%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 07:03:11 PM UTC 2026
% Result : Theorem 26.52s 26.82s
% Output : Proof 26.52s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_d_unsorted,type,
d_unsorted: $tType ).
thf(ty_subrel,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(ty_total,type,
total: ( $i > $i > $o ) > $o ).
thf(ty_confl,type,
confl: ( $i > $i > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_refl,type,
refl: ( $i > $i > $o ) > $o ).
thf(ty_symm,type,
symm: ( $i > $i > $o ) > $o ).
thf(ty_d_unsorted_0,type,
d_unsorted_0: d_unsorted ).
thf(ty_infl,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(ty_sconfl,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(ty_ind,type,
ind: ( $i > $i > $o ) > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_lconfl,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(ty_mono,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(ty_trsc,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_d2unsorted,type,
d2unsorted: d_unsorted > $i ).
thf(ty_so,type,
so: ( $i > $i > $o ) > $o ).
thf(ty_sc,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_rc,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_antisymm,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(ty_join,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_term,type,
term: ( $i > $i > $o ) > $o ).
thf(ty_trc,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_nfof,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_inv,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_innf,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(ty_irrefl,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(ty_asymm,type,
asymm: ( $i > $i > $o ) > $o ).
thf(ty_tc,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(ty_trans,type,
trans: ( $i > $i > $o ) > $o ).
thf(ty_cr,type,
cr: ( $i > $i > $o ) > $o ).
thf(ty_idem,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(ty_norm,type,
norm: ( $i > $i > $o ) > $o ).
thf(ty_po,type,
po: ( $i > $i > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ( ( tc @ eigen__0 )
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( trsc @ eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( tc @ eigen__0 @ eigen__2 @ eigen__1 )
= ( ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( tc @ eigen__0 @ eigen__1 @ X1 )
= ( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( rc @ ( tc @ eigen__0 ) )
= ( ^ [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ( tc @ eigen__0 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP6
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( trsc @ eigen__0 @ eigen__1 @ X1 )
= ( ~ ( ( eigen__1 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X1 @ eigen__1 ) ) )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> $false ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ X1 )
= ( ( eigen__1 != X1 )
=> ( tc @ eigen__0 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( rc @ ( tc @ eigen__0 ) @ eigen__2 @ eigen__1 )
=> ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( trsc @ eigen__0 @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $i > $o] :
( ( trsc @ X1 )
= ( ^ [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $i > $o] :
( ( sc @ X1 )
= ( ^ [X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( rc @ ( tc @ eigen__0 ) @ eigen__2 )
= ( ^ [X1: $i] :
( ( eigen__2 != X1 )
=> ( tc @ eigen__0 @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__2 != eigen__1 )
=> ( tc @ eigen__0 @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( tc @ eigen__0 @ eigen__1 @ eigen__2 )
= ( ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( trsc @ eigen__0 @ eigen__1 )
= ( ^ [X1: $i] :
( ~ ( ( eigen__1 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X1 @ eigen__1 ) ) )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( tc @ eigen__0 @ X1 )
= ( ^ [X2: $i] :
! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 @ X1 )
= ( ~ ( rc @ ( tc @ eigen__0 ) @ X1 @ eigen__1 )
=> ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ eigen__2 )
= ( ~ sP6
=> ( tc @ eigen__0 @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( trsc @ eigen__0 @ X1 )
= ( ^ [X2: $i] :
( ~ ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X2 @ X1 ) ) )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 @ eigen__2 )
= sP11 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( tc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( rc @ ( tc @ eigen__0 ) @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ eigen__1 )
=> ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( tc @ eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP12 = ( ~ sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( sc @ ( rc @ ( tc @ eigen__0 ) ) )
= ( ^ [X1: $i,X2: $i] :
( ~ ( rc @ ( tc @ eigen__0 ) @ X2 @ X1 )
=> ( rc @ ( tc @ eigen__0 ) @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( rc @ ( tc @ eigen__0 ) @ eigen__2 @ X1 )
= ( ( eigen__2 != X1 )
=> ( tc @ eigen__0 @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i] :
( ( tc @ eigen__0 @ eigen__2 @ X1 )
= ( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( rc @ ( tc @ eigen__0 ) @ X1 )
= ( ^ [X2: $i] :
( ( X1 != X2 )
=> ( tc @ eigen__0 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i > $i > $o] :
( ( tc @ X1 )
= ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 @ eigen__1 )
= sP28 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ X1 )
= ( ^ [X2: $i] :
( ~ ( rc @ ( tc @ eigen__0 ) @ X2 @ X1 )
=> ( rc @ ( tc @ eigen__0 ) @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 )
= ( ^ [X1: $i] :
( ~ ( rc @ ( tc @ eigen__0 ) @ X1 @ eigen__1 )
=> ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( trsc @ eigen__0 @ eigen__1 @ eigen__1 )
= ( ~ sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( trsc @ eigen__0 @ eigen__2 )
