%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP104^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:07 AM UTC 2026
% Result : Theorem 13.78s 2.54s
% Output : CNFRefutation 13.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 34
% Syntax : Number of formulae : 989 ( 237 unt; 0 typ; 0 def)
% Number of atoms : 8208 (4170 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 18014 (3600 ~;2801 |; 24 &;11454 @)
% ( 0 <=>; 135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 18 ( 17 usr)
% Number of type conns : 585 ( 585 >; 0 *; 0 +; 0 <<)
% Number of symbols : 132 ( 129 usr; 6 con; 0-4 aty)
% Number of variables : 3399 ( 99 ^;3279 !; 21 ?;3399 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_list_a,type,
list_a: $tType ).
thf(tp_list_l2071841302list_a,type,
list_l2071841302list_a: $tType ).
thf(tp_list_list_a,type,
list_list_a: $tType ).
thf(tp_list_list_list_a,type,
list_list_list_a: $tType ).
thf(tp_list_list_list_nat,type,
list_list_list_nat: $tType ).
thf(tp_list_list_nat,type,
list_list_nat: $tType ).
thf(tp_list_nat,type,
list_nat: $tType ).
thf(tp_list_set_a,type,
list_set_a: $tType ).
thf(tp_list_set_list_a,type,
list_set_list_a: $tType ).
thf(tp_list_set_nat,type,
list_set_nat: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_set_list_a,type,
set_list_a: $tType ).
thf(tp_set_list_list_a,type,
set_list_list_a: $tType ).
thf(tp_set_list_nat,type,
set_list_nat: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_butlast_a,type,
butlast_a: list_a > list_a ).
thf(tp_butlast_list_a,type,
butlast_list_a: list_list_a > list_list_a ).
thf(tp_butlast_list_list_a,type,
butlast_list_list_a: list_list_list_a > list_list_list_a ).
thf(tp_butlast_list_nat,type,
butlast_list_nat: list_list_nat > list_list_nat ).
thf(tp_butlast_nat,type,
butlast_nat: list_nat > list_nat ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_collect_list_a,type,
collect_list_a: ( list_a > $o ) > set_list_a ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_distinct_a,type,
distinct_a: list_a > $o ).
thf(tp_distinct_list_a,type,
distinct_list_a: list_list_a > $o ).
thf(tp_distinct_list_list_a,type,
distinct_list_list_a: list_list_list_a > $o ).
thf(tp_distinct_list_nat,type,
distinct_list_nat: list_list_nat > $o ).
thf(tp_distinct_nat,type,
distinct_nat: list_nat > $o ).
thf(tp_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(tp_f_image_a,type,
f_image_a: list_a > set_nat > set_a ).
thf(tp_f_image_list_a,type,
f_image_list_a: list_list_a > set_nat > set_list_a ).
thf(tp_f_image_list_list_a,type,
f_image_list_list_a: list_list_list_a > set_nat > set_list_list_a ).
thf(tp_f_image_list_nat,type,
f_image_list_nat: list_list_nat > set_nat > set_list_nat ).
thf(tp_f_image_nat,type,
f_image_nat: list_nat > set_nat > set_nat ).
thf(tp_k,type,
k: nat ).
thf(tp_listSl1174287072ice2_a,type,
listSl1174287072ice2_a: list_a > nat > list_list_a ).
thf(tp_listSl1495374126_aux_a,type,
listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
thf(tp_listSl1506485424st_nat,type,
listSl1506485424st_nat: list_list_nat > nat > nat > list_list_list_nat ).
thf(tp_listSl162220270list_a,type,
listSl162220270list_a: list_list_a > nat > list_list_list_a ).
thf(tp_listSl1630398182ce_nat,type,
listSl1630398182ce_nat: list_nat > nat > list_list_nat ).
thf(tp_listSl1794011552ux_nat,type,
listSl1794011552ux_nat: list_nat > nat > nat > list_list_nat ).
thf(tp_listSl2099749758st_nat,type,
listSl2099749758st_nat: list_list_nat > nat > list_list_list_nat ).
thf(tp_listSl2102238196list_a,type,
listSl2102238196list_a: list_list_list_a > nat > list_l2071841302list_a ).
thf(tp_listSl703198822list_a,type,
listSl703198822list_a: list_list_a > nat > list_list_list_a ).
thf(tp_listSl729562870st_nat,type,
listSl729562870st_nat: list_list_nat > nat > list_list_list_nat ).
thf(tp_listSl769338732list_a,type,
listSl769338732list_a: list_list_list_a > nat > list_l2071841302list_a ).
thf(tp_listSl856612276list_a,type,
listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
thf(tp_listSl882585454e2_nat,type,
listSl882585454e2_nat: list_nat > nat > list_list_nat ).
thf(tp_listSl902632890list_a,type,
listSl902632890list_a: list_list_list_a > nat > nat > list_l2071841302list_a ).
thf(tp_listSl97544552lice_a,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(tp_list_asc_nat,type,
list_asc_nat: list_nat > $o ).
thf(tp_list_asc_set_a,type,
list_asc_set_a: list_set_a > $o ).
thf(tp_list_asc_set_list_a,type,
list_asc_set_list_a: list_set_list_a > $o ).
thf(tp_list_asc_set_nat,type,
list_asc_set_nat: list_set_nat > $o ).
thf(tp_list_desc_nat,type,
list_desc_nat: list_nat > $o ).
thf(tp_list_desc_set_a,type,
list_desc_set_a: list_set_a > $o ).
thf(tp_list_desc_set_list_a,type,
list_desc_set_list_a: list_set_list_a > $o ).
thf(tp_list_desc_set_nat,type,
list_desc_set_nat: list_set_nat > $o ).
thf(tp_list_ex_a,type,
list_ex_a: ( a > $o ) > list_a > $o ).
thf(tp_list_ex_list_a,type,
list_ex_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(tp_list_ex_list_list_a,type,
list_ex_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
thf(tp_list_ex_list_nat,type,
list_ex_list_nat: ( list_nat > $o ) > list_list_nat > $o ).
thf(tp_list_ex_nat,type,
list_ex_nat: ( nat > $o ) > list_nat > $o ).
thf(tp_list_strict_asc_nat,type,
list_strict_asc_nat: list_nat > $o ).
thf(tp_list_strict_desc_nat,type,
list_strict_desc_nat: list_nat > $o ).
thf(tp_list_u1330012152list_a,type,
list_u1330012152list_a: list_list_list_a > nat > list_list_a > list_list_list_a ).
thf(tp_list_update_a,type,
list_update_a: list_a > nat > a > list_a ).
thf(tp_list_update_list_a,type,
list_update_list_a: list_list_a > nat > list_a > list_list_a ).
thf(tp_list_update_list_nat,type,
list_update_list_nat: list_list_nat > nat > list_nat > list_list_nat ).
thf(tp_list_update_nat,type,
list_update_nat: list_nat > nat > nat > list_nat ).
thf(tp_m,type,
m: nat ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_list_a,type,
member_list_a: list_a > set_list_a > $o ).
thf(tp_member_list_list_a,type,
member_list_list_a: list_list_a > set_list_list_a > $o ).
thf(tp_member_list_nat,type,
member_list_nat: list_nat > set_list_nat > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_nth_a,type,
nth_a: list_a > nat > a ).
thf(tp_nth_list_a,type,
nth_list_a: list_list_a > nat > list_a ).
thf(tp_nth_list_list_a,type,
nth_list_list_a: list_list_list_a > nat > list_list_a ).
thf(tp_nth_list_list_list_a,type,
nth_list_list_list_a: list_l2071841302list_a > nat > list_list_list_a ).
thf(tp_nth_list_list_nat,type,
nth_list_list_nat: list_list_list_nat > nat > list_list_nat ).
thf(tp_nth_list_nat,type,
nth_list_nat: list_list_nat > nat > list_nat ).
thf(tp_nth_nat,type,
nth_nat: list_nat > nat > nat ).
thf(tp_nth_set_a,type,
nth_set_a: list_set_a > nat > set_a ).
thf(tp_nth_set_list_a,type,
nth_set_list_a: list_set_list_a > nat > set_list_a ).
thf(tp_nth_set_nat,type,
nth_set_nat: list_set_nat > nat > set_nat ).
thf(tp_ord_le1301786372list_a,type,
ord_le1301786372list_a: set_list_a > set_list_a > $o ).
thf(tp_ord_le1747345782st_nat,type,
ord_le1747345782st_nat: set_list_nat > set_list_nat > $o ).
thf(tp_ord_le1756736906list_a,type,
ord_le1756736906list_a: set_list_list_a > set_list_list_a > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_sK10_SY226,type,
sK10_SY226: list_list_a > nat ).
thf(tp_sK11_SY220,type,
sK11_SY220: list_a > list_a > nat ).
thf(tp_sK12_SY221,type,
sK12_SY221: ( a > $o ) > list_a > nat ).
thf(tp_sK13_SY222,type,
sK13_SY222: list_list_a > list_list_a > nat ).
thf(tp_sK14_SY223,type,
sK14_SY223: ( list_a > $o ) > list_list_a > nat ).
thf(tp_sK15_SY195,type,
sK15_SY195: ( nat > list_a > $o ) > nat > list_list_a ).
thf(tp_sK16_SY229,type,
sK16_SY229: list_list_a > ( nat > list_a > $o ) > nat > nat ).
thf(tp_sK17_SY206,type,
sK17_SY206: ( nat > a > $o ) > nat > list_a ).
thf(tp_sK18_SY230,type,
sK18_SY230: list_a > ( nat > a > $o ) > nat > nat ).
thf(tp_sK19_SY195,type,
sK19_SY195: list_a > ( nat > list_a > $o ) > nat > list_list_a ).
thf(tp_sK1_SY119,type,
sK1_SY119: nat > list_a ).
thf(tp_sK20_SY206,type,
sK20_SY206: a > ( nat > a > $o ) > nat > list_a ).
thf(tp_sK21_SY235,type,
sK21_SY235: nat > nat > ( nat > list_a > $o ) > list_a ).
thf(tp_sK22_SY236,type,
sK22_SY236: nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK23_SY241,type,
sK23_SY241: list_a > nat > nat > ( nat > list_a > $o ) > list_a ).
thf(tp_sK24_SY242,type,
sK24_SY242: a > nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK25_SY221,type,
sK25_SY221: nat > ( a > $o ) > list_a > nat ).
thf(tp_sK26_SY195,type,
sK26_SY195: list_list_a > ( nat > list_a > $o ) > nat > list_list_a ).
thf(tp_sK27_SY206,type,
sK27_SY206: list_a > ( nat > a > $o ) > nat > list_a ).
thf(tp_sK28_SY223,type,
sK28_SY223: nat > ( list_a > $o ) > list_list_a > nat ).
thf(tp_sK29_SY195,type,
sK29_SY195: list_list_a > ( nat > list_a > $o ) > nat > list_list_a ).
thf(tp_sK2_SY152,type,
sK2_SY152: list_a > ( list_a > $o ) > list_a ).
thf(tp_sK30_SY206,type,
sK30_SY206: list_a > ( nat > a > $o ) > nat > list_a ).
thf(tp_sK31_SY249,type,
sK31_SY249: list_list_a > nat > nat > ( nat > list_a > $o ) > list_a ).
thf(tp_sK32_SY250,type,
sK32_SY250: list_a > nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK33_SY251,type,
sK33_SY251: list_list_a > nat > nat > ( nat > list_a > $o ) > list_a ).
thf(tp_sK34_SY253,type,
sK34_SY253: list_a > nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK3_SY182,type,
sK3_SY182: list_a > nat ).
thf(tp_sK4_SY189,type,
sK4_SY189: list_list_a > nat ).
thf(tp_sK5_SY192,type,
sK5_SY192: list_list_a > list_list_a > nat ).
thf(tp_sK6_SY193,type,
sK6_SY193: ( nat > list_a > $o ) > nat > nat ).
thf(tp_sK7_SY201,type,
sK7_SY201: list_a > list_a > nat ).
thf(tp_sK8_SY204,type,
sK8_SY204: ( nat > a > $o ) > nat > nat ).
thf(tp_sK9_SY225,type,
sK9_SY225: list_a > nat ).
thf(tp_set_a2,type,
set_a2: list_a > set_a ).
thf(tp_set_list_a2,type,
set_list_a2: list_list_a > set_list_a ).
thf(tp_set_list_list_a2,type,
set_list_list_a2: list_list_list_a > set_list_list_a ).
thf(tp_set_list_nat2,type,
set_list_nat2: list_list_nat > set_list_nat ).
thf(tp_set_nat2,type,
set_nat2: list_nat > set_nat ).
thf(tp_size_s1321307156st_nat,type,
size_s1321307156st_nat: list_list_list_nat > nat ).
thf(tp_size_s1427607542list_a,type,
size_s1427607542list_a: list_list_a > nat ).
thf(tp_size_s1635937238list_a,type,
size_s1635937238list_a: list_set_list_a > nat ).
thf(tp_size_s1764310658list_a,type,
size_s1764310658list_a: list_l2071841302list_a > nat ).
thf(tp_size_s1898481668st_nat,type,
size_s1898481668st_nat: list_list_nat > nat ).
thf(tp_size_s575106428list_a,type,
size_s575106428list_a: list_list_list_a > nat ).
thf(tp_size_s577819178et_nat,type,
size_s577819178et_nat: list_set_nat > nat ).
thf(tp_size_size_list_a,type,
size_size_list_a: list_a > nat ).
thf(tp_size_size_list_nat,type,
size_size_list_nat: list_nat > nat ).
thf(tp_size_size_list_set_a,type,
size_size_list_set_a: list_set_a > nat ).
thf(tp_top_top_set_nat,type,
top_top_set_nat: set_nat ).
thf(tp_xs,type,
xs: list_a ).
thf(139,axiom,
( distinct_list_a
= ( ^ [Xs2: list_list_a] :
! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
=> ! [J: nat] :
( ( ord_less_nat @ J @ ( size_s1427607542list_a @ Xs2 ) )
=> ( ( I2 != J )
=> ( ( nth_list_a @ Xs2 @ I2 )
!= ( nth_list_a @ Xs2 @ J ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_distinct__conv__nth) ).
thf(140,axiom,
( distinct_a
= ( ^ [Xs2: list_a] :
! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
=> ! [J: nat] :
( ( ord_less_nat @ J @ ( size_size_list_a @ Xs2 ) )
=> ( ( I2 != J )
=> ( ( nth_a @ Xs2 @ I2 )
!= ( nth_a @ Xs2 @ J ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_distinct__conv__nth) ).
thf(142,axiom,
! [Xs: list_list_a,I3: nat,J2: nat] :
( ( distinct_list_a @ Xs )
=> ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( nth_list_a @ Xs @ I3 )
= ( nth_list_a @ Xs @ J2 ) )
= ( I3 = J2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_nth__eq__iff__index__eq) ).
thf(143,axiom,
! [Xs: list_a,I3: nat,J2: nat] :
( ( distinct_a @ Xs )
=> ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
=> ( ( ( nth_a @ Xs @ I3 )
= ( nth_a @ Xs @ J2 ) )
= ( I3 = J2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_nth__eq__iff__index__eq) ).
thf(160,axiom,
! [Xs: list_a,I3: nat,X2: a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ I3 )
=> ( ( list_update_a @ Xs @ I3 @ X2 )
= Xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_list__update__beyond) ).
thf(209,axiom,
! [I3: nat,Xs: list_list_a,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( list_update_list_a @ Xs @ I3 @ X2 )
= Xs )
= ( ( nth_list_a @ Xs @ I3 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_list__update__same__conv) ).
thf(210,axiom,
! [I3: nat,Xs: list_a,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ( list_update_a @ Xs @ I3 @ X2 )
= Xs )
= ( ( nth_a @ Xs @ I3 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_list__update__same__conv) ).
thf(214,axiom,
! [I3: nat,Xs: list_list_a,J2: nat,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( I3 = J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= X2 ) )
& ( ( I3 != J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_list_a @ Xs @ J2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_nth__list__update) ).
thf(215,axiom,
! [I3: nat,Xs: list_a,J2: nat,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ( I3 = J2 )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
= X2 ) )
& ( ( I3 != J2 )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_a @ Xs @ J2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_nth__list__update) ).
thf(226,axiom,
! [I3: nat,J2: nat,Xs: list_list_a,X2: list_a] :
( ( I3 != J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_list_a @ Xs @ J2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_nth__list__update__neq) ).
thf(231,axiom,
! [Xs: list_list_a,I3: nat] :
( ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ I3 ) )
= Xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_list__update__id) ).
thf(236,axiom,
! [Xs: list_a,I3: nat,X2: a] :
( ( size_size_list_a @ ( list_update_a @ Xs @ I3 @ X2 ) )
= ( size_size_list_a @ Xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_length__list__update) ).
thf(253,axiom,
! [N: nat,Xs: list_list_a] :
( ( ord_less_nat @ N @ ( size_s1427607542list_a @ ( butlast_list_a @ Xs ) ) )
=> ( ( nth_list_a @ ( butlast_list_a @ Xs ) @ N )
= ( nth_list_a @ Xs @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_nth__butlast) ).
