) | ~(X252 @ X261 @ X262)) | (X257 @ X255 @ X256)) | (X253 @ X256)))))) = ind) & ((^[X263 : $i > $i > $o] : (! [X264 : $i,X265 : $i] : (~(X263 @ X265 @ X264) | ~(X263 @ X264 @ X265)) & ! [X266 : $i,X267 : $i,X268 : $i] : ((X263 @ X267 @ X268) | ~(X263 @ X267 @ X266) | ~(X263 @ X266 @ X268)))) = so) & (trc = (^[X269 : $i > $i > $o, X270 : $i, X271 : $i] : ((X270 = X271) | ! [X272 : $i > $i > $o] : (~! [X273 : $i,X274 : $i] : ((X272 @ X273 @ X274) | ~(X269 @ X273 @ X274)) | ~! [X275 : $i,X276 : $i,X277 : $i] : (~(X272 @ X275 @ X277) | ~(X272 @ X277 @ X276) | (X272 @ X275 @ X276)) | (X272 @ X270 @ X271))))) & (irrefl = (^[X278 : $i > $i > $o] : (! [X279 : $i] : ~(X278 @ X279 @ X279)))) & ((^[X280 : $i > $i > $o] : (! [X281 : $i > $o,X282 : $i] : (~(X281 @ X282) | ~! [X283 : $i] : (~! [X284 : $i] : (~(X280 @ X283 @ X284) | ~(X281 @ X284)) | ~(X281 @ X283))))) = term) & (sc = (^[X285 : $i > $i > $o, X286 : $i, X287 : $i] : ((X285 @ X287 @ X286) | (X285 @ X286 @ X287)))) & ! [X288 : $i] : ? [X289 : d_unsorted] : ((d2unsorted @ X289) = X288) & (subrel = (^[X290 : $i > $i > $o, X291 : $i > $i > $o] : (! [X292 : $i,X293 : $i] : ((X291 @ X292 @ X293) | ~(X290 @ X292 @ X293))))) & (refl = (^[X294 : $i > $i > $o] : (! [X295 : $i] : (X294 @ X295 @ X295)))) & ((^[X296 : $i > $i > $o, X297 : $i, X298 : $i] : ((X296 @ X297 @ X298) | (X297 = X298))) = rc) & ((^[X299 : $i > $i > $o] : (! [X300 : $i,X301 : $i,X302 : $i] : ((X299 @ X300 @ X301) | ~(X299 @ X300 @ X302) | ~(X299 @ X302 @ X301)) & ! [X303 : $i] : (X299 @ X303 @ X303) & ! [X304 : $i,X305 : $i] : (~(X299 @ X305 @ X304) | (X304 = X305) | ~(X299 @ X304 @ X305)))) = po) & ! [X306 : d_unsorted] : (d_unsorted_0 = X306) & ((^[X307 : $i > $i > $o] : (! [X308 : $i,X309 : $i] : (~(X307 @ X309 @ X308) | (X307 @ X308 @ X309)))) = symm)),
% 69.45/11.19 inference(rectify,[status(thm)],[f1])).
% 69.45/11.19 thf(f1,axiom,(
% 69.45/11.19 (total = (^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : ((X4 @ X7 @ X6) | (X6 = X7) | (X4 @ X6 @ X7))))) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (X4 @ X7 @ X6)) = inv) & ((^[X4 : $i > $i > $o] : (! [X11 : $i,X7 : $i,X6 : $i,X31 : $i > $i > $o,X30 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X31 @ X14 @ X15)) | (X7 = X11) | ~! [X12 : $i,X26 : $i,X13 : $i] : (~(X31 @ X13 @ X26) | ~(X31 @ X12 @ X13) | (X31 @ X12 @ X26)) | (X31 @ X11 @ X7) | (X30 @ X7 @ X11) | ~! [X25 : $i,X12 : $i,X13 : $i] : ((X30 @ X12 @ X25) | ~(X30 @ X12 @ X13) | ~(X30 @ X13 @ X25)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : ((X5 @ X11 @ X27) | ~! [X13 : $i,X26 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26)) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))) | ~! [X5 : $i > $i > $o] : (~! [X25 : $i,X12 : $i,X13 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X7 @ X27))) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X30 @ X14 @ X15)) | (~! [X5 : $i > $i > $o] : ((X5 @ X6 @ X7) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X32 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X32) | (X5 @ X12 @ X32))) & (X6 != X7)) | ~(X4 @ X6 @ X11)))) = sconfl) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6)))) = asymm) & (idem = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X4 : $i > $i > $o] : ((X8 @ X4) = (X8 @ (X8 @ X4)))))) & (antisymm = (^[X4 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : (~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7) | (X6 = X7))))) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (~(~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X25 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X25) | ~(X5 @ X13 @ X25))) & ! [X27 : $i] : (~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X27) | ~! [X13 : $i,X25 : $i,X12 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25)) | ~! [X14 : $i,X15 : $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 @ X12 @ X13) | (X5 @ X12 @ X26) | ~(X5 @ X13 @ X26)) | (X5 @ X6 @ X27))) & ~! [X5 : $i > $i > $o] : ((X5 @ X6 @ X7) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X26 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26))) & (X6 != X7)))) = join) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X29 : $i > $i > $o,X7 : $i,X28 : $i > $i > $o,X11 : $i] : (~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X12 : $i,X26 : $i,X13 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X11 @ X27) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) | ~! [X5 : $i > $i > $o] : (~! [X13 : $i,X12 : $i,X25 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25)) | (X5 @ X7 @ X27) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)))) | (X29 @ X11 @ X7) | (X28 @ X7 @ X11) | ~! [X25 : $i,X13 : $i,X12 : $i] : (~(X28 @ X12 @ X13) | ~(X28 @ X13 @ X25) | (X28 @ X12 @ X25)) | ~(X4 @ X6 @ X7) | ~! [X13 : $i,X26 : $i,X12 : $i] : (~(X29 @ X13 @ X26) | (X29 @ X12 @ X26) | ~(X29 @ X12 @ X13)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X29 @ X14 @ X15)) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X28 @ X14 @ X15)) | ~(X4 @ X6 @ X11) | (X7 = X11)))) = lconfl) & ((^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X5 : $i > $i > $o,X9 : $i,X10 : $i,X4 : $i > $i > $o] : ((X8 @ X5 @ X9 @ X10) | ~(X8 @ X4 @ X9 @ X10) | ~! [X6 : $i,X7 : $i] : (~(X4 @ X6 @ X7) | (X5 @ X6 @ X7))))) = mono) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X11 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)) | (X5 @ X6 @ X7)))) = tc) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X23 : $i] : (~(X4 @ X6 @ X23) | ~! [X24 : $i] : (~! [X5 : $i > $i > $o] : ((X5 @ X6 @ X24) | ~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X11 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11))) | ~! [X22 : $i] : ~(X4 @ X24 @ X22))))) = norm) & ((^[X4 : $i > $i > $o] : (! [X11 : $i,X33 : $i > $i > $o,X34 : $i > $i > $o,X7 : $i,X6 : $i] : (~! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X34 @ X14 @ X15)) | ~! [X15 : $i,X14 : $i] : ((X33 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X13 : $i,X26 : $i,X12 : $i] : ((X5 @ X12 @ X26) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26)) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X11 @ X27)) | ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X7 @ X27) | ~! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X25) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X25)))) | ~! [X13 : $i,X25 : $i,X12 : $i] : ((X33 @ X12 @ X25) | ~(X33 @ X13 @ X25) | ~(X33 @ X12 @ X13)) | ((X6 != X7) & ~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X13 : $i,X12 : $i,X35 : $i] : ((X5 @ X12 @ X35) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X35)) | (X5 @ X6 @ X7))) | (~! [X5 : $i > $i > $o] : (~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X11) | ~! [X26 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13))) & (X6 != X11)) | ~! [X13 : $i,X12 : $i,X26 : $i] : ((X34 @ X12 @ X26) | ~(X34 @ X12 @ X13) | ~(X34 @ X13 @ X26)) | (X33 @ X7 @ X11) | (X34 @ X11 @ X7) | (X7 = X11)))) = confl) & (nfof = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : (((X6 = X7) | ! [X5 : $i > $i > $o] : (~! [X13 : $i,X11 : $i,X12 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13)) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X7 @ X6))) & ! [X22 : $i] : ~(X4 @ X6 @ X22)))) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X36 : $i > $i > $o,X6 : $i,X37 : $i > $i > $o] : ((X37 @ X6 @ X7) | ~! [X12 : $i,X26 : $i,X13 : $i] : (~(X37 @ X13 @ X26) | (X37 @ X12 @ X26) | ~(X37 @ X12 @ X13)) | (~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X6) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~! [X12 : $i,X11 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11))) & (X6 != X7) & ~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X11) | (X5 @ X12 @ X11) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X7))) | ~! [X27 : $i] : (~! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X13 : $i,X26 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26) | (X5 @ X12 @ X26)) | (X5 @ X6 @ X27)) | ~! [X5 : $i > $i > $o] : ((X5 @ X7 @ X27) | ~! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X25 : $i,X13 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25)))) | (X36 @ X7 @ X6) | ~! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X36 @ X14 @ X15)) | ~! [X25 : $i,X13 : $i,X12 : $i] : (~(X36 @ X13 @ X25) | (X36 @ X12 @ X25) | ~(X36 @ X12 @ X13)) | (X6 = X7) | ~! [X14 : $i,X15 : $i] : ((X37 @ X14 @ X15) | ~(X4 @ X14 @ X15))))) = cr) & (trsc = (^[X4 : $i > $i > $o, X16 : $i, X17 : $i] : (! [X5 : $i > $i > $o] : (~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X11) | ~(X5 @ X13 @ X11)) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X16 @ X17)) | ! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X17 @ X16) | ~! [X11 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11))) | (X16 = X17)))) & (infl = (^[X8 : ($i > $i > $o) > $i > $i > $o] : (! [X6 : $i,X7 : $i,X4 : $i > $i > $o] : (~(X4 @ X6 @ X7) | (X8 @ X4 @ X6 @ X7))))) & (innf = (^[X4 : $i > $i > $o, X6 : $i] : (! [X7 : $i] : ~(X4 @ X6 @ X7)))) & ! [X2 : d_unsorted,X3 : d_unsorted] : (((d2unsorted @ X2) = (d2unsorted @ X3)) => (X2 = X3)) & (trans = (^[X4 : $i > $i > $o] : (! [X11 : $i,X6 : $i,X7 : $i] : (~(X4 @ X7 @ X11) | (X4 @ X6 @ X11) | ~(X4 @ X6 @ X7))))) & ((^[X4 : $i > $i > $o] : (! [X20 : $i > $o,X21 : $i] : ((X20 @ X21) | ~! [X6 : $i] : ((X20 @ X6) | ~! [X7 : $i] : (~! [X5 : $i > $i > $o] : (~! [X11 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11) | (X5 @ X12 @ X11)) | ~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X7)) | (X20 @ X7)))))) = ind) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6)) & ! [X7 : $i,X6 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11)))) = so) & (trc = (^[X4 : $i > $i > $o, X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : $i > $i > $o] : (~! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~! [X12 : $i,X11 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11) | (X5 @ X12 @ X11)) | (X5 @ X16 @ X17))))) & (irrefl = (^[X4 : $i > $i > $o] : (! [X6 : $i] : ~(X4 @ X6 @ X6)))) & ((^[X4 : $i > $i > $o] : (! [X18 : $i > $o,X19 : $i] : (~(X18 @ X19) | ~! [X6 : $i] : (~! [X7 : $i] : (~(X4 @ X6 @ X7) | ~(X18 @ X7)) | ~(X18 @ X6))))) = term) & (sc = (^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7)))) & ! [X0 : $i] : ? [X1 : d_unsorted] : ((d2unsorted @ X1) = X0) & (subrel = (^[X4 : $i > $i > $o, X5 : $i > $i > $o] : (! [X6 : $i,X7 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & (refl = (^[X4 : $i > $i > $o] : (! [X6 : $i] : (X4 @ X6 @ X6)))) & ((^[X4 : $i > $i > $o, X6 : $i, X7 : $i] : ((X4 @ X6 @ X7) | (X6 = X7))) = rc) & ((^[X4 : $i > $i > $o] : (! [X6 : $i,X11 : $i,X7 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11)) & ! [X6 : $i] : (X4 @ X6 @ X6) & ! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | (X6 = X7) | ~(X4 @ X7 @ X6)))) = po) & ! [X1 : d_unsorted] : (d_unsorted_0 = X1) & ((^[X4 : $i > $i > $o] : (! [X7 : $i,X6 : $i] : (~(X4 @ X6 @ X7) | (X4 @ X7 @ X6)))) = symm)),
% 69.45/11.19 file('/export/starexec/sandbox/tmp/tmp.qqkWGq3eP8/DTF2THF_20128.p',sev441_1)).
% 69.45/11.19 thf(f185,plain,(
% 69.45/11.19 ( ! [X1 : $i] : (((d2unsorted @ (sK3 @ X1)) = X1)) )),
% 69.45/11.19 inference(equality_proxy_clausification,[status(thm)],[f184])).
% 69.45/11.19 thf(f184,plain,(
% 69.45/11.19 ( ! [X1 : $i] : ((((d2unsorted @ (sK3 @ X1)) = X1) = $true)) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f183])).
% 69.45/11.19 thf(f183,plain,(
% 69.45/11.19 ( ! [X1 : $i] : ((((^[Y0 : d_unsorted]: ((d2unsorted @ Y0) = X1)) @ (sK3 @ X1)) = $true)) )),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f178])).
% 69.45/11.19 thf(f178,plain,(
% 69.45/11.19 ( ! [X1 : $i] : (((?? @ d_unsorted @ (^[Y0 : d_unsorted]: ((d2unsorted @ Y0) = X1))) = $true)) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f177])).
% 69.45/11.19 thf(f177,plain,(
% 69.45/11.19 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0)))) @ X1) = $true)) )),
% 69.45/11.19 inference(pi_clausification,[status(thm)],[f74])).
% 69.45/11.19 thf(f74,plain,(
% 69.45/11.19 ((!! @ $i @ (^[Y0 : $i]: (?? @ d_unsorted @ (^[Y1 : d_unsorted]: ((d2unsorted @ Y1) = Y0))))) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 69.45/11.19 thf(f2778,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((lconfl @ X1) = $true) | ((sK24 @ X1) != (sK22 @ X1))) )),
% 69.45/11.19 inference(equality_proxy_clausification,[status(thm)],[f2777])).
% 69.45/11.19 thf(f2777,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : ((((sK24 @ X1) = (sK22 @ X1)) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2775])).
% 69.45/11.19 thf(f2775,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((lconfl @ X1) = $true) | ($false = (((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))))) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2773])).
% 69.45/11.19 thf(f2773,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (($false = ((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1)))))))))) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2770])).
% 69.45/11.19 thf(f2770,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((lconfl @ X1) = $true) | ($false = (((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK25 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))))) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2767])).