= ( ^ [X1: $i] :
( ~ ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X1 @ eigen__2 ) ) )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( rc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP2 = sP37 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( tc @ eigen__0 @ eigen__1 )
= ( ^ [X1: $i] :
! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ sP6
=> ( tc @ eigen__0 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ eigen__1 )
= ( ~ sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( trsc @ eigen__0 @ eigen__2 @ X1 )
= ( ~ ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ X1 @ eigen__2 ) ) )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( tc @ eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ( trsc @ eigen__0 )
= ( ^ [X1: $i,X2: $i] :
( ~ ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X2 @ X1 ) ) )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ( tc @ eigen__0 @ eigen__2 )
= ( ^ [X1: $i] :
! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ sP7
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( trsc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP27 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP2 = sP54 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( rc @ ( tc @ eigen__0 ) @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( trsc @ eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i > $i > $o] :
( ( rc @ X1 )
= ( ^ [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ( rc @ ( tc @ eigen__0 ) @ eigen__1 )
= ( ^ [X1: $i] :
( ( eigen__1 != X1 )
=> ( tc @ eigen__0 @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(transitive_reflexive_symmetric_closure,conjecture,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).
thf(h0,negated_conjecture,
( trsc
!= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[transitive_reflexive_symmetric_closure]) ).
thf(h1,assumption,
~ ! [X1: $i > $i > $o] :
( ( trsc @ X1 )
= ( sc @ ( rc @ ( tc @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( trsc @ eigen__0 )
!= ( sc @ ( rc @ ( tc @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( trsc @ eigen__0 @ X1 )
= ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( trsc @ eigen__0 @ eigen__1 )
!= ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( trsc @ eigen__0 @ eigen__1 @ X1 )
= ( sc @ ( rc @ ( tc @ eigen__0 ) ) @ eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP46,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( nfof
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ) )
=> ( norm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) ) ) ) ) )
=> ( join
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ) )
=> ( lconfl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) )
=> ( sconfl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( ( X2 != X3 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X3 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) )
=> ( confl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X2 != X4 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X3 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
( cr
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i > $i > $o,X5: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ( X2 != X3 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X2 ) ) )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ( X2 = X3 ) )
=> ~ ! [X6: $i] :
( ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X3 @ X6 ) )
=> ~ ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X6 ) ) ) )
=> ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X4 @ X6 @ X7 )
=> ~ ( X4 @ X7 @ X8 ) )
=> ( X4 @ X6 @ X8 ) ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X4 @ X6 @ X7 ) ) )
=> ( X4 @ X3 @ X2 ) )
=> ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( nfof
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ) )
=> ( norm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) ) ) ) ) )
=> ( join
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ) )
=> ( lconfl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) )
=> ( sconfl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( ( X2 != X3 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X3 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
( confl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X2 != X4 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X3 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( nfof
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ) )
=> ( norm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) ) ) ) ) )
=> ( join
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ) )
=> ( lconfl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( sconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( ( X2 != X3 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X3 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( nfof
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ) )
=> ( norm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) ) ) ) ) )
=> ( join
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( lconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( nfof
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ) )
=> ( norm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
( join
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( nfof
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
( norm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
( nfof
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
( innf
= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
( term
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
( total
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
( so
= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 ),
introduced(assumption,[]) ).