thf(254,axiom,
! [N: nat,Xs: list_a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ ( butlast_a @ Xs ) ) )
=> ( ( nth_a @ ( butlast_a @ Xs ) @ N )
= ( nth_a @ Xs @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_nth__butlast) ).
thf(268,axiom,
! [I3: nat,Xs: list_list_a,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_nth__list__update__eq) ).
thf(269,axiom,
! [I3: nat,Xs: list_a,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_nth__list__update__eq) ).
thf(279,axiom,
( list_ex_list_a
= ( ^ [P2: list_a > $o,Xs2: list_list_a] :
? [N3: nat] :
( ( ord_less_nat @ N3 @ ( size_s1427607542list_a @ Xs2 ) )
& ( P2 @ ( nth_list_a @ Xs2 @ N3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_list__ex__length) ).
thf(280,axiom,
( list_ex_a
= ( ^ [P2: a > $o,Xs2: list_a] :
? [N3: nat] :
( ( ord_less_nat @ N3 @ ( size_size_list_a @ Xs2 ) )
& ( P2 @ ( nth_a @ Xs2 @ N3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_list__ex__length) ).
thf(284,axiom,
( listSl97544552lice_a
= ( ^ [Xs2: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs2 ) @ K2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_list__slice__def) ).
thf(296,axiom,
! [Xs: list_a,K: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
= ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_list__slice__length) ).
thf(304,axiom,
! [X2: list_a,Y2: list_a] :
( ( ( size_size_list_a @ X2 )
!= ( size_size_list_a @ Y2 ) )
=> ( X2 != Y2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_size__neq__size__imp__neq) ).
thf(307,axiom,
! [Xs: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs )
!= ( size_size_list_a @ Ys ) )
=> ( Xs != Ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_neq__if__length__neq) ).
thf(312,axiom,
! [N: nat] :
? [Xs3: list_a] :
( ( size_size_list_a @ Xs3 )
= N ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Ex__list__of__length) ).
thf(318,axiom,
! [M: nat,Xs: list_a,K: nat] :
( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) )
= K ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_list__slice__nth__length) ).
thf(324,axiom,
! [P: list_a > $o,Xs: list_a] :
( ! [Xs3: list_a] :
( ! [Ys3: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
=> ( P @ Ys3 ) )
=> ( P @ Xs3 ) )
=> ( P @ Xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_length__induct) ).
thf(329,axiom,
! [M: nat,Xs: list_a,K: nat] :
( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ Xs @ K ) @ M )
= ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_list__slice2__list__slice__nth) ).
thf(334,axiom,
( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
= ( ^ [Xs2: list_a,Ys2: list_a] :
( ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ Xs2 @ I2 )
= ( nth_a @ Ys2 @ I2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_list__eq__iff__nth__eq) ).
thf(335,axiom,
( ( ^ [Y: list_list_a,Z: list_list_a] : ( Y = Z ) )
= ( ^ [Xs2: list_list_a,Ys2: list_list_a] :
( ( ( size_s1427607542list_a @ Xs2 )
= ( size_s1427607542list_a @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
=> ( ( nth_list_a @ Xs2 @ I2 )
= ( nth_list_a @ Ys2 @ I2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_list__eq__iff__nth__eq) ).
thf(339,axiom,
! [K: nat,P: nat > a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X: a] : ( P @ I2 @ X ) ) )
= ( ? [Xs2: list_a] :
( ( ( size_size_list_a @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Skolem__list__nth) ).
thf(340,axiom,
! [K: nat,P: nat > list_a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X: list_a] : ( P @ I2 @ X ) ) )
= ( ? [Xs2: list_list_a] :
( ( ( size_s1427607542list_a @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_list_a @ Xs2 @ I2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Skolem__list__nth) ).
thf(344,axiom,
! [Xs: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs )
= ( size_size_list_a @ Ys ) )
=> ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
=> ( ( nth_a @ Xs @ I )
= ( nth_a @ Ys @ I ) ) )
=> ( Xs = Ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nth__equalityI) ).
thf(345,axiom,
! [Xs: list_list_a,Ys: list_list_a] :
( ( ( size_s1427607542list_a @ Xs )
= ( size_s1427607542list_a @ Ys ) )
=> ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
=> ( ( nth_list_a @ Xs @ I )
= ( nth_list_a @ Ys @ I ) ) )
=> ( Xs = Ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nth__equalityI) ).
thf(349,axiom,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(350,conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(351,negated_conjecture,
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k )
= $false ),
inference(negate_conjecture,[status(cth)],[350]) ).
thf(352,plain,
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k )
= $false ),
inference(unfold_def,[status(thm)],[351]) ).
thf(353,plain,
( ( distinct_list_a
= ( ^ [Xs2: list_list_a] :
! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
=> ! [J: nat] :
( ( ord_less_nat @ J @ ( size_s1427607542list_a @ Xs2 ) )
=> ( ( I2 != J )
=> ( ( nth_list_a @ Xs2 @ I2 )
!= ( nth_list_a @ Xs2 @ J ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(354,plain,
( ( distinct_a
= ( ^ [Xs2: list_a] :
! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
=> ! [J: nat] :
( ( ord_less_nat @ J @ ( size_size_list_a @ Xs2 ) )
=> ( ( I2 != J )
=> ( ( nth_a @ Xs2 @ I2 )
!= ( nth_a @ Xs2 @ J ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(355,plain,
( ( ! [Xs: list_list_a,I3: nat,J2: nat] :
( ( distinct_list_a @ Xs )
=> ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( nth_list_a @ Xs @ I3 )
= ( nth_list_a @ Xs @ J2 ) )
= ( I3 = J2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(356,plain,
( ( ! [Xs: list_a,I3: nat,J2: nat] :
( ( distinct_a @ Xs )
=> ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
=> ( ( ( nth_a @ Xs @ I3 )
= ( nth_a @ Xs @ J2 ) )
= ( I3 = J2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(357,plain,
( ( ! [Xs: list_a,I3: nat,X2: a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ I3 )
=> ( ( list_update_a @ Xs @ I3 @ X2 )
= Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(358,plain,
( ( ! [I3: nat,Xs: list_list_a,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( list_update_list_a @ Xs @ I3 @ X2 )
= Xs )
= ( ( nth_list_a @ Xs @ I3 )
= X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(359,plain,
( ( ! [I3: nat,Xs: list_a,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ( list_update_a @ Xs @ I3 @ X2 )
= Xs )
= ( ( nth_a @ Xs @ I3 )
= X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(360,plain,
( ( ! [I3: nat,Xs: list_list_a,J2: nat,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( I3 = J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= X2 ) )
& ( ( I3 != J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_list_a @ Xs @ J2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(361,plain,
( ( ! [I3: nat,Xs: list_a,J2: nat,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ( I3 = J2 )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
= X2 ) )
& ( ( I3 != J2 )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_a @ Xs @ J2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(362,plain,
( ( ! [I3: nat,J2: nat,Xs: list_list_a,X2: list_a] :
( ( I3 != J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_list_a @ Xs @ J2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(363,plain,
( ( ! [Xs: list_list_a,I3: nat] :
( ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ I3 ) )
= Xs ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(364,plain,
( ( ! [Xs: list_a,I3: nat,X2: a] :
( ( size_size_list_a @ ( list_update_a @ Xs @ I3 @ X2 ) )
= ( size_size_list_a @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(365,plain,
( ( ! [N: nat,Xs: list_list_a] :
( ( ord_less_nat @ N @ ( size_s1427607542list_a @ ( butlast_list_a @ Xs ) ) )
=> ( ( nth_list_a @ ( butlast_list_a @ Xs ) @ N )
= ( nth_list_a @ Xs @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(366,plain,
( ( ! [N: nat,Xs: list_a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ ( butlast_a @ Xs ) ) )
=> ( ( nth_a @ ( butlast_a @ Xs ) @ N )
= ( nth_a @ Xs @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(367,plain,
( ( ! [I3: nat,Xs: list_list_a,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 )
= X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(368,plain,
( ( ! [I3: nat,Xs: list_a,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 )
= X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(369,plain,
( ( list_ex_list_a
= ( ^ [P2: list_a > $o,Xs2: list_list_a] :
? [N3: nat] :
( ( ord_less_nat @ N3 @ ( size_s1427607542list_a @ Xs2 ) )
& ( P2 @ ( nth_list_a @ Xs2 @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(370,plain,
( ( list_ex_a
= ( ^ [P2: a > $o,Xs2: list_a] :
? [N3: nat] :
( ( ord_less_nat @ N3 @ ( size_size_list_a @ Xs2 ) )
& ( P2 @ ( nth_a @ Xs2 @ N3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(371,plain,
( ( listSl97544552lice_a
= ( ^ [Xs2: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs2 ) @ K2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(372,plain,
( ( ! [Xs: list_a,K: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
= ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(373,plain,
( ( ! [X2: list_a,Y2: list_a] :
( ( ( size_size_list_a @ X2 )
!= ( size_size_list_a @ Y2 ) )
=> ( X2 != Y2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(374,plain,
( ( ! [Xs: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs )
!= ( size_size_list_a @ Ys ) )
=> ( Xs != Ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(375,plain,
( ( ! [N: nat] :
? [Xs3: list_a] :
( ( size_size_list_a @ Xs3 )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(376,plain,
( ( ! [M: nat,Xs: list_a,K: nat] :
( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) )
= K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(377,plain,
( ( ! [P: list_a > $o,Xs: list_a] :
( ! [Xs3: list_a] :
( ! [Ys3: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
=> ( P @ Ys3 ) )
=> ( P @ Xs3 ) )
=> ( P @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(378,plain,
( ( ! [M: nat,Xs: list_a,K: nat] :
( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ Xs @ K ) @ M )
= ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(379,plain,
( ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
= ( ^ [Xs2: list_a,Ys2: list_a] :
( ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ Xs2 @ I2 )
= ( nth_a @ Ys2 @ I2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(380,plain,
( ( ( ^ [Y: list_list_a,Z: list_list_a] : ( Y = Z ) )
= ( ^ [Xs2: list_list_a,Ys2: list_list_a] :
( ( ( size_s1427607542list_a @ Xs2 )
= ( size_s1427607542list_a @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
=> ( ( nth_list_a @ Xs2 @ I2 )
= ( nth_list_a @ Ys2 @ I2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(381,plain,
( ( ! [K: nat,P: nat > a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X: a] : ( P @ I2 @ X ) ) )
= ( ? [Xs2: list_a] :
( ( ( size_size_list_a @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(382,plain,
( ( ! [K: nat,P: nat > list_a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X: list_a] : ( P @ I2 @ X ) ) )
= ( ? [Xs2: list_list_a] :
( ( ( size_s1427607542list_a @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_list_a @ Xs2 @ I2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(383,plain,
( ( ! [Xs: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs )
= ( size_size_list_a @ Ys ) )
=> ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
=> ( ( nth_a @ Xs @ I )
= ( nth_a @ Ys @ I ) ) )
=> ( Xs = Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(384,plain,
( ( ! [Xs: list_list_a,Ys: list_list_a] :
( ( ( size_s1427607542list_a @ Xs )
= ( size_s1427607542list_a @ Ys ) )
=> ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
=> ( ( nth_list_a @ Xs @ I )
= ( nth_list_a @ Ys @ I ) ) )
=> ( Xs = Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(385,plain,
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(386,plain,
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k )
= $true ),
inference(polarity_switch,[status(thm)],[352]) ).
thf(387,plain,
( ( ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(388,plain,
( ( ! [Xs: list_list_a,Ys: list_list_a] :
( ( ( size_s1427607542list_a @ Xs )
= ( size_s1427607542list_a @ Ys ) )
=> ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Xs ) )
=> ( ( nth_list_a @ Xs @ I )
= ( nth_list_a @ Ys @ I ) ) )
=> ( Xs = Ys ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(389,plain,
( ( ! [Xs: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs )
= ( size_size_list_a @ Ys ) )
=> ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
=> ( ( nth_a @ Xs @ I )
= ( nth_a @ Ys @ I ) ) )
=> ( Xs = Ys ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(390,plain,
( ( ! [K: nat,P: nat > list_a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X: list_a] : ( P @ I2 @ X ) ) )
= ( ? [Xs2: list_list_a] :
( ( ( size_s1427607542list_a @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_list_a @ Xs2 @ I2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(391,plain,
( ( ! [K: nat,P: nat > a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X: a] : ( P @ I2 @ X ) ) )
= ( ? [Xs2: list_a] :
( ( ( size_size_list_a @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(392,plain,
( ( ( ^ [Y: list_list_a,Z: list_list_a] : ( Y = Z ) )
= ( ^ [Xs2: list_list_a,Ys2: list_list_a] :
( ( ( size_s1427607542list_a @ Xs2 )
= ( size_s1427607542list_a @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
=> ( ( nth_list_a @ Xs2 @ I2 )
= ( nth_list_a @ Ys2 @ I2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(393,plain,
( ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) )
= ( ^ [Xs2: list_a,Ys2: list_a] :
( ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ Xs2 @ I2 )
= ( nth_a @ Ys2 @ I2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(394,plain,
( ( ! [M: nat,Xs: list_a,K: nat] :
( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ Xs @ K ) @ M )
= ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(395,plain,
( ( ! [P: list_a > $o,Xs: list_a] :
( ! [Xs3: list_a] :
( ! [Ys3: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) )
=> ( P @ Ys3 ) )
=> ( P @ Xs3 ) )
=> ( P @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(396,plain,
( ( ! [M: nat,Xs: list_a,K: nat] :
( ( ord_less_nat @ M @ ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ Xs @ K ) @ M ) )
= K ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(397,plain,
( ( ! [N: nat] :
? [Xs3: list_a] :
( ( size_size_list_a @ Xs3 )
= N ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(398,plain,
( ( ! [Xs: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs )
!= ( size_size_list_a @ Ys ) )
=> ( Xs != Ys ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(399,plain,
( ( ! [X2: list_a,Y2: list_a] :
( ( ( size_size_list_a @ X2 )
!= ( size_size_list_a @ Y2 ) )
=> ( X2 != Y2 ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(400,plain,
( ( ! [Xs: list_a,K: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
= ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(401,plain,
( ( listSl97544552lice_a
= ( ^ [Xs2: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs2 ) @ K2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(402,plain,
( ( list_ex_a
= ( ^ [P2: a > $o,Xs2: list_a] :
? [N3: nat] :
( ( ord_less_nat @ N3 @ ( size_size_list_a @ Xs2 ) )
& ( P2 @ ( nth_a @ Xs2 @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(403,plain,
( ( list_ex_list_a
= ( ^ [P2: list_a > $o,Xs2: list_list_a] :
? [N3: nat] :
( ( ord_less_nat @ N3 @ ( size_s1427607542list_a @ Xs2 ) )
& ( P2 @ ( nth_list_a @ Xs2 @ N3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(404,plain,
( ( ! [I3: nat,Xs: list_a,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ I3 )
= X2 ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(405,plain,
( ( ! [I3: nat,Xs: list_list_a,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ I3 )
= X2 ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(406,plain,
( ( ! [N: nat,Xs: list_a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ ( butlast_a @ Xs ) ) )
=> ( ( nth_a @ ( butlast_a @ Xs ) @ N )
= ( nth_a @ Xs @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(407,plain,
( ( ! [N: nat,Xs: list_list_a] :
( ( ord_less_nat @ N @ ( size_s1427607542list_a @ ( butlast_list_a @ Xs ) ) )
=> ( ( nth_list_a @ ( butlast_list_a @ Xs ) @ N )