% 69.45/11.19 thf(f2767,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : ((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK25 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK25 @ X1 @ Y0 @ Y2)) | (sK25 @ X1 @ Y0 @ Y1)) | (~ (sK25 @ X1 @ Y2 @ Y1))))))))))) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2764])).
% 69.45/11.19 thf(f2764,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (($false = (((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK25 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK25 @ X1 @ Y0 @ Y2)) | (sK25 @ X1 @ Y0 @ Y1)) | (~ (sK25 @ X1 @ Y2 @ Y1))))))))))) | (~ (X1 @ (sK26 @ X1) @ (sK24 @ X1))))) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2762])).
% 69.45/11.19 thf(f2762,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((lconfl @ X1) = $true) | ($false = ((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK25 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK25 @ X1 @ Y0 @ Y2)) | (sK25 @ X1 @ Y0 @ Y1)) | (~ (sK25 @ X1 @ Y2 @ Y1))))))))))) | (~ (X1 @ (sK26 @ X1) @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK23 @ X1 @ Y0 @ Y2) | (~ (sK23 @ X1 @ Y1 @ Y2))) | (~ (sK23 @ X1 @ Y0 @ Y1))))))))))))) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2760])).
% 69.45/11.19 thf(f2760,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK25 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK25 @ X1 @ Y0 @ Y2)) | (sK25 @ X1 @ Y0 @ Y1)) | (~ (sK25 @ X1 @ Y2 @ Y1))))))))))) | (~ (X1 @ (sK26 @ X1) @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK23 @ X1 @ Y0 @ Y2) | (~ (sK23 @ X1 @ Y1 @ Y2))) | (~ (sK23 @ X1 @ Y0 @ Y1))))))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1))) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2758])).
% 69.45/11.19 thf(f2758,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : ((((((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK25 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK25 @ X1 @ Y0 @ Y2)) | (sK25 @ X1 @ Y0 @ Y1)) | (~ (sK25 @ X1 @ Y2 @ Y1))))))))))) | (~ (X1 @ (sK26 @ X1) @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK23 @ X1 @ Y0 @ Y2) | (~ (sK23 @ X1 @ Y1 @ Y2))) | (~ (sK23 @ X1 @ Y0 @ Y1))))))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1))) | (sK25 @ X1 @ (sK22 @ X1) @ (sK24 @ X1))) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f2756])).
% 69.45/11.19 thf(f2756,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((lconfl @ X1) = $true) | ($false = (((((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ (sK26 @ X1) @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK23 @ X1 @ Y0 @ Y1) | (~ (X1 @ Y0 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK25 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK25 @ X1 @ Y0 @ Y2)) | (sK25 @ X1 @ Y0 @ Y1)) | (~ (sK25 @ X1 @ Y2 @ Y1))))))))))) | (~ (X1 @ (sK26 @ X1) @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK23 @ X1 @ Y0 @ Y2) | (~ (sK23 @ X1 @ Y1 @ Y2))) | (~ (sK23 @ X1 @ Y0 @ Y1))))))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1))) | (sK25 @ X1 @ (sK22 @ X1) @ (sK24 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))) | (Y1 @ (sK24 @ X1) @ 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]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3)))))))) | (Y1 @ (sK22 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y2 @ Y3))) | (Y1 @ Y4 @ Y3)))))))))))))))))))) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f2751])).
% 69.45/11.19 thf(f2751,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (($false = ((^[Y0 : $i]: (((((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ Y0 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK23 @ X1 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK25 @ X1 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK25 @ X1 @ Y1 @ Y3)) | (sK25 @ X1 @ Y1 @ Y2)) | (~ (sK25 @ X1 @ Y3 @ Y2))))))))))) | (~ (X1 @ Y0 @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK23 @ X1 @ Y1 @ Y3) | (~ (sK23 @ X1 @ Y2 @ Y3))) | (~ (sK23 @ X1 @ Y1 @ Y2))))))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1))) | (sK25 @ X1 @ (sK22 @ X1) @ (sK24 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))) | (Y2 @ (sK24 @ X1) @ 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]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4)))))))) | (Y2 @ (sK22 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y3 @ Y4))) | (Y2 @ Y5 @ Y4))))))))))))))))))) @ (sK26 @ X1))) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f2747])).
% 69.45/11.19 thf(f2747,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (((((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ Y0 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK23 @ X1 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK25 @ X1 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK25 @ X1 @ Y1 @ Y3)) | (sK25 @ X1 @ Y1 @ Y2)) | (~ (sK25 @ X1 @ Y3 @ Y2))))))))))) | (~ (X1 @ Y0 @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK23 @ X1 @ Y1 @ Y3) | (~ (sK23 @ X1 @ Y2 @ Y3))) | (~ (sK23 @ X1 @ Y1 @ Y2))))))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1))) | (sK25 @ X1 @ (sK22 @ X1) @ (sK24 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))) | (Y2 @ (sK24 @ X1) @ 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]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4)))))))) | (Y2 @ (sK22 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y3 @ Y4))) | (Y2 @ Y5 @ Y4)))))))))))))))))))) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f2744])).