thf(h32,assumption,
( po
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
sP55,
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h36,assumption,
( trc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP25,
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h40,assumption,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
sP26,
introduced(assumption,[]) ).
thf(h43,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 ),
introduced(assumption,[]) ).
thf(h48,assumption,
( symm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h49,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h50,assumption,
sP45,
introduced(assumption,[]) ).
thf(h51,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h52,assumption,
( irrefl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h53,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h54,assumption,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h55,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h56,assumption,
( mono
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ),
introduced(assumption,[]) ).
thf(h57,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h58,assumption,
( infl
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h59,assumption,
~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h60,assumption,
( idem
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h61,assumption,
~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h62,assumption,
( inv
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h63,assumption,
~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h64,assumption,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h65,assumption,
~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) ),
introduced(assumption,[]) ).
thf(h66,assumption,
! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h67,assumption,
! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) ),
introduced(assumption,[]) ).
thf(h68,assumption,
! [X1: d_unsorted] : ( X1 = d_unsorted_0 ),
introduced(assumption,[]) ).
thf(1,plain,
( sP7
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| sP6
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP17
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP48
| ~ sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP11
| ~ sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP11
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP11
| sP27
| sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP28
| ~ sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP54
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP54
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP54
| sP7
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP56
| ~ sP27
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP56
| sP27
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP22
| ~ sP38
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP22
| sP38
| ~ sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP49
| sP58
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP24
| ~ sP37
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP24
| sP37
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP39
| sP59
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP3
| ~ sP29
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP3
| sP29
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP18
| ~ sP51
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP18
| sP51
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP30
| sP12
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP57
| ~ sP2
| sP54 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP57
| sP2
| ~ sP54 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP43
| sP60
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP17
| sP41
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP48
| sP6
| sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP59
| sP37
| ~ sP6
| sP9
| sP9 ),
inference(mating_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP12
| sP2
| sP9
| ~ sP41
| sP9 ),
inference(mating_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP60
| sP2
| ~ sP6
| sP9
| sP9 ),
inference(mating_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP32
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP10
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP10
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP21
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP21
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP34
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP4
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP50
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP8
| sP57 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP8
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
~ sP9,
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP16
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP62
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP42
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP53
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP47
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP44
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP19
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP35
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP35
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP40
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP20
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP20
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP23
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP23
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP5
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP31
| sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP1
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP52
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP61
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP15
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP36
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP14
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP45
| sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP26
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP25
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP55
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( sP46
| ~ sP2
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( sP46
| sP2
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,h50,h42,h38,h34,h6]) ).
thf(73,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h67,h68])],[h65,72,h67,h68]) ).
thf(74,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h65,h66])],[h63,73,h65,h66]) ).
thf(75,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h63,h64])],[h61,74,h63,h64]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h61,h62])],[h59,75,h61,h62]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h59,h60])],[h57,76,h59,h60]) ).
thf(78,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h57,h58])],[h55,77,h57,h58]) ).
thf(79,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h55,h56])],[h53,78,h55,h56]) ).
thf(80,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h51,h52,h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h53,h54])],[h51,79,h53,h54]) ).
thf(81,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h49,h50,h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h51,h52])],[h49,80,h51,h52]) ).
thf(82,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h47,h48,h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h49,h50])],[h47,81,h49,h50]) ).
thf(83,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h46,h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h47,h48])],[h45,82,h47,h48]) ).
thf(84,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h43,h44,h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h45,h46])],[h43,83,h45,h46]) ).
thf(85,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h41,84,h43,h44]) ).
thf(86,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h40,h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h41,h42])],[h39,85,h41,h42]) ).
thf(87,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h39,h40])],[h37,86,h39,h40]) ).
thf(88,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h37,h38])],[h35,87,h37,h38]) ).
thf(89,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h35,h36])],[h33,88,h35,h36]) ).
thf(90,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h31,89,h33,h34]) ).
thf(91,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,90,h31,h32]) ).
thf(92,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h27,91,h29,h30]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h25,92,h27,h28]) ).