= ( nth_list_a @ Xs @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(408,plain,
( ( ! [Xs: list_a,I3: nat,X2: a] :
( ( size_size_list_a @ ( list_update_a @ Xs @ I3 @ X2 ) )
= ( size_size_list_a @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(409,plain,
( ( ! [Xs: list_list_a,I3: nat] :
( ( list_update_list_a @ Xs @ I3 @ ( nth_list_a @ Xs @ I3 ) )
= Xs ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(410,plain,
( ( ! [I3: nat,J2: nat,Xs: list_list_a,X2: list_a] :
( ( I3 != J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_list_a @ Xs @ J2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(411,plain,
( ( ! [I3: nat,Xs: list_a,J2: nat,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ( I3 = J2 )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
= X2 ) )
& ( ( I3 != J2 )
=> ( ( nth_a @ ( list_update_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_a @ Xs @ J2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(412,plain,
( ( ! [I3: nat,Xs: list_list_a,J2: nat,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( I3 = J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= X2 ) )
& ( ( I3 != J2 )
=> ( ( nth_list_a @ ( list_update_list_a @ Xs @ I3 @ X2 ) @ J2 )
= ( nth_list_a @ Xs @ J2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(413,plain,
( ( ! [I3: nat,Xs: list_a,X2: a] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ( list_update_a @ Xs @ I3 @ X2 )
= Xs )
= ( ( nth_a @ Xs @ I3 )
= X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(414,plain,
( ( ! [I3: nat,Xs: list_list_a,X2: list_a] :
( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( list_update_list_a @ Xs @ I3 @ X2 )
= Xs )
= ( ( nth_list_a @ Xs @ I3 )
= X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(415,plain,
( ( ! [Xs: list_a,I3: nat,X2: a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ I3 )
=> ( ( list_update_a @ Xs @ I3 @ X2 )
= Xs ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(416,plain,
( ( ! [Xs: list_a,I3: nat,J2: nat] :
( ( distinct_a @ Xs )
=> ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
=> ( ( ord_less_nat @ J2 @ ( size_size_list_a @ Xs ) )
=> ( ( ( nth_a @ Xs @ I3 )
= ( nth_a @ Xs @ J2 ) )
= ( I3 = J2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(417,plain,
( ( ! [Xs: list_list_a,I3: nat,J2: nat] :
( ( distinct_list_a @ Xs )
=> ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ord_less_nat @ J2 @ ( size_s1427607542list_a @ Xs ) )
=> ( ( ( nth_list_a @ Xs @ I3 )
= ( nth_list_a @ Xs @ J2 ) )
= ( I3 = J2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(418,plain,
( ( distinct_a
= ( ^ [Xs2: list_a] :
! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) )
=> ! [J: nat] :
( ( ord_less_nat @ J @ ( size_size_list_a @ Xs2 ) )
=> ( ( I2 != J )
=> ( ( nth_a @ Xs2 @ I2 )
!= ( nth_a @ Xs2 @ J ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(419,plain,
( ( distinct_list_a
= ( ^ [Xs2: list_list_a] :
! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Xs2 ) )
=> ! [J: nat] :
( ( ord_less_nat @ J @ ( size_s1427607542list_a @ Xs2 ) )
=> ( ( I2 != J )
=> ( ( nth_list_a @ Xs2 @ I2 )
!= ( nth_list_a @ Xs2 @ J ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(420,plain,
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(421,plain,
( ( ! [SX0: nat,SX1: list_a] :
( ~ ( ord_less_nat @ SX0 @ ( size_size_list_a @ ( butlast_a @ SX1 ) ) )
| ( ( nth_a @ ( butlast_a @ SX1 ) @ SX0 )
= ( nth_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(422,plain,
( ( ! [SX0: nat,SX1: nat,SX2: list_list_a,SX3: list_a] :
( ~ ( ( SX0 != SX1 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SX2 @ SX0 @ SX3 ) @ SX1 )
= ( nth_list_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(423,plain,
( ( ( ^ [SX0: list_a,SX1: list_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: list_a,SX1: list_a] :
~ ( ( ( size_size_list_a @ SX0 )
!= ( size_size_list_a @ SX1 ) )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX0 ) )
| ( ( nth_a @ SX0 @ SX2 )
= ( nth_a @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(424,plain,
( ( ! [SX0: nat,SX1: list_a,SX2: nat,SX3: a] :
( ~ ( ord_less_nat @ SX0 @ ( size_size_list_a @ SX1 ) )
| ~ ( ~ ( ( SX0 != SX2 )
| ( ( nth_a @ ( list_update_a @ SX1 @ SX0 @ SX3 ) @ SX2 )
= SX3 ) )
| ~ ( ~ ( ( SX0 != SX2 ) )
| ( ( nth_a @ ( list_update_a @ SX1 @ SX0 @ SX3 ) @ SX2 )
= ( nth_a @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(425,plain,
( ( ! [SX0: nat,SX1: list_a,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ ( divide_divide_nat @ ( size_size_list_a @ SX1 ) @ SX2 ) )
| ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ SX1 @ SX2 ) @ SX0 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(426,plain,
( ( ! [SX0: nat] :
~ ! [SX1: list_a] :
( ( size_size_list_a @ SX1 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(427,plain,
( ( ! [SX0: nat,SX1: list_a,SX2: nat] :
( ~ ( ord_less_nat @ SX0 @ ( divide_divide_nat @ ( size_size_list_a @ SX1 ) @ SX2 ) )
| ( ( nth_list_a @ ( listSl1174287072ice2_a @ SX1 @ SX2 ) @ SX0 )
= ( nth_list_a @ ( listSl97544552lice_a @ SX1 @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(428,plain,
( ( ! [SX0: nat,SX1: list_a,SX2: a] :
( ~ ( ord_less_nat @ SX0 @ ( size_size_list_a @ SX1 ) )
| ( ( ( list_update_a @ SX1 @ SX0 @ SX2 )
= SX1 )
= ( ( nth_a @ SX1 @ SX0 )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(429,plain,
( ( distinct_a
= ( ^ [SX0: list_a] :
! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( size_size_list_a @ SX0 ) )
| ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX0 ) )
| ~ ( ( SX1 != SX2 ) )
| ( ( nth_a @ SX0 @ SX1 )
!= ( nth_a @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(430,plain,
( ( ! [SX0: nat,SX1: list_list_a,SX2: list_a] :
( ~ ( ord_less_nat @ SX0 @ ( size_s1427607542list_a @ SX1 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SX1 @ SX0 @ SX2 ) @ SX0 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(431,plain,
( ( ! [SX0: nat,SX1: list_list_a,SX2: nat,SX3: list_a] :
( ~ ( ord_less_nat @ SX0 @ ( size_s1427607542list_a @ SX1 ) )
| ~ ( ~ ( ( SX0 != SX2 )
| ( ( nth_list_a @ ( list_update_list_a @ SX1 @ SX0 @ SX3 ) @ SX2 )
= SX3 ) )
| ~ ( ~ ( ( SX0 != SX2 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SX1 @ SX0 @ SX3 ) @ SX2 )
= ( nth_list_a @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(432,plain,
( ( list_ex_a
= ( ^ [SX0: a > $o,SX1: list_a] :
~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX1 ) )
| ~ ( SX0 @ ( nth_a @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(433,plain,
( ( distinct_list_a
= ( ^ [SX0: list_list_a] :
! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( size_s1427607542list_a @ SX0 ) )
| ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX0 ) )
| ~ ( ( SX1 != SX2 ) )
| ( ( nth_list_a @ SX0 @ SX1 )
!= ( nth_list_a @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(434,plain,
( ( ! [SX0: nat,SX1: list_list_a,SX2: list_a] :
( ~ ( ord_less_nat @ SX0 @ ( size_s1427607542list_a @ SX1 ) )
| ( ( ( list_update_list_a @ SX1 @ SX0 @ SX2 )
= SX1 )
= ( ( nth_list_a @ SX1 @ SX0 )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(435,plain,
( ( ! [SX0: list_list_a,SX1: list_list_a] :
( ( ( size_s1427607542list_a @ SX0 )
!= ( size_s1427607542list_a @ SX1 ) )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX0 ) )
| ( ( nth_list_a @ SX0 @ SX2 )
= ( nth_list_a @ SX1 @ SX2 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(436,plain,
( ( ! [SX0: nat,SX1: nat > list_a > $o] :
( ( ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ~ ! [SX3: list_a] :
~ ( SX1 @ SX2 @ SX3 ) ) )
= ( ~ ! [SX2: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SX2 )
!= SX0 )
| ~ ! [SX3: nat] :
( ~ ( ord_less_nat @ SX3 @ SX0 )
| ( SX1 @ SX3 @ ( nth_list_a @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(437,plain,
( ( ! [SX0: list_a,SX1: nat,SX2: a] :
( ~ ( ord_less_eq_nat @ ( size_size_list_a @ SX0 ) @ SX1 )
| ( ( list_update_a @ SX0 @ SX1 @ SX2 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(438,plain,
( ( ! [SX0: nat,SX1: list_list_a] :
( ~ ( ord_less_nat @ SX0 @ ( size_s1427607542list_a @ ( butlast_list_a @ SX1 ) ) )
| ( ( nth_list_a @ ( butlast_list_a @ SX1 ) @ SX0 )
= ( nth_list_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(439,plain,
( ( ! [SX0: list_a,SX1: list_a] :
( ~ ( ( ( size_size_list_a @ SX0 )
!= ( size_size_list_a @ SX1 ) ) )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(440,plain,
( ( ! [SX0: list_a,SX1: list_a] :
( ~ ( ( ( size_size_list_a @ SX0 )
!= ( size_size_list_a @ SX1 ) ) )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(441,plain,
( ( ! [SX0: list_list_a,SX1: nat,SX2: nat] :
( ~ ( distinct_list_a @ SX0 )
| ~ ( ord_less_nat @ SX1 @ ( size_s1427607542list_a @ SX0 ) )
| ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX0 ) )
| ( ( ( nth_list_a @ SX0 @ SX1 )
= ( nth_list_a @ SX0 @ SX2 ) )
= ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(442,plain,
( ( ! [SX0: list_a > $o,SX1: list_a] :
( ~ ! [SX2: list_a] :
( ~ ! [SX3: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SX3 ) @ ( size_size_list_a @ SX2 ) )
| ( SX0 @ SX3 ) )
| ( SX0 @ SX2 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(443,plain,
( ( ! [SX0: list_a,SX1: list_a] :
( ( ( size_size_list_a @ SX0 )
!= ( size_size_list_a @ SX1 ) )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX0 ) )
| ( ( nth_a @ SX0 @ SX2 )
= ( nth_a @ SX1 @ SX2 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(444,plain,
( ( ! [SX0: list_a,SX1: nat,SX2: nat] :
( ~ ( distinct_a @ SX0 )
| ~ ( ord_less_nat @ SX1 @ ( size_size_list_a @ SX0 ) )
| ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX0 ) )
| ( ( ( nth_a @ SX0 @ SX1 )
= ( nth_a @ SX0 @ SX2 ) )
= ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(445,plain,
( ( ! [SX0: nat,SX1: list_a,SX2: a] :
( ~ ( ord_less_nat @ SX0 @ ( size_size_list_a @ SX1 ) )
| ( ( nth_a @ ( list_update_a @ SX1 @ SX0 @ SX2 ) @ SX0 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(446,plain,
( ( ! [SX0: nat,SX1: nat > a > $o] :
( ( ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ~ ! [SX3: a] :
~ ( SX1 @ SX2 @ SX3 ) ) )
= ( ~ ! [SX2: list_a] :
~ ~ ( ( ( size_size_list_a @ SX2 )
!= SX0 )
| ~ ! [SX3: nat] :
( ~ ( ord_less_nat @ SX3 @ SX0 )
| ( SX1 @ SX3 @ ( nth_a @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(447,plain,
( ( ( ^ [SX0: list_list_a,SX1: list_list_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: list_list_a,SX1: list_list_a] :
~ ( ( ( size_s1427607542list_a @ SX0 )
!= ( size_s1427607542list_a @ SX1 ) )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX0 ) )
| ( ( nth_list_a @ SX0 @ SX2 )
= ( nth_list_a @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(448,plain,
( ( list_ex_list_a
= ( ^ [SX0: list_a > $o,SX1: list_list_a] :
~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX1 ) )
| ~ ( SX0 @ ( nth_list_a @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(449,plain,
! [SV1: list_a] :
( ( ! [SY102: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ SV1 @ SY102 ) )
= ( divide_divide_nat @ ( size_size_list_a @ SV1 ) @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(450,plain,
( ( ! [SV2: list_a] :
( ( listSl97544552lice_a @ SV2 )
= ( ^ [SY103: nat] : ( listSl1495374126_aux_a @ SV2 @ SY103 @ ( divide_divide_nat @ ( size_size_list_a @ SV2 ) @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[401]) ).
thf(451,plain,
( ( listSl97544552lice_a
= ( ^ [Xs2: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs2 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs2 ) @ K2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[401]) ).
thf(452,plain,
! [SV3: list_a] :
( ( ! [SY104: nat,SY105: a] :
( ( size_size_list_a @ ( list_update_a @ SV3 @ SY104 @ SY105 ) )
= ( size_size_list_a @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(453,plain,
! [SV4: list_list_a] :
( ( ! [SY106: nat] :
( ( list_update_list_a @ SV4 @ SY106 @ ( nth_list_a @ SV4 @ SY106 ) )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(454,plain,
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(455,plain,
! [SV5: nat] :
( ( ! [SY107: list_a] :
( ~ ( ord_less_nat @ SV5 @ ( size_size_list_a @ ( butlast_a @ SY107 ) ) )
| ( ( nth_a @ ( butlast_a @ SY107 ) @ SV5 )
= ( nth_a @ SY107 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(456,plain,
! [SV6: nat] :
( ( ! [SY108: nat,SY109: list_list_a,SY110: list_a] :
( ~ ( ( SV6 != SY108 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SY109 @ SV6 @ SY110 ) @ SY108 )
= ( nth_list_a @ SY109 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(457,plain,
( ( ! [SV7: list_a] :
( ( ^ [SY111: list_a] : ( SV7 = SY111 ) )
= ( ^ [SY112: list_a] :
~ ( ( ( size_size_list_a @ SV7 )
!= ( size_size_list_a @ SY112 ) )
| ~ ! [SY113: nat] :
( ~ ( ord_less_nat @ SY113 @ ( size_size_list_a @ SV7 ) )
| ( ( nth_a @ SV7 @ SY113 )
= ( nth_a @ SY112 @ SY113 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[423]) ).
thf(458,plain,
( ( ( ^ [SX0: list_a,SX1: list_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: list_a,SX1: list_a] :
~ ( ( ( size_size_list_a @ SX0 )
!= ( size_size_list_a @ SX1 ) )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX0 ) )
| ( ( nth_a @ SX0 @ SX2 )
= ( nth_a @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[423]) ).
thf(459,plain,
! [SV8: nat] :
( ( ! [SY114: list_a,SY115: nat,SY116: a] :
( ~ ( ord_less_nat @ SV8 @ ( size_size_list_a @ SY114 ) )
| ~ ( ~ ( ( SV8 != SY115 )
| ( ( nth_a @ ( list_update_a @ SY114 @ SV8 @ SY116 ) @ SY115 )
= SY116 ) )
| ~ ( ~ ( ( SV8 != SY115 ) )
| ( ( nth_a @ ( list_update_a @ SY114 @ SV8 @ SY116 ) @ SY115 )
= ( nth_a @ SY114 @ SY115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(460,plain,
! [SV9: nat] :
( ( ! [SY117: list_a,SY118: nat] :
( ~ ( ord_less_nat @ SV9 @ ( divide_divide_nat @ ( size_size_list_a @ SY117 ) @ SY118 ) )
| ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ SY117 @ SY118 ) @ SV9 ) )
= SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(461,plain,
! [SV10: nat] :
( ( ~ ! [SY119: list_a] :
( ( size_size_list_a @ SY119 )
!= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(462,plain,
! [SV11: nat] :
( ( ! [SY120: list_a,SY121: nat] :
( ~ ( ord_less_nat @ SV11 @ ( divide_divide_nat @ ( size_size_list_a @ SY120 ) @ SY121 ) )
| ( ( nth_list_a @ ( listSl1174287072ice2_a @ SY120 @ SY121 ) @ SV11 )
= ( nth_list_a @ ( listSl97544552lice_a @ SY120 @ SY121 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(463,plain,
! [SV12: nat] :
( ( ! [SY122: list_a,SY123: a] :
( ~ ( ord_less_nat @ SV12 @ ( size_size_list_a @ SY122 ) )
| ( ( ( list_update_a @ SY122 @ SV12 @ SY123 )
= SY122 )
= ( ( nth_a @ SY122 @ SV12 )
= SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(464,plain,
( ( ! [SV13: list_a] :
( ( distinct_a @ SV13 )
= ( ! [SY124: nat] :
( ~ ( ord_less_nat @ SY124 @ ( size_size_list_a @ SV13 ) )
| ! [SY125: nat] :
( ~ ( ord_less_nat @ SY125 @ ( size_size_list_a @ SV13 ) )
| ~ ( ( SY124 != SY125 ) )
| ( ( nth_a @ SV13 @ SY124 )
!= ( nth_a @ SV13 @ SY125 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[429]) ).
thf(465,plain,
( ( distinct_a
= ( ^ [SX0: list_a] :
! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( size_size_list_a @ SX0 ) )
| ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX0 ) )
| ~ ( ( SX1 != SX2 ) )
| ( ( nth_a @ SX0 @ SX1 )
!= ( nth_a @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[429]) ).
thf(466,plain,
! [SV14: nat] :
( ( ! [SY126: list_list_a,SY127: list_a] :
( ~ ( ord_less_nat @ SV14 @ ( size_s1427607542list_a @ SY126 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SY126 @ SV14 @ SY127 ) @ SV14 )
= SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(467,plain,
! [SV15: nat] :
( ( ! [SY128: list_list_a,SY129: nat,SY130: list_a] :
( ~ ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SY128 ) )
| ~ ( ~ ( ( SV15 != SY129 )
| ( ( nth_list_a @ ( list_update_list_a @ SY128 @ SV15 @ SY130 ) @ SY129 )
= SY130 ) )
| ~ ( ~ ( ( SV15 != SY129 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SY128 @ SV15 @ SY130 ) @ SY129 )
= ( nth_list_a @ SY128 @ SY129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(468,plain,
( ( ! [SV16: a > $o] :
( ( list_ex_a @ SV16 )
= ( ^ [SY131: list_a] :
~ ! [SY132: nat] :
~ ~ ( ~ ( ord_less_nat @ SY132 @ ( size_size_list_a @ SY131 ) )
| ~ ( SV16 @ ( nth_a @ SY131 @ SY132 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[432]) ).