% 69.45/11.19 thf(f2744,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (((((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ Y1 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK23 @ X1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y2 @ Y4)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y4 @ Y3))))))))))) | (~ (X1 @ Y1 @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK23 @ X1 @ Y2 @ Y4) | (~ (sK23 @ X1 @ Y3 @ Y4))) | (~ (sK23 @ X1 @ Y2 @ Y3))))))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1))) | (Y0 @ (sK22 @ X1) @ (sK24 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ (sK24 @ X1) @ 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]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5)))))))) | (Y3 @ (sK22 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))))))))))) @ (sK25 @ X1)) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f2730])).
% 69.45/11.19 thf(f2730,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (((((((((((sK24 @ X1) = (sK22 @ X1)) | (~ (X1 @ Y1 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK23 @ X1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y0 @ Y2 @ Y4)) | (Y0 @ Y2 @ Y3)) | (~ (Y0 @ Y4 @ Y3))))))))))) | (~ (X1 @ Y1 @ (sK24 @ X1)))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK23 @ X1 @ Y2 @ Y4) | (~ (sK23 @ X1 @ Y3 @ Y4))) | (~ (sK23 @ X1 @ Y2 @ Y3))))))))))) | (sK23 @ X1 @ (sK24 @ X1) @ (sK22 @ X1))) | (Y0 @ (sK22 @ X1) @ (sK24 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (Y3 @ (sK24 @ X1) @ 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]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5)))))))) | (Y3 @ (sK22 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y6 @ Y5))))))))))))))))))))))) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f2726])).
% 69.45/11.19 thf(f2726,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((lconfl @ X1) = $true) | (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((((((((((Y0 = (sK22 @ X1)) | (~ (X1 @ Y2 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK23 @ X1 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y1 @ Y3 @ Y5)) | (Y1 @ Y3 @ Y4)) | (~ (Y1 @ Y5 @ Y4))))))))))) | (~ (X1 @ Y2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((sK23 @ X1 @ Y3 @ Y5) | (~ (sK23 @ X1 @ Y4 @ Y5))) | (~ (sK23 @ X1 @ Y3 @ Y4))))))))))) | (sK23 @ X1 @ Y0 @ (sK22 @ X1))) | (Y1 @ (sK22 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (Y4 @ Y0 @ 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]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6)))))))) | (Y4 @ (sK22 @ X1) @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y7 @ Y6))))))))))))))))))))))) @ (sK24 @ X1)) = $false)) )),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f2711])).
% 69.45/11.19 thf(f2711,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((((((((((Y0 = (sK22 @ X1)) | (~ (X1 @ Y2 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK23 @ X1 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y1 @ Y3 @ Y5)) | (Y1 @ Y3 @ Y4)) | (~ (Y1 @ Y5 @ Y4))))))))))) | (~ (X1 @ Y2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((sK23 @ X1 @ Y3 @ Y5) | (~ (sK23 @ X1 @ Y4 @ Y5))) | (~ (sK23 @ X1 @ Y3 @ Y4))))))))))) | (sK23 @ X1 @ Y0 @ (sK22 @ X1))) | (Y1 @ (sK22 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (Y4 @ Y0 @ 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]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6)))))))) | (Y4 @ (sK22 @ X1) @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y5 @ Y6))) | (Y4 @ Y7 @ Y6)))))))))))))))))))))))) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f2706])).
% 69.45/11.19 thf(f2706,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (($false = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((((((((((Y1 = (sK22 @ X1)) | (~ (X1 @ Y3 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y2 @ Y4 @ Y6)) | (Y2 @ Y4 @ Y5)) | (~ (Y2 @ Y6 @ Y5))))))))))) | (~ (X1 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y4 @ Y6) | (~ (Y0 @ Y5 @ Y6))) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y0 @ Y1 @ (sK22 @ X1))) | (Y2 @ (sK22 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))) | (Y5 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y7 @ Y6))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (X1 @ Y6 @ Y7)))))))) | (Y5 @ (sK22 @ X1) @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y6 @ Y7))) | (Y5 @ Y8 @ Y7))))))))))))))))))))))))) @ (sK23 @ X1))) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f2681])).
% 69.45/11.19 thf(f2681,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((((((((((Y1 = (sK22 @ X1)) | (~ (X1 @ Y3 @ (sK22 @ X1)))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y2 @ Y4 @ Y6)) | (Y2 @ Y4 @ Y5)) | (~ (Y2 @ Y6 @ Y5))))))))))) | (~ (X1 @ Y3 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y0 @ Y4 @ Y6) | (~ (Y0 @ Y5 @ Y6))) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y0 @ Y1 @ (sK22 @ X1))) | (Y2 @ (sK22 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y7 @ Y6)) | (Y5 @ Y7 @ Y6))))))) | (Y5 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y7 @ Y8))) | (Y5 @ Y7 @ Y6))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (X1 @ Y6 @ Y7)))))))) | (Y5 @ (sK22 @ X1) @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y6 @ Y7))) | (Y5 @ Y8 @ Y7))))))))))))))))))))))))))) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f2676])).
% 69.45/11.19 thf(f2676,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (($false = ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((((((((((Y2 = Y0) | (~ (X1 @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (X1 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y7)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y7 @ Y6))))))))))) | (~ (X1 @ Y4 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y0)) | (Y3 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (X1 @ Y7 @ Y8)))))))) | (Y6 @ Y0 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8))))))))))))))))))))))))))) @ (sK22 @ X1))) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f1523])).