thf(94,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h23,93,h25,h26]) ).
thf(95,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,94,h23,h24]) ).
thf(96,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,95,h21,h22]) ).
thf(97,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,96,h19,h20]) ).
thf(98,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,97,h17,h18]) ).
thf(99,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,98,h15,h16]) ).
thf(100,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,99,h13,h14]) ).
thf(101,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,100,h11,h12]) ).
thf(102,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,101,h9,h10]) ).
thf(sev441_1,axiom,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: $i] :
~ ! [X2: d_unsorted] :
( X1
!= ( d2unsorted @ X2 ) )
=> ~ ! [X1: d_unsorted] : ( X1 = d_unsorted_0 ) )
=> ~ ! [X1: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X1 )
= ( d2unsorted @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( subrel
!= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) )
=> ( inv
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) )
=> ( idem
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ) ) ) )
=> ( infl
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ( X1 @ X2 @ X3 @ X4 ) ) ) ) )
=> ( mono
!= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o,X4: $i,X5: $i] :
( ~ ( ! [X6: $i,X7: $i] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ X7 ) )
=> ~ ( X1 @ X2 @ X4 @ X5 ) )
=> ( X1 @ X3 @ X4 @ X5 ) ) ) ) )
=> ( refl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) )
=> ( irrefl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) )
=> ~ sP45 )
=> ( symm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( antisymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( asymm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) )
=> ~ sP26 )
=> ( trans
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) )
=> ~ sP25 )
=> ( trc
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ) )
=> ~ sP55 )
=> ( po
!= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( so
!= ( ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ) )
=> ( total
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) )
=> ( term
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X2 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ) )
=> ( ind
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o,X3: $i] :
( ! [X4: $i] :
( ! [X5: $i] :
( ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ( X2 @ X5 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) ) ) )
=> ( innf
!= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) )
=> ( nfof
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ~ ! [X4: $i] :
~ ( X1 @ X2 @ X4 ) ) ) ) )
=> ( norm
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
~ ( X1 @ X4 @ X5 ) ) ) ) ) )
=> ( join
!= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X3 @ X2 ) ) )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( X1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ) )
=> ( lconfl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) )
=> ( sconfl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( ( X2 != X3 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X3 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) )
=> ( confl
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i > $i > $o,X6: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X2 != X4 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X3 ) ) ) )
=> ( X3 = X4 ) )
=> ~ ! [X7: $i] :
( ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X3 @ X7 ) )
=> ~ ! [X8: $i > $i > $o] :
( ~ ( ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) )
=> ~ ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X4 @ X7 ) ) ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X5 @ X7 @ X8 )
=> ~ ( X5 @ X8 @ X9 ) )
=> ( X5 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X5 @ X7 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X3 ) ) ) ) )
=> ( cr
!= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i > $i > $o,X5: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ( X2 != X3 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X2 ) ) )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X2 @ X3 ) ) )
=> ( X2 = X3 ) )
=> ~ ! [X6: $i] :
( ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X3 @ X6 ) )
=> ~ ! [X7: $i > $i > $o] :
( ~ ( ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) )
=> ~ ! [X8: $i,X9: $i] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) ) )
=> ( X7 @ X2 @ X6 ) ) ) )
=> ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X4 @ X6 @ X7 )
=> ~ ( X4 @ X7 @ X8 ) )
=> ( X4 @ X6 @ X8 ) ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X4 @ X6 @ X7 ) ) )
=> ( X4 @ X3 @ X2 ) )
=> ~ ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X3 ) ) ) ) ) ).
thf(103,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[sev441_1,102,h7,h8]) ).
thf(104,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,103,h6]) ).
thf(105,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,104,h5]) ).
thf(106,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,105,h4]) ).
thf(107,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,106,h3]) ).
thf(108,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,107,h2]) ).
thf(109,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,108,h1]) ).
thf(0,theorem,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[109,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 09:29:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 26.52/26.82 % SZS status Theorem
% 26.52/26.82 % Mode: cade22grackle2x798d
% 26.52/26.82 % Steps: 16792
% 26.52/26.82 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------