thf(469,plain,
( ( list_ex_a
= ( ^ [SX0: a > $o,SX1: list_a] :
~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ ( size_size_list_a @ SX1 ) )
| ~ ( SX0 @ ( nth_a @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[432]) ).
thf(470,plain,
( ( ! [SV17: list_list_a] :
( ( distinct_list_a @ SV17 )
= ( ! [SY133: nat] :
( ~ ( ord_less_nat @ SY133 @ ( size_s1427607542list_a @ SV17 ) )
| ! [SY134: nat] :
( ~ ( ord_less_nat @ SY134 @ ( size_s1427607542list_a @ SV17 ) )
| ~ ( ( SY133 != SY134 ) )
| ( ( nth_list_a @ SV17 @ SY133 )
!= ( nth_list_a @ SV17 @ SY134 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[433]) ).
thf(471,plain,
( ( distinct_list_a
= ( ^ [SX0: list_list_a] :
! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( size_s1427607542list_a @ SX0 ) )
| ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX0 ) )
| ~ ( ( SX1 != SX2 ) )
| ( ( nth_list_a @ SX0 @ SX1 )
!= ( nth_list_a @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[433]) ).
thf(472,plain,
! [SV18: nat] :
( ( ! [SY135: list_list_a,SY136: list_a] :
( ~ ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SY135 ) )
| ( ( ( list_update_list_a @ SY135 @ SV18 @ SY136 )
= SY135 )
= ( ( nth_list_a @ SY135 @ SV18 )
= SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(473,plain,
! [SV19: list_list_a] :
( ( ! [SY137: list_list_a] :
( ( ( size_s1427607542list_a @ SV19 )
!= ( size_s1427607542list_a @ SY137 ) )
| ~ ! [SY138: nat] :
( ~ ( ord_less_nat @ SY138 @ ( size_s1427607542list_a @ SV19 ) )
| ( ( nth_list_a @ SV19 @ SY138 )
= ( nth_list_a @ SY137 @ SY138 ) ) )
| ( SV19 = SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(474,plain,
! [SV20: nat] :
( ( ! [SY139: nat > list_a > $o] :
( ( ! [SY140: nat] :
( ~ ( ord_less_nat @ SY140 @ SV20 )
| ~ ! [SX3: list_a] :
~ ( SY139 @ SY140 @ SX3 ) ) )
= ( ~ ! [SY142: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY142 )
!= SV20 )
| ~ ! [SY143: nat] :
( ~ ( ord_less_nat @ SY143 @ SV20 )
| ( SY139 @ SY143 @ ( nth_list_a @ SY142 @ SY143 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(475,plain,
! [SV21: list_a] :
( ( ! [SY144: nat,SY145: a] :
( ~ ( ord_less_eq_nat @ ( size_size_list_a @ SV21 ) @ SY144 )
| ( ( list_update_a @ SV21 @ SY144 @ SY145 )
= SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(476,plain,
! [SV22: nat] :
( ( ! [SY146: list_list_a] :
( ~ ( ord_less_nat @ SV22 @ ( size_s1427607542list_a @ ( butlast_list_a @ SY146 ) ) )
| ( ( nth_list_a @ ( butlast_list_a @ SY146 ) @ SV22 )
= ( nth_list_a @ SY146 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(477,plain,
! [SV23: list_a] :
( ( ! [SY147: list_a] :
( ~ ( ( ( size_size_list_a @ SV23 )
!= ( size_size_list_a @ SY147 ) ) )
| ( SV23 != SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(478,plain,
! [SV24: list_a] :
( ( ! [SY148: list_a] :
( ~ ( ( ( size_size_list_a @ SV24 )
!= ( size_size_list_a @ SY148 ) ) )
| ( SV24 != SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(479,plain,
! [SV25: list_list_a] :
( ( ! [SY149: nat,SY150: nat] :
( ~ ( distinct_list_a @ SV25 )
| ~ ( ord_less_nat @ SY149 @ ( size_s1427607542list_a @ SV25 ) )
| ~ ( ord_less_nat @ SY150 @ ( size_s1427607542list_a @ SV25 ) )
| ( ( ( nth_list_a @ SV25 @ SY149 )
= ( nth_list_a @ SV25 @ SY150 ) )
= ( SY149 = SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(480,plain,
! [SV26: list_a > $o] :
( ( ! [SY151: list_a] :
( ~ ! [SY152: list_a] :
( ~ ! [SY153: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY153 ) @ ( size_size_list_a @ SY152 ) )
| ( SV26 @ SY153 ) )
| ( SV26 @ SY152 ) )
| ( SV26 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(481,plain,
! [SV27: list_a] :
( ( ! [SY154: list_a] :
( ( ( size_size_list_a @ SV27 )
!= ( size_size_list_a @ SY154 ) )
| ~ ! [SY155: nat] :
( ~ ( ord_less_nat @ SY155 @ ( size_size_list_a @ SV27 ) )
| ( ( nth_a @ SV27 @ SY155 )
= ( nth_a @ SY154 @ SY155 ) ) )
| ( SV27 = SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(482,plain,
! [SV28: list_a] :
( ( ! [SY156: nat,SY157: nat] :
( ~ ( distinct_a @ SV28 )
| ~ ( ord_less_nat @ SY156 @ ( size_size_list_a @ SV28 ) )
| ~ ( ord_less_nat @ SY157 @ ( size_size_list_a @ SV28 ) )
| ( ( ( nth_a @ SV28 @ SY156 )
= ( nth_a @ SV28 @ SY157 ) )
= ( SY156 = SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(483,plain,
! [SV29: nat] :
( ( ! [SY158: list_a,SY159: a] :
( ~ ( ord_less_nat @ SV29 @ ( size_size_list_a @ SY158 ) )
| ( ( nth_a @ ( list_update_a @ SY158 @ SV29 @ SY159 ) @ SV29 )
= SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(484,plain,
! [SV30: nat] :
( ( ! [SY160: nat > a > $o] :
( ( ! [SY161: nat] :
( ~ ( ord_less_nat @ SY161 @ SV30 )
| ~ ! [SX3: a] :
~ ( SY160 @ SY161 @ SX3 ) ) )
= ( ~ ! [SY163: list_a] :
~ ~ ( ( ( size_size_list_a @ SY163 )
!= SV30 )
| ~ ! [SY164: nat] :
( ~ ( ord_less_nat @ SY164 @ SV30 )
| ( SY160 @ SY164 @ ( nth_a @ SY163 @ SY164 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(485,plain,
( ( ! [SV31: list_list_a] :
( ( ^ [SY165: list_list_a] : ( SV31 = SY165 ) )
= ( ^ [SY166: list_list_a] :
~ ( ( ( size_s1427607542list_a @ SV31 )
!= ( size_s1427607542list_a @ SY166 ) )
| ~ ! [SY167: nat] :
( ~ ( ord_less_nat @ SY167 @ ( size_s1427607542list_a @ SV31 ) )
| ( ( nth_list_a @ SV31 @ SY167 )
= ( nth_list_a @ SY166 @ SY167 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[447]) ).
thf(486,plain,
( ( ( ^ [SX0: list_list_a,SX1: list_list_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: list_list_a,SX1: list_list_a] :
~ ( ( ( size_s1427607542list_a @ SX0 )
!= ( size_s1427607542list_a @ SX1 ) )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX0 ) )
| ( ( nth_list_a @ SX0 @ SX2 )
= ( nth_list_a @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[447]) ).
thf(487,plain,
( ( ! [SV32: list_a > $o] :
( ( list_ex_list_a @ SV32 )
= ( ^ [SY168: list_list_a] :
~ ! [SY169: nat] :
~ ~ ( ~ ( ord_less_nat @ SY169 @ ( size_s1427607542list_a @ SY168 ) )
| ~ ( SV32 @ ( nth_list_a @ SY168 @ SY169 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[448]) ).
thf(488,plain,
( ( list_ex_list_a
= ( ^ [SX0: list_a > $o,SX1: list_list_a] :
~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ ( size_s1427607542list_a @ SX1 ) )
| ~ ( SX0 @ ( nth_list_a @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[448]) ).
thf(489,plain,
! [SV33: nat,SV1: list_a] :
( ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ SV1 @ SV33 ) )
= ( divide_divide_nat @ ( size_size_list_a @ SV1 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(490,plain,
! [SV34: list_a] :
( ( ( listSl97544552lice_a @ SV34 )
= ( ^ [SY170: nat] : ( listSl1495374126_aux_a @ SV34 @ SY170 @ ( divide_divide_nat @ ( size_size_list_a @ SV34 ) @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(491,plain,
! [SV35: nat,SV3: list_a] :
( ( ! [SY171: a] :
( ( size_size_list_a @ ( list_update_a @ SV3 @ SV35 @ SY171 ) )
= ( size_size_list_a @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(492,plain,
! [SV36: nat,SV4: list_list_a] :
( ( ( list_update_list_a @ SV4 @ SV36 @ ( nth_list_a @ SV4 @ SV36 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(493,plain,
! [SV37: list_a,SV5: nat] :
( ( ~ ( ord_less_nat @ SV5 @ ( size_size_list_a @ ( butlast_a @ SV37 ) ) )
| ( ( nth_a @ ( butlast_a @ SV37 ) @ SV5 )
= ( nth_a @ SV37 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(494,plain,
! [SV38: nat,SV6: nat] :
( ( ! [SY172: list_list_a,SY173: list_a] :
( ~ ( ( SV6 != SV38 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SY172 @ SV6 @ SY173 ) @ SV38 )
= ( nth_list_a @ SY172 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(495,plain,
! [SV39: list_a] :
( ( ( ^ [SY174: list_a] : ( SV39 = SY174 ) )
= ( ^ [SY175: list_a] :
~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SY175 ) )
| ~ ! [SY176: nat] :
( ~ ( ord_less_nat @ SY176 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY176 )
= ( nth_a @ SY175 @ SY176 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(496,plain,
! [SV40: list_a,SV8: nat] :
( ( ! [SY177: nat,SY178: a] :
( ~ ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
| ~ ( ~ ( ( SV8 != SY177 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SY178 ) @ SY177 )
= SY178 ) )
| ~ ( ~ ( ( SV8 != SY177 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SY178 ) @ SY177 )
= ( nth_a @ SV40 @ SY177 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(497,plain,
! [SV41: list_a,SV9: nat] :
( ( ! [SY179: nat] :
( ~ ( ord_less_nat @ SV9 @ ( divide_divide_nat @ ( size_size_list_a @ SV41 ) @ SY179 ) )
| ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ SV41 @ SY179 ) @ SV9 ) )
= SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(498,plain,
! [SV10: nat] :
( ( ! [SY119: list_a] :
( ( size_size_list_a @ SY119 )
!= SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(499,plain,
! [SV42: list_a,SV11: nat] :
( ( ! [SY180: nat] :
( ~ ( ord_less_nat @ SV11 @ ( divide_divide_nat @ ( size_size_list_a @ SV42 ) @ SY180 ) )
| ( ( nth_list_a @ ( listSl1174287072ice2_a @ SV42 @ SY180 ) @ SV11 )
= ( nth_list_a @ ( listSl97544552lice_a @ SV42 @ SY180 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(500,plain,
! [SV43: list_a,SV12: nat] :
( ( ! [SY181: a] :
( ~ ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
| ( ( ( list_update_a @ SV43 @ SV12 @ SY181 )
= SV43 )
= ( ( nth_a @ SV43 @ SV12 )
= SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(501,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(502,plain,
! [SV45: list_list_a,SV14: nat] :
( ( ! [SY184: list_a] :
( ~ ( ord_less_nat @ SV14 @ ( size_s1427607542list_a @ SV45 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV45 @ SV14 @ SY184 ) @ SV14 )
= SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(503,plain,
! [SV46: list_list_a,SV15: nat] :
( ( ! [SY185: nat,SY186: list_a] :
( ~ ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
| ~ ( ~ ( ( SV15 != SY185 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SY186 ) @ SY185 )
= SY186 ) )
| ~ ( ~ ( ( SV15 != SY185 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SY186 ) @ SY185 )
= ( nth_list_a @ SV46 @ SY185 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(504,plain,
! [SV47: a > $o] :
( ( ( list_ex_a @ SV47 )
= ( ^ [SY187: list_a] :
~ ! [SY188: nat] :
~ ~ ( ~ ( ord_less_nat @ SY188 @ ( size_size_list_a @ SY187 ) )
| ~ ( SV47 @ ( nth_a @ SY187 @ SY188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(505,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(506,plain,
! [SV49: list_list_a,SV18: nat] :
( ( ! [SY191: list_a] :
( ~ ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
| ( ( ( list_update_list_a @ SV49 @ SV18 @ SY191 )
= SV49 )
= ( ( nth_list_a @ SV49 @ SV18 )
= SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(507,plain,
! [SV50: list_list_a,SV19: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV19 )
!= ( size_s1427607542list_a @ SV50 ) )
| ~ ! [SY192: nat] :
( ~ ( ord_less_nat @ SY192 @ ( size_s1427607542list_a @ SV19 ) )
| ( ( nth_list_a @ SV19 @ SY192 )
= ( nth_list_a @ SV50 @ SY192 ) ) )
| ( SV19 = SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(508,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= ( ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(509,plain,
! [SV52: nat,SV21: list_a] :
( ( ! [SY197: a] :
( ~ ( ord_less_eq_nat @ ( size_size_list_a @ SV21 ) @ SV52 )
| ( ( list_update_a @ SV21 @ SV52 @ SY197 )
= SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(510,plain,
! [SV53: list_list_a,SV22: nat] :
( ( ~ ( ord_less_nat @ SV22 @ ( size_s1427607542list_a @ ( butlast_list_a @ SV53 ) ) )
| ( ( nth_list_a @ ( butlast_list_a @ SV53 ) @ SV22 )
= ( nth_list_a @ SV53 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(511,plain,
! [SV54: list_a,SV23: list_a] :
( ( ~ ( ( ( size_size_list_a @ SV23 )
!= ( size_size_list_a @ SV54 ) ) )
| ( SV23 != SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(512,plain,
! [SV55: list_a,SV24: list_a] :
( ( ~ ( ( ( size_size_list_a @ SV24 )
!= ( size_size_list_a @ SV55 ) ) )
| ( SV24 != SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(513,plain,
! [SV56: nat,SV25: list_list_a] :
( ( ! [SY198: nat] :
( ~ ( distinct_list_a @ SV25 )
| ~ ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
| ~ ( ord_less_nat @ SY198 @ ( size_s1427607542list_a @ SV25 ) )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SY198 ) )
= ( SV56 = SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(514,plain,
! [SV57: list_a,SV26: list_a > $o] :
( ( ~ ! [SY152: list_a] :
( ~ ! [SY153: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY153 ) @ ( size_size_list_a @ SY152 ) )
| ( SV26 @ SY153 ) )
| ( SV26 @ SY152 ) )
| ( SV26 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(515,plain,
! [SV58: list_a,SV27: list_a] :
( ( ( ( size_size_list_a @ SV27 )
!= ( size_size_list_a @ SV58 ) )
| ~ ! [SY201: nat] :
( ~ ( ord_less_nat @ SY201 @ ( size_size_list_a @ SV27 ) )
| ( ( nth_a @ SV27 @ SY201 )
= ( nth_a @ SV58 @ SY201 ) ) )
| ( SV27 = SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(516,plain,
! [SV59: nat,SV28: list_a] :
( ( ! [SY202: nat] :
( ~ ( distinct_a @ SV28 )
| ~ ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
| ~ ( ord_less_nat @ SY202 @ ( size_size_list_a @ SV28 ) )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SY202 ) )
= ( SV59 = SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(517,plain,
! [SV60: list_a,SV29: nat] :
( ( ! [SY203: a] :
( ~ ( ord_less_nat @ SV29 @ ( size_size_list_a @ SV60 ) )
| ( ( nth_a @ ( list_update_a @ SV60 @ SV29 @ SY203 ) @ SV29 )
= SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(518,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= ( ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(519,plain,
! [SV62: list_list_a] :
( ( ( ^ [SY208: list_list_a] : ( SV62 = SY208 ) )
= ( ^ [SY209: list_list_a] :
~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SY209 ) )
| ~ ! [SY210: nat] :
( ~ ( ord_less_nat @ SY210 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY210 )
= ( nth_list_a @ SY209 @ SY210 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(520,plain,
! [SV63: list_a > $o] :
( ( ( list_ex_list_a @ SV63 )
= ( ^ [SY211: list_list_a] :
~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ ( size_s1427607542list_a @ SY211 ) )
| ~ ( SV63 @ ( nth_list_a @ SY211 @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(521,plain,
! [SV34: list_a] :
( ( ! [SV64: nat] :
( ( listSl97544552lice_a @ SV34 @ SV64 )
= ( listSl1495374126_aux_a @ SV34 @ SV64 @ ( divide_divide_nat @ ( size_size_list_a @ SV34 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[490]) ).