% 69.45/11.19 thf(f1523,plain,(
% 69.45/11.19 ( ! [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]: ((((((((((Y2 = Y0) | (~ (X1 @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (X1 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y7)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y7 @ Y6))))))))))) | (~ (X1 @ Y4 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y0)) | (Y3 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (X1 @ Y7 @ Y8)))))))) | (Y6 @ Y0 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))))))))))))))))))))) = $false) | ((lconfl @ X1) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f1521])).
% 69.45/11.19 thf(f1521,plain,(
% 69.45/11.19 ( ! [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]: ((((((((((Y2 = Y0) | (~ (X1 @ Y4 @ Y0))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) | (~ (X1 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y3 @ Y5 @ Y7)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y7 @ Y6))))))))))) | (~ (X1 @ Y4 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y1 @ Y5 @ Y7) | (~ (Y1 @ Y6 @ Y7))) | (~ (Y1 @ Y5 @ Y6))))))))))) | (Y1 @ Y2 @ Y0)) | (Y3 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (Y6 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y9))) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (X1 @ Y7 @ Y8)))))))) | (Y6 @ Y0 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))))))))))))))))))))) = (lconfl @ X1))) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f1520])).
% 69.45/11.19 thf(f1520,plain,(
% 69.45/11.19 ( ! [X1 : $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]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) @ X1) = (lconfl @ X1))) )),
% 69.45/11.19 inference(argument_congruence,[status(thm)],[f31])).
% 69.45/11.19 thf(f31,plain,(
% 69.45/11.19 (lconfl = (^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))))),
% 69.45/11.19 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 69.45/11.19 thf(f29,plain,(
% 69.45/11.19 (((^[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]: ((((((((((Y3 = Y1) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y6 @ Y8)) | (Y4 @ Y6 @ Y7)) | (~ (Y4 @ Y8 @ Y7))))))))))) | (~ (Y0 @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y2 @ Y6 @ Y8) | (~ (Y2 @ Y7 @ Y8))) | (~ (Y2 @ Y6 @ Y7))))))))))) | (Y2 @ Y3 @ Y1)) | (Y4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))) | (Y7 @ Y3 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y9 @ Y8))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y10 @ Y9))))))))))))))))))))))))))))) = lconfl) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 69.45/11.19 thf(f131,plain,(
% 69.45/11.19 ((lconfl @ sK2) = $false) | ~spl0_4),
% 69.45/11.19 inference(avatar_component_clause,[status(thm)],[f129])).
% 69.45/11.19 thf(f129,definition,(
% 69.45/11.19 spl0_4 <=> ((lconfl @ sK2) = $false)),
% 69.45/11.19 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 69.45/11.19 thf(f1822,plain,(
% 69.45/11.19 ~spl0_5),
% 69.45/11.19 inference(avatar_contradiction_clause,[status(thm)],[f1821])).
% 69.45/11.19 thf(f1821,plain,(
% 69.45/11.19 $false | ~spl0_5),
% 69.45/11.19 inference(trivial_inequality_removal,[status(thm)],[f1777])).
% 69.45/11.19 thf(f1777,plain,(
% 69.45/11.19 ($false = $true) | ~spl0_5),
% 69.45/11.19 inference(superposition,[status(thm)],[f1766,f717])).
% 69.45/11.19 thf(f717,plain,(
% 69.45/11.19 ($false = (join @ sK2 @ sK15 @ sK13)) | ~spl0_5),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f716])).
% 69.45/11.19 thf(f716,plain,(
% 69.45/11.19 ((((sK2 @ sK14 @ sK15) & (sK2 @ sK14 @ sK13)) => (join @ sK2 @ sK15 @ sK13)) = $false) | ~spl0_5),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f715])).
% 69.45/11.19 thf(f715,plain,(
% 69.45/11.19 ($false = ((^[Y0 : $i]: (((sK2 @ sK14 @ Y0) & (sK2 @ sK14 @ sK13)) => (join @ sK2 @ Y0 @ sK13))) @ sK15)) | ~spl0_5),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f674])).
% 69.45/11.19 thf(f674,plain,(
% 69.45/11.19 ((!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK14 @ Y0) & (sK2 @ sK14 @ sK13)) => (join @ sK2 @ Y0 @ sK13)))) = $false) | ~spl0_5),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f673])).
% 69.45/11.19 thf(f673,plain,(
% 69.45/11.19 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ Y1) & (sK2 @ Y0 @ sK13)) => (join @ sK2 @ Y1 @ sK13))))) @ sK14) = $false) | ~spl0_5),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f636])).
% 69.45/11.19 thf(f636,plain,(
% 69.45/11.19 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ Y1) & (sK2 @ Y0 @ sK13)) => (join @ sK2 @ Y1 @ sK13)))))) = $false) | ~spl0_5),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f635])).
% 69.45/11.19 thf(f635,plain,(
% 69.45/11.19 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y2) & (sK2 @ Y1 @ Y0)) => (join @ sK2 @ Y2 @ Y0))))))) @ sK13) = $false) | ~spl0_5),
% 69.45/11.19 inference(sigma_clausification,[status(thm)],[f135])).
% 69.45/11.19 thf(f135,plain,(
% 69.45/11.19 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y2) & (sK2 @ Y1 @ Y0)) => (join @ sK2 @ Y2 @ Y0))))))))) | ~spl0_5),
% 69.45/11.19 inference(avatar_component_clause,[status(thm)],[f133])).
% 69.45/11.19 thf(f133,definition,(
% 69.45/11.19 spl0_5 <=> ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y2) & (sK2 @ Y1 @ Y0)) => (join @ sK2 @ Y2 @ Y0)))))))))),
% 69.45/11.19 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 69.45/11.19 thf(f1766,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (join @ X1 @ X2 @ X3))) )),
% 69.45/11.19 inference(subsumption_resolution,[status(thm)],[f1765,f192])).
% 69.45/11.19 thf(f1765,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : ((X2 != X3) | ($true = (join @ X1 @ X2 @ X3))) )),
% 69.45/11.19 inference(equality_proxy_clausification,[status(thm)],[f1764])).
% 69.45/11.19 thf(f1764,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((X2 = X3) = $false) | ($true = (join @ X1 @ X2 @ X3))) )),
% 69.45/11.19 inference(not_proxy_clausification,[status(thm)],[f1763])).
% 69.45/11.19 thf(f1763,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (join @ X1 @ X2 @ X3)) | ((~ (X2 = X3)) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f1761])).
% 69.45/11.19 thf(f1761,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (join @ X1 @ X2 @ X3)) | (((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X2 @ X3)))))) = $true)) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f1758])).
% 69.45/11.19 thf(f1758,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X2 @ X3)))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3))))))))))) | (~ (!! @ ($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 @ Y4 @ Y3)) | (~ (Y1 @ Y2 @ Y4))) | (Y1 @ Y2 @ Y3)))))))))) | (Y1 @ X3 @ Y0))))))))) = $true) | ($true = (join @ X1 @ X2 @ X3))) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f1756])).
% 69.45/11.19 thf(f1756,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (join @ X1 @ X2 @ X3)) | ($true = ((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X2 @ X3)))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3))))))))))) | (~ (!! @ ($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 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y2 @ Y4))) | (Y1 @ Y2 @ Y3)))))))))) | (Y1 @ X3 @ Y0))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X3 @ X2)))))))) )),
% 69.45/11.19 inference(not_proxy_clausification,[status(thm)],[f1755])).
% 69.45/11.19 thf(f1755,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (join @ X1 @ X2 @ X3)) | ($false = (~ ((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X2 @ X3)))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3))))))))))) | (~ (!! @ ($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 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y2 @ Y4))) | (Y1 @ Y2 @ Y3)))))))))) | (Y1 @ X3 @ Y0))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X3 @ X2))))))))) )),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f1753])).
% 69.45/11.19 thf(f1753,plain,(
% 69.45/11.19 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((~ ((((~ (X2 = X3)) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y2 @ Y3))) | (~ (Y0 @ Y3 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X2 @ X3)))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3))))))))))) | (~ (!! @ ($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 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (~ (Y1 @ Y2 @ Y4))) | (Y1 @ Y2 @ Y3)))))))))) | (Y1 @ X3 @ Y0))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))) | (Y0 @ X3 @ X2))))))) = (join @ X1 @ X2 @ X3))) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f1752])).
% 69.45/11.19 thf(f1752,plain,(
% 69.45/11.19 ( ! [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]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (Y1 @ X2 @ Y0)))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ X2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ ($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 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y3 @ Y5))) | (Y2 @ Y3 @ Y4)))))))))) | (Y2 @ Y0 @ Y1))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y2)) | (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ Y0 @ X2)))))))) @ X3) = (join @ X1 @ X2 @ X3))) )),
% 69.45/11.19 inference(argument_congruence,[status(thm)],[f1423])).
% 69.45/11.19 thf(f1423,plain,(
% 69.45/11.19 ( ! [X2 : $i,X1 : $i > $i > $o] : (((join @ X1 @ X2) = (^[Y0 : $i]: (~ ((((~ (X2 = Y0)) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) | (~ (Y1 @ Y3 @ Y4))) | (~ (Y1 @ Y4 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (Y1 @ X2 @ Y0)))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ X2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))) | (~ (!! @ ($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 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (~ (Y2 @ Y3 @ Y5))) | (Y2 @ Y3 @ Y4)))))))))) | (Y2 @ Y0 @ Y1))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y2)) | (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ Y0 @ X2)))))))))) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f1422])).
% 69.45/11.19 thf(f1422,plain,(
% 69.45/11.19 ( ! [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]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (Y2 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y4 @ Y5)))))))))) | (Y3 @ Y1 @ Y2))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y1 @ Y0)))))))))) @ X2) = (join @ X1 @ X2))) )),
% 69.45/11.19 inference(argument_congruence,[status(thm)],[f1134])).