thf(522,plain,
! [SV34: list_a] :
( ( ( listSl97544552lice_a @ SV34 )
= ( ^ [SY170: nat] : ( listSl1495374126_aux_a @ SV34 @ SY170 @ ( divide_divide_nat @ ( size_size_list_a @ SV34 ) @ SY170 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[490]) ).
thf(523,plain,
! [SV65: a,SV35: nat,SV3: list_a] :
( ( ( size_size_list_a @ ( list_update_a @ SV3 @ SV35 @ SV65 ) )
= ( size_size_list_a @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(524,plain,
! [SV37: list_a,SV5: nat] :
( ( ( ~ ( ord_less_nat @ SV5 @ ( size_size_list_a @ ( butlast_a @ SV37 ) ) ) )
= $true )
| ( ( ( nth_a @ ( butlast_a @ SV37 ) @ SV5 )
= ( nth_a @ SV37 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(525,plain,
! [SV66: list_list_a,SV38: nat,SV6: nat] :
( ( ! [SY213: list_a] :
( ~ ( ( SV6 != SV38 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV66 @ SV6 @ SY213 ) @ SV38 )
= ( nth_list_a @ SV66 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(526,plain,
! [SV39: list_a] :
( ( ! [SV67: list_a] :
( ( SV39 = SV67 )
= ( ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV67 ) )
| ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY214 )
= ( nth_a @ SV67 @ SY214 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[495]) ).
thf(527,plain,
! [SV39: list_a] :
( ( ( ^ [SY174: list_a] : ( SV39 = SY174 ) )
= ( ^ [SY175: list_a] :
~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SY175 ) )
| ~ ! [SY176: nat] :
( ~ ( ord_less_nat @ SY176 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY176 )
= ( nth_a @ SY175 @ SY176 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[495]) ).
thf(528,plain,
! [SV68: nat,SV40: list_a,SV8: nat] :
( ( ! [SY215: a] :
( ~ ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
| ~ ( ~ ( ( SV8 != SV68 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SY215 ) @ SV68 )
= SY215 ) )
| ~ ( ~ ( ( SV8 != SV68 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SY215 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(529,plain,
! [SV69: nat,SV41: list_a,SV9: nat] :
( ( ~ ( ord_less_nat @ SV9 @ ( divide_divide_nat @ ( size_size_list_a @ SV41 ) @ SV69 ) )
| ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ SV41 @ SV69 ) @ SV9 ) )
= SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(530,plain,
! [SV10: nat] :
( ( ( size_size_list_a @ ( sK1_SY119 @ SV10 ) )
!= SV10 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[498]) ).
thf(531,plain,
! [SV70: nat,SV42: list_a,SV11: nat] :
( ( ~ ( ord_less_nat @ SV11 @ ( divide_divide_nat @ ( size_size_list_a @ SV42 ) @ SV70 ) )
| ( ( nth_list_a @ ( listSl1174287072ice2_a @ SV42 @ SV70 ) @ SV11 )
= ( nth_list_a @ ( listSl97544552lice_a @ SV42 @ SV70 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(532,plain,
! [SV71: a,SV43: list_a,SV12: nat] :
( ( ~ ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
| ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= ( ( nth_a @ SV43 @ SV12 )
= SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(533,plain,
! [SV44: list_a] :
( ( ~ ( ( distinct_a @ SV44 )
| ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
| ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[501]) ).
thf(534,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[501]) ).
thf(535,plain,
! [SV72: list_a,SV45: list_list_a,SV14: nat] :
( ( ~ ( ord_less_nat @ SV14 @ ( size_s1427607542list_a @ SV45 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV45 @ SV14 @ SV72 ) @ SV14 )
= SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(536,plain,
! [SV73: nat,SV46: list_list_a,SV15: nat] :
( ( ! [SY216: list_a] :
( ~ ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
| ~ ( ~ ( ( SV15 != SV73 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SY216 ) @ SV73 )
= SY216 ) )
| ~ ( ~ ( ( SV15 != SV73 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SY216 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(537,plain,
! [SV47: a > $o] :
( ( ! [SV74: list_a] :
( ( list_ex_a @ SV47 @ SV74 )
= ( ~ ! [SY217: nat] :
~ ~ ( ~ ( ord_less_nat @ SY217 @ ( size_size_list_a @ SV74 ) )
| ~ ( SV47 @ ( nth_a @ SV74 @ SY217 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[504]) ).
thf(538,plain,
! [SV47: a > $o] :
( ( ( list_ex_a @ SV47 )
= ( ^ [SY187: list_a] :
~ ! [SY188: nat] :
~ ~ ( ~ ( ord_less_nat @ SY188 @ ( size_size_list_a @ SY187 ) )
| ~ ( SV47 @ ( nth_a @ SY187 @ SY188 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[504]) ).
thf(539,plain,
! [SV48: list_list_a] :
( ( ~ ( ( distinct_list_a @ SV48 )
| ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
| ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[505]) ).
thf(540,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[505]) ).
thf(541,plain,
! [SV75: list_a,SV49: list_list_a,SV18: nat] :
( ( ~ ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
| ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= ( ( nth_list_a @ SV49 @ SV18 )
= SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(542,plain,
! [SV50: list_list_a,SV19: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV19 )
!= ( size_s1427607542list_a @ SV50 ) )
= $true )
| ( ( ~ ! [SY192: nat] :
( ~ ( ord_less_nat @ SY192 @ ( size_s1427607542list_a @ SV19 ) )
| ( ( nth_list_a @ SV19 @ SY192 )
= ( nth_list_a @ SV50 @ SY192 ) ) )
| ( SV19 = SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(543,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ~ ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
| ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[508]) ).
thf(544,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= ( ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[508]) ).
thf(545,plain,
! [SV76: a,SV52: nat,SV21: list_a] :
( ( ~ ( ord_less_eq_nat @ ( size_size_list_a @ SV21 ) @ SV52 )
| ( ( list_update_a @ SV21 @ SV52 @ SV76 )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(546,plain,
! [SV53: list_list_a,SV22: nat] :
( ( ( ~ ( ord_less_nat @ SV22 @ ( size_s1427607542list_a @ ( butlast_list_a @ SV53 ) ) ) )
= $true )
| ( ( ( nth_list_a @ ( butlast_list_a @ SV53 ) @ SV22 )
= ( nth_list_a @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(547,plain,
! [SV54: list_a,SV23: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV23 )
!= ( size_size_list_a @ SV54 ) ) ) )
= $true )
| ( ( SV23 != SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(548,plain,
! [SV55: list_a,SV24: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV24 )
!= ( size_size_list_a @ SV55 ) ) ) )
= $true )
| ( ( SV24 != SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(549,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ~ ( distinct_list_a @ SV25 )
| ~ ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
| ~ ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(550,plain,
! [SV57: list_a,SV26: list_a > $o] :
( ( ( ~ ! [SY152: list_a] :
( ~ ! [SY153: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY153 ) @ ( size_size_list_a @ SY152 ) )
| ( SV26 @ SY153 ) )
| ( SV26 @ SY152 ) ) )
= $true )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(551,plain,
! [SV58: list_a,SV27: list_a] :
( ( ( ( size_size_list_a @ SV27 )
!= ( size_size_list_a @ SV58 ) )
= $true )
| ( ( ~ ! [SY201: nat] :
( ~ ( ord_less_nat @ SY201 @ ( size_size_list_a @ SV27 ) )
| ( ( nth_a @ SV27 @ SY201 )
= ( nth_a @ SV58 @ SY201 ) ) )
| ( SV27 = SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(552,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ~ ( distinct_a @ SV28 )
| ~ ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
| ~ ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(553,plain,
! [SV79: a,SV60: list_a,SV29: nat] :
( ( ~ ( ord_less_nat @ SV29 @ ( size_size_list_a @ SV60 ) )
| ( ( nth_a @ ( list_update_a @ SV60 @ SV29 @ SV79 ) @ SV29 )
= SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(554,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ~ ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
| ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[518]) ).
thf(555,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= ( ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[518]) ).
thf(556,plain,
! [SV62: list_list_a] :
( ( ! [SV80: list_list_a] :
( ( SV62 = SV80 )
= ( ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV80 ) )
| ~ ! [SY218: nat] :
( ~ ( ord_less_nat @ SY218 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY218 )
= ( nth_list_a @ SV80 @ SY218 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[519]) ).
thf(557,plain,
! [SV62: list_list_a] :
( ( ( ^ [SY208: list_list_a] : ( SV62 = SY208 ) )
= ( ^ [SY209: list_list_a] :
~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SY209 ) )
| ~ ! [SY210: nat] :
( ~ ( ord_less_nat @ SY210 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY210 )
= ( nth_list_a @ SY209 @ SY210 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[519]) ).
thf(558,plain,
! [SV63: list_a > $o] :
( ( ! [SV81: list_list_a] :
( ( list_ex_list_a @ SV63 @ SV81 )
= ( ~ ! [SY219: nat] :
~ ~ ( ~ ( ord_less_nat @ SY219 @ ( size_s1427607542list_a @ SV81 ) )
| ~ ( SV63 @ ( nth_list_a @ SV81 @ SY219 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[520]) ).
thf(559,plain,
! [SV63: list_a > $o] :
( ( ( list_ex_list_a @ SV63 )
= ( ^ [SY211: list_list_a] :
~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ ( size_s1427607542list_a @ SY211 ) )
| ~ ( SV63 @ ( nth_list_a @ SY211 @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[520]) ).
thf(560,plain,
! [SV82: nat,SV34: list_a] :
( ( ( listSl97544552lice_a @ SV34 @ SV82 )
= ( listSl1495374126_aux_a @ SV34 @ SV82 @ ( divide_divide_nat @ ( size_size_list_a @ SV34 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(561,plain,
! [SV37: list_a,SV5: nat] :
( ( ( ord_less_nat @ SV5 @ ( size_size_list_a @ ( butlast_a @ SV37 ) ) )
= $false )
| ( ( ( nth_a @ ( butlast_a @ SV37 ) @ SV5 )
= ( nth_a @ SV37 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(562,plain,
! [SV83: list_a,SV66: list_list_a,SV38: nat,SV6: nat] :
( ( ~ ( ( SV6 != SV38 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV66 @ SV6 @ SV83 ) @ SV38 )
= ( nth_list_a @ SV66 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(563,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 = SV84 )
= ( ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(564,plain,
! [SV85: a,SV68: nat,SV40: list_a,SV8: nat] :
( ( ~ ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
| ~ ( ~ ( ( SV8 != SV68 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 ) )
| ~ ( ~ ( ( SV8 != SV68 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(565,plain,
! [SV69: nat,SV41: list_a,SV9: nat] :
( ( ( ~ ( ord_less_nat @ SV9 @ ( divide_divide_nat @ ( size_size_list_a @ SV41 ) @ SV69 ) ) )
= $true )
| ( ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ SV41 @ SV69 ) @ SV9 ) )
= SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(566,plain,
! [SV10: nat] :
( ( ( size_size_list_a @ ( sK1_SY119 @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(567,plain,
! [SV70: nat,SV42: list_a,SV11: nat] :
( ( ( ~ ( ord_less_nat @ SV11 @ ( divide_divide_nat @ ( size_size_list_a @ SV42 ) @ SV70 ) ) )
= $true )
| ( ( ( nth_list_a @ ( listSl1174287072ice2_a @ SV42 @ SV70 ) @ SV11 )
= ( nth_list_a @ ( listSl97544552lice_a @ SV42 @ SV70 ) @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(568,plain,
! [SV71: a,SV43: list_a,SV12: nat] :
( ( ( ~ ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) ) )
= $true )
| ( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= ( ( nth_a @ SV43 @ SV12 )
= SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(569,plain,
! [SV44: list_a] :
( ( ( ~ ( ( distinct_a @ SV44 )
| ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(570,plain,
! [SV72: list_a,SV45: list_list_a,SV14: nat] :
( ( ( ~ ( ord_less_nat @ SV14 @ ( size_s1427607542list_a @ SV45 ) ) )
= $true )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV45 @ SV14 @ SV72 ) @ SV14 )
= SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(571,plain,
! [SV86: list_a,SV73: nat,SV46: list_list_a,SV15: nat] :
( ( ~ ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
| ~ ( ~ ( ( SV15 != SV73 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 ) )
| ~ ( ~ ( ( SV15 != SV73 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(572,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( list_ex_a @ SV47 @ SV87 )
= ( ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(573,plain,
! [SV48: list_list_a] :
( ( ( ~ ( ( distinct_list_a @ SV48 )
| ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(574,plain,
! [SV75: list_a,SV49: list_list_a,SV18: nat] :
( ( ( ~ ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) ) )
= $true )
| ( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= ( ( nth_list_a @ SV49 @ SV18 )
= SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(575,plain,
! [SV50: list_list_a,SV19: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV19 )
= ( size_s1427607542list_a @ SV50 ) )
= $false )
| ( ( ~ ! [SY192: nat] :
( ~ ( ord_less_nat @ SY192 @ ( size_s1427607542list_a @ SV19 ) )
| ( ( nth_list_a @ SV19 @ SY192 )
= ( nth_list_a @ SV50 @ SY192 ) ) )
| ( SV19 = SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(576,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(577,plain,
! [SV76: a,SV52: nat,SV21: list_a] :
( ( ( ~ ( ord_less_eq_nat @ ( size_size_list_a @ SV21 ) @ SV52 ) )
= $true )
| ( ( ( list_update_a @ SV21 @ SV52 @ SV76 )
= SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(578,plain,
! [SV53: list_list_a,SV22: nat] :
( ( ( ord_less_nat @ SV22 @ ( size_s1427607542list_a @ ( butlast_list_a @ SV53 ) ) )
= $false )
| ( ( ( nth_list_a @ ( butlast_list_a @ SV53 ) @ SV22 )
= ( nth_list_a @ SV53 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(579,plain,
! [SV54: list_a,SV23: list_a] :
( ( ( ( size_size_list_a @ SV23 )
!= ( size_size_list_a @ SV54 ) )
= $false )
| ( ( SV23 != SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(580,plain,
! [SV55: list_a,SV24: list_a] :
( ( ( ( size_size_list_a @ SV24 )
!= ( size_size_list_a @ SV55 ) )
= $false )
| ( ( SV24 != SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(581,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV25 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
| ~ ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(582,plain,
! [SV57: list_a,SV26: list_a > $o] :
( ( ( ! [SY152: list_a] :
( ~ ! [SY153: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY153 ) @ ( size_size_list_a @ SY152 ) )
| ( SV26 @ SY153 ) )
| ( SV26 @ SY152 ) ) )
= $false )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(583,plain,
! [SV58: list_a,SV27: list_a] :
( ( ( ( size_size_list_a @ SV27 )
= ( size_size_list_a @ SV58 ) )
= $false )
| ( ( ~ ! [SY201: nat] :
( ~ ( ord_less_nat @ SY201 @ ( size_size_list_a @ SV27 ) )
| ( ( nth_a @ SV27 @ SY201 )
= ( nth_a @ SV58 @ SY201 ) ) )
| ( SV27 = SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(584,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ~ ( distinct_a @ SV28 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
| ~ ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(585,plain,
! [SV79: a,SV60: list_a,SV29: nat] :
( ( ( ~ ( ord_less_nat @ SV29 @ ( size_size_list_a @ SV60 ) ) )
= $true )
| ( ( ( nth_a @ ( list_update_a @ SV60 @ SV29 @ SV79 ) @ SV29 )
= SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(586,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(587,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 = SV88 )
= ( ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(588,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( list_ex_list_a @ SV63 @ SV89 )
= ( ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(589,plain,
! [SV83: list_a,SV66: list_list_a,SV38: nat,SV6: nat] :
( ( ( ~ ( ( SV6 != SV38 ) ) )
= $true )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV66 @ SV6 @ SV83 ) @ SV38 )
= ( nth_list_a @ SV66 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(590,plain,
! [SV84: list_a,SV39: list_a] :
( ( ~ ( ( SV39 = SV84 )
| ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
| ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[563]) ).
thf(591,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 = SV84 )
= ( ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[563]) ).
thf(592,plain,
! [SV85: a,SV68: nat,SV40: list_a,SV8: nat] :
( ( ( ~ ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV8 != SV68 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 ) )
| ~ ( ~ ( ( SV8 != SV68 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(593,plain,
! [SV69: nat,SV41: list_a,SV9: nat] :
( ( ( ord_less_nat @ SV9 @ ( divide_divide_nat @ ( size_size_list_a @ SV41 ) @ SV69 ) )
= $false )
| ( ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ SV41 @ SV69 ) @ SV9 ) )
= SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(594,plain,
! [SV70: nat,SV42: list_a,SV11: nat] :
( ( ( ord_less_nat @ SV11 @ ( divide_divide_nat @ ( size_size_list_a @ SV42 ) @ SV70 ) )
= $false )
| ( ( ( nth_list_a @ ( listSl1174287072ice2_a @ SV42 @ SV70 ) @ SV11 )
= ( nth_list_a @ ( listSl97544552lice_a @ SV42 @ SV70 ) @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(595,plain,
! [SV71: a,SV43: list_a,SV12: nat] :
( ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false )
| ( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= ( ( nth_a @ SV43 @ SV12 )
= SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(596,plain,
! [SV44: list_a] :
( ( ( ( distinct_a @ SV44 )
| ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(597,plain,
! [SV72: list_a,SV45: list_list_a,SV14: nat] :
( ( ( ord_less_nat @ SV14 @ ( size_s1427607542list_a @ SV45 ) )
= $false )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV45 @ SV14 @ SV72 ) @ SV14 )
= SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(598,plain,
! [SV86: list_a,SV73: nat,SV46: list_list_a,SV15: nat] :
( ( ( ~ ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV15 != SV73 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 ) )
| ~ ( ~ ( ( SV15 != SV73 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(599,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ~ ( ( list_ex_a @ SV47 @ SV87 )
| ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
| ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[572]) ).
thf(600,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( list_ex_a @ SV47 @ SV87 )
= ( ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[572]) ).
thf(601,plain,
! [SV48: list_list_a] :
( ( ( ( distinct_list_a @ SV48 )
| ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(602,plain,
! [SV75: list_a,SV49: list_list_a,SV18: nat] :
( ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false )
| ( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= ( ( nth_list_a @ SV49 @ SV18 )
= SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(603,plain,
! [SV50: list_list_a,SV19: list_list_a] :
( ( ( ~ ! [SY192: nat] :
( ~ ( ord_less_nat @ SY192 @ ( size_s1427607542list_a @ SV19 ) )
| ( ( nth_list_a @ SV19 @ SY192 )
= ( nth_list_a @ SV50 @ SY192 ) ) ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ( size_s1427607542list_a @ SV19 )
= ( size_s1427607542list_a @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(604,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(605,plain,
! [SV76: a,SV52: nat,SV21: list_a] :
( ( ( ord_less_eq_nat @ ( size_size_list_a @ SV21 ) @ SV52 )
= $false )
| ( ( ( list_update_a @ SV21 @ SV52 @ SV76 )
= SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(606,plain,
! [SV54: list_a,SV23: list_a] :
( ( ( ( size_size_list_a @ SV23 )
= ( size_size_list_a @ SV54 ) )
= $true )
| ( ( SV23 != SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(607,plain,
! [SV55: list_a,SV24: list_a] :
( ( ( ( size_size_list_a @ SV24 )
= ( size_size_list_a @ SV55 ) )
= $true )
| ( ( SV24 != SV55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(608,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( distinct_list_a @ SV25 )
= $false )
| ( ( ~ ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
| ~ ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(609,plain,
! [SV26: list_a > $o,SV57: list_a] :
( ( ( ~ ! [SY224: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY224 ) @ ( size_size_list_a @ ( sK2_SY152 @ SV57 @ SV26 ) ) )
| ( SV26 @ SY224 ) )
| ( SV26 @ ( sK2_SY152 @ SV57 @ SV26 ) ) )
= $false )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[582]) ).
thf(610,plain,
! [SV58: list_a,SV27: list_a] :
( ( ( ~ ! [SY201: nat] :
( ~ ( ord_less_nat @ SY201 @ ( size_size_list_a @ SV27 ) )
| ( ( nth_a @ SV27 @ SY201 )
= ( nth_a @ SV58 @ SY201 ) ) ) )
= $true )
| ( ( SV27 = SV58 )
= $true )
| ( ( ( size_size_list_a @ SV27 )
= ( size_size_list_a @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(611,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( distinct_a @ SV28 )
= $false )
| ( ( ~ ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
| ~ ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(612,plain,
! [SV79: a,SV60: list_a,SV29: nat] :
( ( ( ord_less_nat @ SV29 @ ( size_size_list_a @ SV60 ) )
= $false )
| ( ( ( nth_a @ ( list_update_a @ SV60 @ SV29 @ SV79 ) @ SV29 )
= SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(613,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(614,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ~ ( ( SV62 = SV88 )
| ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
| ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[587]) ).
thf(615,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 = SV88 )
= ( ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[587]) ).
thf(616,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ~ ( ( list_ex_list_a @ SV63 @ SV89 )
| ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
| ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[588]) ).
thf(617,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( list_ex_list_a @ SV63 @ SV89 )
= ( ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[588]) ).
thf(618,plain,
! [SV83: list_a,SV66: list_list_a,SV38: nat,SV6: nat] :
( ( ( SV6 != SV38 )
= $false )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV66 @ SV6 @ SV83 ) @ SV38 )
= ( nth_list_a @ SV66 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(619,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ( ( SV39 = SV84 )
| ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(620,plain,
! [SV85: a,SV68: nat,SV40: list_a,SV8: nat] :
( ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false )
| ( ( ~ ( ~ ( ( SV8 != SV68 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 ) )
| ~ ( ~ ( ( SV8 != SV68 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(621,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ~ ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
= SV71 ) )
| ~ ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
!= SV71 ) ) )
= $true )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[595]) ).
thf(622,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= ( ( nth_a @ SV43 @ SV12 )
= SV71 ) )
= $true )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[595]) ).
thf(623,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(624,plain,
! [SV44: list_a] :
( ( ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(625,plain,
! [SV86: list_a,SV73: nat,SV46: list_list_a,SV15: nat] :
( ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false )
| ( ( ~ ( ~ ( ( SV15 != SV73 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 ) )
| ~ ( ~ ( ( SV15 != SV73 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(626,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ( ( list_ex_a @ SV47 @ SV87 )
| ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(627,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[601]) ).
thf(628,plain,
! [SV48: list_list_a] :
( ( ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[601]) ).
thf(629,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ~ ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
= SV75 ) )
| ~ ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 ) ) )
= $true )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[602]) ).
thf(630,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= ( ( nth_list_a @ SV49 @ SV18 )
= SV75 ) )
= $true )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[602]) ).
thf(631,plain,
! [SV50: list_list_a,SV19: list_list_a] :
( ( ( ! [SY192: nat] :
( ~ ( ord_less_nat @ SY192 @ ( size_s1427607542list_a @ SV19 ) )
| ( ( nth_list_a @ SV19 @ SY192 )
= ( nth_list_a @ SV50 @ SY192 ) ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ( size_s1427607542list_a @ SV19 )
= ( size_s1427607542list_a @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(632,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(633,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(634,plain,
! [SV54: list_a,SV23: list_a] :
( ( ( SV23 = SV54 )
= $false )
| ( ( ( size_size_list_a @ SV23 )
= ( size_size_list_a @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(635,plain,
! [SV55: list_a,SV24: list_a] :
( ( ( SV24 = SV55 )
= $false )
| ( ( ( size_size_list_a @ SV24 )
= ( size_size_list_a @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(636,plain,
! [SV77: nat,SV25: list_list_a,SV56: nat] :
( ( ( ~ ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) ) )
= $true )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(637,plain,
! [SV26: list_a > $o,SV57: list_a] :
( ( ( ~ ! [SY224: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY224 ) @ ( size_size_list_a @ ( sK2_SY152 @ SV57 @ SV26 ) ) )
| ( SV26 @ SY224 ) ) )
= $false )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(638,plain,
! [SV57: list_a,SV26: list_a > $o] :
( ( ( SV26 @ ( sK2_SY152 @ SV57 @ SV26 ) )
= $false )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(639,plain,
! [SV58: list_a,SV27: list_a] :
( ( ( ! [SY201: nat] :
( ~ ( ord_less_nat @ SY201 @ ( size_size_list_a @ SV27 ) )
| ( ( nth_a @ SV27 @ SY201 )
= ( nth_a @ SV58 @ SY201 ) ) ) )
= $false )
| ( ( SV27 = SV58 )
= $true )
| ( ( ( size_size_list_a @ SV27 )
= ( size_size_list_a @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(640,plain,
! [SV78: nat,SV28: list_a,SV59: nat] :
( ( ( ~ ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) ) )
= $true )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(641,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(642,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(643,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ( ( SV62 = SV88 )
| ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(644,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( ( list_ex_list_a @ SV63 @ SV89 )
| ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(645,plain,
! [SV83: list_a,SV66: list_list_a,SV38: nat,SV6: nat] :
( ( ( SV6 = SV38 )
= $true )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV66 @ SV6 @ SV83 ) @ SV38 )
= ( nth_list_a @ SV66 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(646,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( SV39 = SV84 )
| ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(647,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( ~ ( ( SV8 != SV68 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 ) )
| ~ ( ~ ( ( SV8 != SV68 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(648,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ~ ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
= SV71 ) ) )
= $true )
| ( ( ~ ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
!= SV71 ) ) )
= $true )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(649,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(650,plain,
! [SV44: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
| ! [SY225: nat] :
( ~ ( ord_less_nat @ SY225 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( ( sK3_SY182 @ SV44 )
!= SY225 ) )
| ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
!= ( nth_a @ SV44 @ SY225 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[624]) ).
thf(651,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( ~ ( ( SV15 != SV73 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 ) )
| ~ ( ~ ( ( SV15 != SV73 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(652,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ( list_ex_a @ SV47 @ SV87 )
| ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(653,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(654,plain,
! [SV48: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY226: nat] :
( ~ ( ord_less_nat @ SY226 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( ( sK4_SY189 @ SV48 )
!= SY226 ) )
| ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
!= ( nth_list_a @ SV48 @ SY226 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[628]) ).
thf(655,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ~ ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
= SV75 ) ) )
= $true )
| ( ( ~ ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 ) ) )
= $true )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(656,plain,
! [SV19: list_list_a,SV50: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK5_SY192 @ SV50 @ SV19 ) @ ( size_s1427607542list_a @ SV19 ) )
| ( ( nth_list_a @ SV19 @ ( sK5_SY192 @ SV50 @ SV19 ) )
= ( nth_list_a @ SV50 @ ( sK5_SY192 @ SV50 @ SV19 ) ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ( size_s1427607542list_a @ SV19 )
= ( size_s1427607542list_a @ SV50 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[631]) ).
thf(657,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
| ~ ! [SY227: list_a] :
~ ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SY227 ) )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[632]) ).
thf(658,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(659,plain,
! [SV77: nat,SV25: list_list_a,SV56: nat] :
( ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) ) )
= $true )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(660,plain,
! [SV26: list_a > $o,SV57: list_a] :
( ( ( ! [SY224: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY224 ) @ ( size_size_list_a @ ( sK2_SY152 @ SV57 @ SV26 ) ) )
| ( SV26 @ SY224 ) ) )
= $true )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(661,plain,
! [SV27: list_a,SV58: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK7_SY201 @ SV58 @ SV27 ) @ ( size_size_list_a @ SV27 ) )
| ( ( nth_a @ SV27 @ ( sK7_SY201 @ SV58 @ SV27 ) )
= ( nth_a @ SV58 @ ( sK7_SY201 @ SV58 @ SV27 ) ) ) )
= $false )
| ( ( SV27 = SV58 )
= $true )
| ( ( ( size_size_list_a @ SV27 )
= ( size_size_list_a @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[639]) ).
thf(662,plain,
! [SV78: nat,SV28: list_a,SV59: nat] :
( ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) ) )
= $true )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(663,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
| ~ ! [SY228: a] :
~ ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SY228 ) )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[641]) ).
thf(664,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(665,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( SV62 = SV88 )
| ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(666,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ( list_ex_list_a @ SV63 @ SV89 )
| ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(667,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 = SV84 )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(668,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(669,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( ~ ( ( SV8 != SV68 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 ) ) )
= $false )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(670,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( ~ ( ~ ( ( SV8 != SV68 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(671,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
= SV71 ) )
= $false )
| ( ( ~ ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
!= SV71 ) ) )
= $true )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(672,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(673,plain,
! [SV44: list_a] :
( ( ( ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(674,plain,
! [SV44: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(675,plain,
! [SV44: list_a] :
( ( ( ! [SY225: nat] :
( ~ ( ord_less_nat @ SY225 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( ( sK3_SY182 @ SV44 )
!= SY225 ) )
| ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
!= ( nth_a @ SV44 @ SY225 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(676,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( ~ ( ( SV15 != SV73 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 ) ) )
= $false )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(677,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( ~ ( ~ ( ( SV15 != SV73 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(678,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( list_ex_a @ SV47 @ SV87 )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(679,plain,
! [SV47: a > $o,SV87: list_a] :
( ( ( ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(680,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(681,plain,
! [SV48: list_list_a] :
( ( ( ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(682,plain,
! [SV48: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(683,plain,
! [SV48: list_list_a] :
( ( ( ! [SY226: nat] :
( ~ ( ord_less_nat @ SY226 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( ( sK4_SY189 @ SV48 )
!= SY226 ) )
| ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
!= ( nth_list_a @ SV48 @ SY226 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(684,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
= SV75 ) )
= $false )
| ( ( ~ ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 ) ) )
= $true )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(685,plain,
! [SV19: list_list_a,SV50: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK5_SY192 @ SV50 @ SV19 ) @ ( size_s1427607542list_a @ SV19 ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ( size_s1427607542list_a @ SV19 )
= ( size_s1427607542list_a @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(686,plain,
! [SV50: list_list_a,SV19: list_list_a] :
( ( ( ( nth_list_a @ SV19 @ ( sK5_SY192 @ SV50 @ SV19 ) )
= ( nth_list_a @ SV50 @ ( sK5_SY192 @ SV50 @ SV19 ) ) )
= $false )
| ( ( SV19 = SV50 )
= $true )
| ( ( ( size_s1427607542list_a @ SV19 )
= ( size_s1427607542list_a @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(687,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 ) )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(688,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ~ ! [SY227: list_a] :
~ ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SY227 ) )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(689,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV90: list_list_a] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ SV90 )
!= SV20 )
| ~ ! [SY229: nat] :
( ~ ( ord_less_nat @ SY229 @ SV20 )
| ( SV51 @ SY229 @ ( nth_list_a @ SV90 @ SY229 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(690,plain,
! [SV56: nat,SV25: list_list_a,SV77: nat] :
( ( ( ~ ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) ) )
= $true )
| ( ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) )
= $true )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(691,plain,
! [SV26: list_a > $o,SV57: list_a,SV91: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV91 ) @ ( size_size_list_a @ ( sK2_SY152 @ SV57 @ SV26 ) ) )
| ( SV26 @ SV91 ) )
= $true )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(692,plain,
! [SV27: list_a,SV58: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK7_SY201 @ SV58 @ SV27 ) @ ( size_size_list_a @ SV27 ) ) )
= $false )
| ( ( SV27 = SV58 )
= $true )
| ( ( ( size_size_list_a @ SV27 )
= ( size_size_list_a @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(693,plain,
! [SV58: list_a,SV27: list_a] :
( ( ( ( nth_a @ SV27 @ ( sK7_SY201 @ SV58 @ SV27 ) )
= ( nth_a @ SV58 @ ( sK7_SY201 @ SV58 @ SV27 ) ) )
= $false )
| ( ( SV27 = SV58 )
= $true )
| ( ( ( size_size_list_a @ SV27 )
= ( size_size_list_a @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(694,plain,
! [SV59: nat,SV28: list_a,SV78: nat] :
( ( ( ~ ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) ) )
= $true )
| ( ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) )
= $true )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(695,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 ) )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(696,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ~ ! [SY228: a] :
~ ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SY228 ) )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(697,plain,
! [SV61: nat > a > $o,SV30: nat,SV92: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV92 )
!= SV30 )
| ~ ! [SY230: nat] :
( ~ ( ord_less_nat @ SY230 @ SV30 )
| ( SV61 @ SY230 @ ( nth_a @ SV92 @ SY230 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(698,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 = SV88 )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(699,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(700,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( list_ex_list_a @ SV63 @ SV89 )
= $false )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(701,plain,
! [SV63: list_a > $o,SV89: list_list_a] :
( ( ( ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(702,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(703,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $true )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(704,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( ( SV8 != SV68 )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 ) )
= $true )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(705,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( ~ ( ( SV8 != SV68 ) )
| ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) ) )
= $true )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(706,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $false )
| ( ( ~ ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
!= SV71 ) ) )
= $true )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(707,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $false )
| ( ( ~ ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
!= SV71 ) ) )
= $true )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(708,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= $true )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(709,plain,
! [SV44: list_a] :
( ( ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $true )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(710,plain,
! [SV44: list_a] :
( ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(711,plain,
! [SV44: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
| ~ ( ( ( sK3_SY182 @ SV44 )
!= ( sK9_SY225 @ SV44 ) ) )
| ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
!= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[675]) ).
thf(712,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( ( SV15 != SV73 )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 ) )
= $true )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(713,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( ~ ( ( SV15 != SV73 ) )
| ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) ) )
= $true )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(714,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(715,plain,
! [SV47: a > $o,SV87: list_a] :
( ( ( ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(716,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= $true )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(717,plain,
! [SV48: list_list_a] :
( ( ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $true )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(718,plain,
! [SV48: list_list_a] :
( ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(719,plain,
! [SV48: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( ( sK4_SY189 @ SV48 )
!= ( sK10_SY226 @ SV48 ) ) )
| ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
!= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[683]) ).