% 69.45/11.19 thf(f1134,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: (~ ((((~ (Y0 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y3) | (~ (Y2 @ Y4 @ Y5))) | (~ (Y2 @ Y5 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (Y2 @ Y0 @ Y1)))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4)))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (~ (Y3 @ Y4 @ Y6))) | (Y3 @ Y4 @ Y5)))))))))) | (Y3 @ Y1 @ Y2))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y1 @ Y0)))))))))) = (join @ X1))) )),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f1133])).
% 69.45/11.19 thf(f1133,plain,(
% 69.45/11.19 ( ! [X1 : $i > $i > $o] : (((join @ X1) = ((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) @ X1))) )),
% 69.45/11.19 inference(argument_congruence,[status(thm)],[f99])).
% 69.45/11.19 thf(f99,plain,(
% 69.45/11.19 (join = (^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))))),
% 69.45/11.19 inference(equality_proxy_clausification,[status(thm)],[f27])).
% 69.45/11.19 thf(f27,plain,(
% 69.45/11.19 (((^[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 @ Y5 @ Y6))) | (~ (Y3 @ Y6 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y1 @ Y2)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)))))))))))) = join) = $true)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 69.45/11.19 thf(f136,plain,(
% 69.45/11.19 spl0_4 | spl0_5),
% 69.45/11.19 inference(avatar_split_clause,[status(thm)],[f127,f133,f129])).
% 69.45/11.19 thf(f127,plain,(
% 69.45/11.19 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y2) & (sK2 @ Y1 @ Y0)) => (join @ sK2 @ Y2 @ Y0))))))))) | ((lconfl @ sK2) = $false)),
% 69.45/11.19 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 69.45/11.19 thf(f125,plain,(
% 69.45/11.19 ((lconfl @ sK2) != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y2) & (sK2 @ Y1 @ Y0)) => (join @ sK2 @ Y2 @ Y0)))))))))),
% 69.45/11.19 inference(beta_eta_normalization,[status(thm)],[f124])).
% 69.45/11.19 thf(f124,plain,(
% 69.45/11.19 ((lconfl @ sK2) != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (join @ Y0 @ Y3 @ Y1))))))))) @ sK2))),
% 69.45/11.19 inference(negative_extensionality,[status(thm)],[f14])).
% 69.45/11.19 thf(f14,plain,(
% 69.45/11.19 (lconfl != (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (join @ Y0 @ Y3 @ Y1))))))))))),
% 69.45/11.19 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 69.45/11.19 thf(f13,plain,(
% 69.45/11.19 ((lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (join @ Y0 @ Y3 @ Y1)))))))))) = $false)),
% 69.45/11.19 inference(not_proxy_clausification,[status(thm)],[f10])).
% 69.45/11.19 thf(f10,plain,(
% 69.45/11.19 ((~ (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (join @ Y0 @ Y3 @ Y1))))))))))) = $true)),
% 69.45/11.19 inference(cnf_transformation,[status(thm)],[f8])).
% 69.45/11.19 thf(f8,plain,(
% 69.45/11.19 ((~ (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (join @ Y0 @ Y3 @ Y1))))))))))) = $true)),
% 69.45/11.19 inference(fool_elimination,[status(thm)],[f7])).
% 69.45/11.19 thf(f7,plain,(
% 69.45/11.19 ~(lconfl = (^[X0 : $i > $i > $o] : (! [X1 : $i,X2 : $i,X3 : $i] : (((X0 @ X2 @ X3) & (X0 @ X2 @ X1)) => (join @ X0 @ X1 @ X3)))))),
% 69.45/11.19 inference(rectify,[status(thm)],[f3])).
% 69.45/11.19 thf(f3,negated_conjecture,(
% 69.45/11.19 ~(lconfl = (^[X4 : $i > $i > $o] : (! [X11 : $i,X6 : $i,X7 : $i] : (((X4 @ X6 @ X7) & (X4 @ X6 @ X11)) => (join @ X4 @ X11 @ X7)))))),
% 69.45/11.19 inference(negated_conjecture,[status(cth)],[f2])).
% 69.45/11.19 thf(f2,conjecture,(
% 69.45/11.19 (lconfl = (^[X4 : $i > $i > $o] : (! [X11 : $i,X6 : $i,X7 : $i] : (((X4 @ X6 @ X7) & (X4 @ X6 @ X11)) => (join @ X4 @ X11 @ X7)))))),
% 69.45/11.19 file('/export/starexec/sandbox/tmp/tmp.qqkWGq3eP8/DTF2THF_20128.p',locally_confluent)).
% 69.45/11.19 % SZS output end Proof for DTF2THF_20128
% 69.45/11.19 % (20489)------------------------------
% 69.45/11.19 % (20489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.45/11.19 % (20489)Termination reason: Refutation
% 69.45/11.19
% 69.45/11.19 % (20489)Memory used [KB]: 10874
% 69.45/11.19 % (20489)Time elapsed: 0.331 s
% 69.45/11.19 % (20489)Instructions burned: 1045 (million)
% 69.45/11.19 % (20489)------------------------------
% 69.45/11.19 % (20489)------------------------------
% 69.45/11.19 % (20226)Success in time 9.76 s
%------------------------------------------------------------------------------