thf(720,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $false )
| ( ( ~ ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 ) ) )
= $true )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(721,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $false )
| ( ( ~ ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 ) ) )
= $true )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(722,plain,
! [SV19: list_list_a,SV50: list_list_a] :
( ( ( ord_less_nat @ ( sK5_SY192 @ SV50 @ SV19 ) @ ( size_s1427607542list_a @ SV19 ) )
= $true )
| ( ( SV19 = SV50 )
= $true )
| ( ( ( size_s1427607542list_a @ SV19 )
= ( size_s1427607542list_a @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(723,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(724,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ! [SY227: list_a] :
~ ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SY227 ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(725,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV90: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ SV90 )
!= SV20 )
| ~ ! [SY229: nat] :
( ~ ( ord_less_nat @ SY229 @ SV20 )
| ( SV51 @ SY229 @ ( nth_list_a @ SV90 @ SY229 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(726,plain,
! [SV56: nat,SV25: list_list_a,SV77: nat] :
( ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) )
= $true )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(727,plain,
! [SV26: list_a > $o,SV57: list_a,SV91: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV91 ) @ ( size_size_list_a @ ( sK2_SY152 @ SV57 @ SV26 ) ) ) )
= $true )
| ( ( SV26 @ SV91 )
= $true )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(728,plain,
! [SV27: list_a,SV58: list_a] :
( ( ( ord_less_nat @ ( sK7_SY201 @ SV58 @ SV27 ) @ ( size_size_list_a @ SV27 ) )
= $true )
| ( ( SV27 = SV58 )
= $true )
| ( ( ( size_size_list_a @ SV27 )
= ( size_size_list_a @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(729,plain,
! [SV59: nat,SV28: list_a,SV78: nat] :
( ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) )
= $true )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(730,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(731,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ! [SY228: a] :
~ ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SY228 ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(732,plain,
! [SV61: nat > a > $o,SV30: nat,SV92: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV92 )
!= SV30 )
| ~ ! [SY230: nat] :
( ~ ( ord_less_nat @ SY230 @ SV30 )
| ( SV61 @ SY230 @ ( nth_a @ SV92 @ SY230 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(733,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(734,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $true )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(735,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(736,plain,
! [SV63: list_a > $o,SV89: list_list_a] :
( ( ( ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(737,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 != SV84 )
= $false )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(738,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(739,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
= $true )
| ( ( ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $true )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(740,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( SV8 != SV68 )
= $true )
| ( ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 )
= $true )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(741,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( ~ ( ( SV8 != SV68 ) ) )
= $true )
| ( ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) )
= $true )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(742,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
!= SV71 ) )
= $false )
| ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(743,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
| ( ( nth_a @ SV43 @ SV12 )
!= SV71 ) )
= $false )
| ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(744,plain,
! [SV44: list_a,SV93: nat] :
( ( ( ~ ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
| ! [SY231: nat] :
( ~ ( ord_less_nat @ SY231 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV93 != SY231 ) )
| ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SY231 ) ) ) )
= $true )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(745,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(746,plain,
! [SV44: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(747,plain,
! [SV44: list_a] :
( ( ( ~ ( ( ( sK3_SY182 @ SV44 )
!= ( sK9_SY225 @ SV44 ) ) )
| ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
!= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(748,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( SV15 != SV73 )
= $true )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 )
= $true )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(749,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( ~ ( ( SV15 != SV73 ) ) )
= $true )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) )
= $true )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(750,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ( list_ex_a @ SV47 @ SV87 ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(751,plain,
! [SV47: a > $o,SV87: list_a] :
( ( ( ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(752,plain,
! [SV47: a > $o,SV87: list_a,SV94: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SV94 ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(753,plain,
! [SV48: list_list_a,SV95: nat] :
( ( ( ~ ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY232: nat] :
( ~ ( ord_less_nat @ SY232 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV95 != SY232 ) )
| ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SY232 ) ) ) )
= $true )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(754,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(755,plain,
! [SV48: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(756,plain,
! [SV48: list_list_a] :
( ( ( ~ ( ( ( sK4_SY189 @ SV48 )
!= ( sK10_SY226 @ SV48 ) ) )
| ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
!= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(757,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 ) )
= $false )
| ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(758,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
| ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 ) )
= $false )
| ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(759,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(760,plain,
! [SV96: list_a,SV20: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(761,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV90: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV90 )
!= SV20 )
| ~ ! [SY229: nat] :
( ~ ( ord_less_nat @ SY229 @ SV20 )
| ( SV51 @ SY229 @ ( nth_list_a @ SV90 @ SY229 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(762,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ~ ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 = SV77 ) )
| ~ ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 != SV77 ) ) )
= $true )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[726]) ).
thf(763,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= ( SV56 = SV77 ) )
= $true )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[726]) ).
thf(764,plain,
! [SV26: list_a > $o,SV57: list_a,SV91: list_a] :
( ( ( ord_less_nat @ ( size_size_list_a @ SV91 ) @ ( size_size_list_a @ ( sK2_SY152 @ SV57 @ SV26 ) ) )
= $false )
| ( ( SV26 @ SV91 )
= $true )
| ( ( SV26 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(765,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ~ ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 = SV78 ) )
| ~ ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 != SV78 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[729]) ).
thf(766,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= ( SV59 = SV78 ) )
= $true )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[729]) ).
thf(767,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(768,plain,
! [SV97: a,SV30: nat,SV61: nat > a > $o] :
( ( ( ~ ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(769,plain,
! [SV61: nat > a > $o,SV30: nat,SV92: list_a] :
( ( ( ( ( size_size_list_a @ SV92 )
!= SV30 )
| ~ ! [SY230: nat] :
( ~ ( ord_less_nat @ SY230 @ SV30 )
| ( SV61 @ SY230 @ ( nth_a @ SV92 @ SY230 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(770,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 != SV88 )
= $false )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(771,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(772,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
= $true )
| ( ( ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $true )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(773,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( list_ex_list_a @ SV63 @ SV89 ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(774,plain,
! [SV63: list_a > $o,SV89: list_list_a] :
( ( ( ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(775,plain,
! [SV63: list_a > $o,SV89: list_list_a,SV98: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(776,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 = SV84 )
= $true )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(777,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $true )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(778,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $true )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(779,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( SV8 = SV68 )
= $false )
| ( ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= SV85 )
= $true )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(780,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( SV8 != SV68 )
= $false )
| ( ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) )
= $true )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(781,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
= $false )
| ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(782,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( nth_a @ SV43 @ SV12 )
!= SV71 )
= $false )
| ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(783,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
!= SV43 )
= $false )
| ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(784,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( nth_a @ SV43 @ SV12 )
!= SV71 )
= $false )
| ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(785,plain,
! [SV44: list_a,SV93: nat] :
( ( ( ~ ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ! [SY231: nat] :
( ~ ( ord_less_nat @ SY231 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV93 != SY231 ) )
| ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SY231 ) ) ) )
= $true )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(786,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(787,plain,
! [SV44: list_a] :
( ( ( ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(788,plain,
! [SV44: list_a] :
( ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(789,plain,
! [SV44: list_a] :
( ( ( ~ ( ( ( sK3_SY182 @ SV44 )
!= ( sK9_SY225 @ SV44 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(790,plain,
! [SV44: list_a] :
( ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
!= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(791,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( SV15 = SV73 )
= $false )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= SV86 )
= $true )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(792,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( SV15 != SV73 )
= $false )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) )
= $true )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(793,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( list_ex_a @ SV47 @ SV87 )
= $true )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(794,plain,
! [SV47: a > $o,SV87: list_a] :
( ( ( ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $true )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(795,plain,
! [SV47: a > $o,SV87: list_a,SV94: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SV94 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(796,plain,
! [SV48: list_list_a,SV95: nat] :
( ( ( ~ ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ! [SY232: nat] :
( ~ ( ord_less_nat @ SY232 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV95 != SY232 ) )
| ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SY232 ) ) ) )
= $true )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(797,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(798,plain,
! [SV48: list_list_a] :
( ( ( ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(799,plain,
! [SV48: list_list_a] :
( ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(800,plain,
! [SV48: list_list_a] :
( ( ( ~ ( ( ( sK4_SY189 @ SV48 )
!= ( sK10_SY226 @ SV48 ) ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(801,plain,
! [SV48: list_list_a] :
( ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
!= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(802,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
= $false )
| ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(803,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 )
= $false )
| ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(804,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
!= SV49 )
= $false )
| ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(805,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( nth_list_a @ SV49 @ SV18 )
!= SV75 )
= $false )
| ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(806,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(807,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(808,plain,
! [SV96: list_a,SV20: nat,SV51: nat > list_a > $o] :
( ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(809,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV90: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV90 )
!= SV20 )
= $true )
| ( ( ~ ! [SY229: nat] :
( ~ ( ord_less_nat @ SY229 @ SV20 )
| ( SV51 @ SY229 @ ( nth_list_a @ SV90 @ SY229 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(810,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ~ ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 = SV77 ) ) )
= $true )
| ( ( ~ ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 != SV77 ) ) )
= $true )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(811,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ~ ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 = SV78 ) ) )
= $true )
| ( ( ~ ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 != SV78 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(812,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(813,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(814,plain,
! [SV97: a,SV30: nat,SV61: nat > a > $o] :
( ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(815,plain,
! [SV61: nat > a > $o,SV30: nat,SV92: list_a] :
( ( ( ( size_size_list_a @ SV92 )
!= SV30 )
= $true )
| ( ( ~ ! [SY230: nat] :
( ~ ( ord_less_nat @ SY230 @ SV30 )
| ( SV61 @ SY230 @ ( nth_a @ SV92 @ SY230 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(816,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 = SV88 )
= $true )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(817,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $true )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(818,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $true )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(819,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( list_ex_list_a @ SV63 @ SV89 )
= $true )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(820,plain,
! [SV63: list_a > $o,SV89: list_list_a] :
( ( ( ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $true )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(821,plain,
! [SV63: list_a > $o,SV89: list_list_a,SV98: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(822,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $false )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(823,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(824,plain,
! [SV85: a,SV40: list_a,SV68: nat,SV8: nat] :
( ( ( SV8 = SV68 )
= $true )
| ( ( ( nth_a @ ( list_update_a @ SV40 @ SV8 @ SV85 ) @ SV68 )
= ( nth_a @ SV40 @ SV68 ) )
= $true )
| ( ( ord_less_nat @ SV8 @ ( size_size_list_a @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(825,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $true )
| ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(826,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $true )
| ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(827,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( list_update_a @ SV43 @ SV12 @ SV71 )
= SV43 )
= $true )
| ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(828,plain,
! [SV71: a,SV12: nat,SV43: list_a] :
( ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $true )
| ( ( ( nth_a @ SV43 @ SV12 )
= SV71 )
= $false )
| ( ( ord_less_nat @ SV12 @ ( size_size_list_a @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(829,plain,
! [SV44: list_a,SV93: nat] :
( ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ! [SY231: nat] :
( ~ ( ord_less_nat @ SY231 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV93 != SY231 ) )
| ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SY231 ) ) ) )
= $true )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(830,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= $true )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(831,plain,
! [SV44: list_a] :
( ( ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(832,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(833,plain,
! [SV44: list_a] :
( ( ( ( sK3_SY182 @ SV44 )
!= ( sK9_SY225 @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(834,plain,
! [SV44: list_a] :
( ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(835,plain,
! [SV86: list_a,SV46: list_list_a,SV73: nat,SV15: nat] :
( ( ( SV15 = SV73 )
= $true )
| ( ( ( nth_list_a @ ( list_update_list_a @ SV46 @ SV15 @ SV86 ) @ SV73 )
= ( nth_list_a @ SV46 @ SV73 ) )
= $true )
| ( ( ord_less_nat @ SV15 @ ( size_s1427607542list_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(836,plain,
! [SV47: a > $o,SV87: list_a] :
( ( ( ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(837,plain,
! [SV47: a > $o,SV87: list_a,SV94: nat] :
( ( ( ~ ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SV94 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(838,plain,
! [SV48: list_list_a,SV95: nat] :
( ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ! [SY232: nat] :
( ~ ( ord_less_nat @ SY232 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV95 != SY232 ) )
| ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SY232 ) ) ) )
= $true )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(839,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= $true )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(840,plain,
! [SV48: list_list_a] :
( ( ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(841,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(842,plain,
! [SV48: list_list_a] :
( ( ( ( sK4_SY189 @ SV48 )
!= ( sK10_SY226 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(843,plain,
! [SV48: list_list_a] :
( ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(844,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $true )
| ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(845,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $true )
| ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(846,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( list_update_list_a @ SV49 @ SV18 @ SV75 )
= SV49 )
= $true )
| ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(847,plain,
! [SV75: list_a,SV18: nat,SV49: list_list_a] :
( ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $true )
| ( ( ( nth_list_a @ SV49 @ SV18 )
= SV75 )
= $false )
| ( ( ord_less_nat @ SV18 @ ( size_s1427607542list_a @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(848,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(849,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(850,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(851,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV90: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ~ ! [SY229: nat] :
( ~ ( ord_less_nat @ SY229 @ SV20 )
| ( SV51 @ SY229 @ ( nth_list_a @ SV90 @ SY229 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(852,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 = SV77 ) )
= $false )
| ( ( ~ ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 != SV77 ) ) )
= $true )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(853,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 = SV78 ) )
= $false )
| ( ( ~ ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 != SV78 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(854,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(855,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(856,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(857,plain,
! [SV61: nat > a > $o,SV30: nat,SV92: list_a] :
( ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ~ ! [SY230: nat] :
( ~ ( ord_less_nat @ SY230 @ SV30 )
| ( SV61 @ SY230 @ ( nth_a @ SV92 @ SY230 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(858,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $false )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(859,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(860,plain,
! [SV63: list_a > $o,SV89: list_list_a] :
( ( ( ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(861,plain,
! [SV63: list_a > $o,SV89: list_list_a,SV98: nat] :
( ( ( ~ ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(862,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(863,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $false )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(864,plain,
! [SV39: list_a,SV84: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[823]) ).
thf(865,plain,
! [SV93: nat,SV44: list_a,SV99: nat] :
( ( ( ~ ( ord_less_nat @ SV99 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV93 != SV99 ) )
| ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SV99 ) ) )
= $true )
| ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(866,plain,
! [SV44: list_a,SV100: nat] :
( ( ( ~ ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
| ! [SY233: nat] :
( ~ ( ord_less_nat @ SY233 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV100 != SY233 ) )
| ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SY233 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(867,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(868,plain,
! [SV44: list_a] :
( ( ( ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(869,plain,
! [SV44: list_a] :
( ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false )
| ( ( ~ ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(870,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(871,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK12_SY221 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ ( sK12_SY221 @ SV47 @ SV87 ) ) ) ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[836]) ).
thf(872,plain,
! [SV47: a > $o,SV87: list_a,SV94: nat] :
( ( ( ~ ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) ) )
= $true )
| ( ( ~ ( SV47 @ ( nth_a @ SV87 @ SV94 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(873,plain,
! [SV95: nat,SV48: list_list_a,SV101: nat] :
( ( ( ~ ( ord_less_nat @ SV101 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV95 != SV101 ) )
| ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SV101 ) ) )
= $true )
| ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(874,plain,
! [SV48: list_list_a,SV102: nat] :
( ( ( ~ ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY234: nat] :
( ~ ( ord_less_nat @ SY234 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV102 != SY234 ) )
| ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SY234 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(875,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[841]) ).
thf(876,plain,
! [SV48: list_list_a] :
( ( ( ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[841]) ).
thf(877,plain,
! [SV48: list_list_a] :
( ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false )
| ( ( ~ ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(878,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(879,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV103: nat] :
( ( ( ~ ( ord_less_nat @ SV103 @ SV20 )
| ~ ! [SY235: list_a] :
~ ( SV51 @ SV103 @ SY235 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(880,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(881,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(882,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(883,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY229: nat] :
( ~ ( ord_less_nat @ SY229 @ SV20 )
| ( SV51 @ SY229 @ ( nth_list_a @ SV90 @ SY229 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(884,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( ~ ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 != SV77 ) ) )
= $true )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(885,plain,
! [SV25: list_list_a,SV77: nat,SV56: nat] :
( ( ( SV56 = SV77 )
= $false )
| ( ( ~ ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 != SV77 ) ) )
= $true )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(886,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( ~ ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 != SV78 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(887,plain,
! [SV28: list_a,SV78: nat,SV59: nat] :
( ( ( SV59 = SV78 )
= $false )
| ( ( ~ ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 != SV78 ) ) )
= $true )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(888,plain,
! [SV61: nat > a > $o,SV30: nat,SV104: nat] :
( ( ( ~ ( ord_less_nat @ SV104 @ SV30 )
| ~ ! [SY236: a] :
~ ( SV61 @ SV104 @ SY236 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(889,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(890,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(891,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(892,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY230: nat] :
( ~ ( ord_less_nat @ SY230 @ SV30 )
| ( SV61 @ SY230 @ ( nth_a @ SV92 @ SY230 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(893,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(894,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $false )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(895,plain,
! [SV62: list_list_a,SV88: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[859]) ).
thf(896,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK14_SY223 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK14_SY223 @ SV63 @ SV89 ) ) ) ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[860]) ).
thf(897,plain,
! [SV63: list_a > $o,SV89: list_list_a,SV98: nat] :
( ( ( ~ ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) ) )
= $true )
| ( ( ~ ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(898,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $true )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(899,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $true )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(900,plain,
! [SV39: list_a,SV84: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(901,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(902,plain,
! [SV93: nat,SV44: list_a,SV99: nat] :
( ( ( ~ ( ord_less_nat @ SV99 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ~ ( ( SV93 != SV99 ) )
| ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SV99 ) ) )
= $true )
| ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(903,plain,
! [SV44: list_a,SV100: nat] :
( ( ( ~ ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ! [SY233: nat] :
( ~ ( ord_less_nat @ SY233 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV100 != SY233 ) )
| ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SY233 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(904,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= $true )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(905,plain,
! [SV44: list_a] :
( ( ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(906,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 )
| ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(907,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(908,plain,
! [SV44: list_a] :
( ( ( ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(909,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK12_SY221 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ ( sK12_SY221 @ SV47 @ SV87 ) ) ) ) )
= $true )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(910,plain,
! [SV47: a > $o,SV87: list_a,SV94: nat] :
( ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( ~ ( SV47 @ ( nth_a @ SV87 @ SV94 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(911,plain,
! [SV95: nat,SV48: list_list_a,SV101: nat] :
( ( ( ~ ( ord_less_nat @ SV101 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ~ ( ( SV95 != SV101 ) )
| ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SV101 ) ) )
= $true )
| ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(912,plain,
! [SV48: list_list_a,SV102: nat] :
( ( ( ~ ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ! [SY234: nat] :
( ~ ( ord_less_nat @ SY234 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV102 != SY234 ) )
| ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SY234 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(913,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= $true )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(914,plain,
! [SV48: list_list_a] :
( ( ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(915,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 )
| ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(916,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[878]) ).
thf(917,plain,
! [SV48: list_list_a] :
( ( ( ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[878]) ).
thf(918,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV103: nat] :
( ( ( ~ ( ord_less_nat @ SV103 @ SV20 ) )
= $true )
| ( ( ~ ! [SY235: list_a] :
~ ( SV51 @ SV103 @ SY235 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(919,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ ( sK15_SY195 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY237: nat] :
( ~ ( ord_less_nat @ SY237 @ SV20 )
| ( SV51 @ SY237 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SY237 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[880]) ).
thf(920,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(921,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(922,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
| ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[883]) ).
thf(923,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 != SV77 ) )
= $false )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(924,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
| ( SV56 != SV77 ) )
= $false )
| ( ( SV56 = SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(925,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 != SV78 ) )
= $false )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(926,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
| ( SV59 != SV78 ) )
= $false )
| ( ( SV59 = SV78 )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(927,plain,
! [SV61: nat > a > $o,SV30: nat,SV104: nat] :
( ( ( ~ ( ord_less_nat @ SV104 @ SV30 ) )
= $true )
| ( ( ~ ! [SY236: a] :
~ ( SV61 @ SV104 @ SY236 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(928,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK17_SY206 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY238: nat] :
( ~ ( ord_less_nat @ SY238 @ SV30 )
| ( SV61 @ SY238 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SY238 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[889]) ).
thf(929,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(930,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(931,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
| ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[892]) ).
thf(932,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $true )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(933,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $true )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(934,plain,
! [SV62: list_list_a,SV88: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(935,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(936,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK14_SY223 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK14_SY223 @ SV63 @ SV89 ) ) ) ) )
= $true )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(937,plain,
! [SV63: list_a > $o,SV89: list_list_a,SV98: nat] :
( ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( ~ ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(938,plain,
! [SV84: list_a,SV39: list_a,SV105: nat] :
( ( ( ~ ( ord_less_nat @ SV105 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SV105 )
= ( nth_a @ SV84 @ SV105 ) ) )
= $true )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(939,plain,
! [SV39: list_a,SV84: list_a] :
( ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ~ ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(940,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(941,plain,
! [SV93: nat,SV44: list_a,SV99: nat] :
( ( ( ord_less_nat @ SV99 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ~ ( ( SV93 != SV99 ) )
| ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SV99 ) ) )
= $true )
| ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(942,plain,
! [SV44: list_a,SV100: nat] :
( ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ! [SY233: nat] :
( ~ ( ord_less_nat @ SY233 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV100 != SY233 ) )
| ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SY233 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(943,plain,
! [SV44: list_a,SV106: nat] :
( ( ( ~ ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
| ! [SY239: nat] :
( ~ ( ord_less_nat @ SY239 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV106 != SY239 ) )
| ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SY239 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(944,plain,
! [SV44: list_a] :
( ( ( ~ ( distinct_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(945,plain,
! [SV44: list_a] :
( ( ( ~ ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(946,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= $true )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(947,plain,
! [SV44: list_a] :
( ( ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[908]) ).
thf(948,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK12_SY221 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ ( sK12_SY221 @ SV47 @ SV87 ) ) ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(949,plain,
! [SV94: nat,SV87: list_a,SV47: a > $o] :
( ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(950,plain,
! [SV95: nat,SV48: list_list_a,SV101: nat] :
( ( ( ord_less_nat @ SV101 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ~ ( ( SV95 != SV101 ) )
| ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SV101 ) ) )
= $true )
| ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(951,plain,
! [SV48: list_list_a,SV102: nat] :
( ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ! [SY234: nat] :
( ~ ( ord_less_nat @ SY234 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV102 != SY234 ) )
| ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SY234 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(952,plain,
! [SV48: list_list_a,SV107: nat] :
( ( ( ~ ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY240: nat] :
( ~ ( ord_less_nat @ SY240 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV107 != SY240 ) )
| ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SY240 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(953,plain,
! [SV48: list_list_a] :
( ( ( ~ ( distinct_list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(954,plain,
! [SV48: list_list_a] :
( ( ( ~ ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(955,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= $true )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(956,plain,
! [SV48: list_list_a] :
( ( ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(957,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV103: nat] :
( ( ( ord_less_nat @ SV103 @ SV20 )
= $false )
| ( ( ~ ! [SY235: list_a] :
~ ( SV51 @ SV103 @ SY235 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(958,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( ( ( size_s1427607542list_a @ ( sK15_SY195 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY237: nat] :
( ~ ( ord_less_nat @ SY237 @ SV20 )
| ( SV51 @ SY237 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SY237 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(959,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat,SV108: nat] :
( ( ( ~ ( ord_less_nat @ SV108 @ SV20 )
| ~ ! [SY241: list_a] :
~ ( SV51 @ SV108 @ SY241 ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(960,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(961,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ~ ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(962,plain,
! [SV20: nat,SV90: list_list_a,SV51: nat > list_a > $o] :
( ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(963,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(964,plain,
! [SV25: list_list_a,SV77: nat,SV56: nat] :
( ( ( SV56 != SV77 )
= $false )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(965,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( nth_list_a @ SV25 @ SV56 )
!= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( SV56 = SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(966,plain,
! [SV25: list_list_a,SV77: nat,SV56: nat] :
( ( ( SV56 != SV77 )
= $false )
| ( ( SV56 = SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(967,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(968,plain,
! [SV28: list_a,SV78: nat,SV59: nat] :
( ( ( SV59 != SV78 )
= $false )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(969,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( nth_a @ SV28 @ SV59 )
!= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( SV59 = SV78 )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(970,plain,
! [SV28: list_a,SV78: nat,SV59: nat] :
( ( ( SV59 != SV78 )
= $false )
| ( ( SV59 = SV78 )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(971,plain,
! [SV61: nat > a > $o,SV30: nat,SV104: nat] :
( ( ( ord_less_nat @ SV104 @ SV30 )
= $false )
| ( ( ~ ! [SY236: a] :
~ ( SV61 @ SV104 @ SY236 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(972,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK17_SY206 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY238: nat] :
( ~ ( ord_less_nat @ SY238 @ SV30 )
| ( SV61 @ SY238 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SY238 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(973,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat,SV109: nat] :
( ( ( ~ ( ord_less_nat @ SV109 @ SV30 )
| ~ ! [SY242: a] :
~ ( SV61 @ SV109 @ SY242 ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(974,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(975,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(976,plain,
! [SV30: nat,SV92: list_a,SV61: nat > a > $o] :
( ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(977,plain,
! [SV88: list_list_a,SV62: list_list_a,SV110: nat] :
( ( ( ~ ( ord_less_nat @ SV110 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SV110 )
= ( nth_list_a @ SV88 @ SV110 ) ) )
= $true )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(978,plain,
! [SV62: list_list_a,SV88: list_list_a] :
( ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ~ ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(979,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(980,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK14_SY223 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK14_SY223 @ SV63 @ SV89 ) ) ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(981,plain,
! [SV98: nat,SV89: list_list_a,SV63: list_a > $o] :
( ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( ~ ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(982,plain,
! [SV84: list_a,SV39: list_a,SV105: nat] :
( ( ( ~ ( ord_less_nat @ SV105 @ ( size_size_list_a @ SV39 ) ) )
= $true )
| ( ( ( nth_a @ SV39 @ SV105 )
= ( nth_a @ SV84 @ SV105 ) )
= $true )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(983,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( SV39 != SV84 )
| ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(984,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 != SV84 )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(985,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(986,plain,
! [SV44: list_a,SV99: nat,SV93: nat] :
( ( ( ~ ( ( SV93 != SV99 ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SV99 ) )
= $true )
| ( ( ord_less_nat @ SV99 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(987,plain,
! [SV100: nat,SV44: list_a,SV111: nat] :
( ( ( ~ ( ord_less_nat @ SV111 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV100 != SV111 ) )
| ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SV111 ) ) )
= $true )
| ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(988,plain,
! [SV44: list_a,SV106: nat] :
( ( ( ~ ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ! [SY239: nat] :
( ~ ( ord_less_nat @ SY239 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV106 != SY239 ) )
| ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SY239 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(989,plain,
! [SV44: list_a] :
( ( ( distinct_a @ SV44 )
= $true )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(990,plain,
! [SV44: list_a] :
( ( ( ! [SY182: nat] :
( ~ ( ord_less_nat @ SY182 @ ( size_size_list_a @ SV44 ) )
| ! [SY183: nat] :
( ~ ( ord_less_nat @ SY183 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SY182 != SY183 ) )
| ( ( nth_a @ SV44 @ SY182 )
!= ( nth_a @ SV44 @ SY183 ) ) ) ) )
= $true )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(991,plain,
! [SV44: list_a,SV112: nat] :
( ( ( ~ ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
| ! [SY243: nat] :
( ~ ( ord_less_nat @ SY243 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV112 != SY243 ) )
| ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SY243 ) ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(992,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK12_SY221 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(993,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ~ ( SV47 @ ( nth_a @ SV87 @ ( sK12_SY221 @ SV47 @ SV87 ) ) ) )
= $false )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(994,plain,
! [SV94: nat,SV87: list_a,SV47: a > $o] :
( ( ( ~ ( list_ex_a @ SV47 @ SV87 )
| ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(995,plain,
! [SV48: list_list_a,SV101: nat,SV95: nat] :
( ( ( ~ ( ( SV95 != SV101 ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SV101 ) )
= $true )
| ( ( ord_less_nat @ SV101 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(996,plain,
! [SV102: nat,SV48: list_list_a,SV113: nat] :
( ( ( ~ ( ord_less_nat @ SV113 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV102 != SV113 ) )
| ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SV113 ) ) )
= $true )
| ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(997,plain,
! [SV48: list_list_a,SV107: nat] :
( ( ( ~ ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ! [SY240: nat] :
( ~ ( ord_less_nat @ SY240 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV107 != SY240 ) )
| ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SY240 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(998,plain,
! [SV48: list_list_a] :
( ( ( distinct_list_a @ SV48 )
= $true )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(999,plain,
! [SV48: list_list_a] :
( ( ( ! [SY189: nat] :
( ~ ( ord_less_nat @ SY189 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY190: nat] :
( ~ ( ord_less_nat @ SY190 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SY189 != SY190 ) )
| ( ( nth_list_a @ SV48 @ SY189 )
!= ( nth_list_a @ SV48 @ SY190 ) ) ) ) )
= $true )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1000,plain,
! [SV48: list_list_a,SV114: nat] :
( ( ( ~ ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY244: nat] :
( ~ ( ord_less_nat @ SY244 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV114 != SY244 ) )
| ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SY244 ) ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1001,plain,
! [SV20: nat,SV103: nat,SV51: nat > list_a > $o] :
( ( ( ! [SY235: list_a] :
~ ( SV51 @ SV103 @ SY235 ) )
= $false )
| ( ( ord_less_nat @ SV103 @ SV20 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1002,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ( ( size_s1427607542list_a @ ( sK15_SY195 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY237: nat] :
( ~ ( ord_less_nat @ SY237 @ SV20 )
| ( SV51 @ SY237 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SY237 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1003,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat,SV108: nat] :
( ( ( ~ ( ord_less_nat @ SV108 @ SV20 ) )
= $true )
| ( ( ~ ! [SY241: list_a] :
~ ( SV51 @ SV108 @ SY241 ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1004,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV96: list_a] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY245: nat] :
( ~ ( ord_less_nat @ SY245 @ SV20 )
| ( SV51 @ SY245 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SY245 ) ) ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[960]) ).
thf(1005,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ~ ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1006,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1007,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $true )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1008,plain,
! [SV25: list_list_a,SV77: nat,SV56: nat] :
( ( ( SV56 = SV77 )
= $true )
| ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[964]) ).
thf(1009,plain,
! [SV77: nat,SV56: nat,SV25: list_list_a] :
( ( ( ( nth_list_a @ SV25 @ SV56 )
= ( nth_list_a @ SV25 @ SV77 ) )
= $true )
| ( ( SV56 = SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1010,plain,
! [SV25: list_list_a,SV77: nat,SV56: nat] :
( ( ( SV56 = SV77 )
= $true )
| ( ( SV56 = SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( ord_less_nat @ SV56 @ ( size_s1427607542list_a @ SV25 ) )
= $false )
| ( ( distinct_list_a @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1011,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $true )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1012,plain,
! [SV28: list_a,SV78: nat,SV59: nat] :
( ( ( SV59 = SV78 )
= $true )
| ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1013,plain,
! [SV78: nat,SV59: nat,SV28: list_a] :
( ( ( ( nth_a @ SV28 @ SV59 )
= ( nth_a @ SV28 @ SV78 ) )
= $true )
| ( ( SV59 = SV78 )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1014,plain,
! [SV28: list_a,SV78: nat,SV59: nat] :
( ( ( SV59 = SV78 )
= $true )
| ( ( SV59 = SV78 )
= $false )
| ( ( ord_less_nat @ SV78 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( ord_less_nat @ SV59 @ ( size_size_list_a @ SV28 ) )
= $false )
| ( ( distinct_a @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1015,plain,
! [SV30: nat,SV104: nat,SV61: nat > a > $o] :
( ( ( ! [SY236: a] :
~ ( SV61 @ SV104 @ SY236 ) )
= $false )
| ( ( ord_less_nat @ SV104 @ SV30 )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1016,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ( ( size_size_list_a @ ( sK17_SY206 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY238: nat] :
( ~ ( ord_less_nat @ SY238 @ SV30 )
| ( SV61 @ SY238 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SY238 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1017,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat,SV109: nat] :
( ( ( ~ ( ord_less_nat @ SV109 @ SV30 ) )
= $true )
| ( ( ~ ! [SY242: a] :
~ ( SV61 @ SV109 @ SY242 ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1018,plain,
! [SV30: nat,SV61: nat > a > $o,SV97: a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY246: nat] :
( ~ ( ord_less_nat @ SY246 @ SV30 )
| ( SV61 @ SY246 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SY246 ) ) ) ) )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[974]) ).
thf(1019,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ~ ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1020,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1021,plain,
! [SV88: list_list_a,SV62: list_list_a,SV110: nat] :
( ( ( ~ ( ord_less_nat @ SV110 @ ( size_s1427607542list_a @ SV62 ) ) )
= $true )
| ( ( ( nth_list_a @ SV62 @ SV110 )
= ( nth_list_a @ SV88 @ SV110 ) )
= $true )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1022,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( SV62 != SV88 )
| ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1023,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 != SV88 )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1024,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1025,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK14_SY223 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1026,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK14_SY223 @ SV63 @ SV89 ) ) ) )
= $false )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1027,plain,
! [SV98: nat,SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( list_ex_list_a @ SV63 @ SV89 )
| ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1028,plain,
! [SV84: list_a,SV39: list_a,SV105: nat] :
( ( ( ord_less_nat @ SV105 @ ( size_size_list_a @ SV39 ) )
= $false )
| ( ( ( nth_a @ SV39 @ SV105 )
= ( nth_a @ SV84 @ SV105 ) )
= $true )
| ( ( SV39 = SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1029,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 != SV84 )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1030,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1031,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 = SV84 )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1032,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1033,plain,
! [SV44: list_a,SV99: nat,SV93: nat] :
( ( ( SV93 != SV99 )
= $false )
| ( ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SV99 ) )
= $true )
| ( ( ord_less_nat @ SV99 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1034,plain,
! [SV100: nat,SV44: list_a,SV111: nat] :
( ( ( ~ ( ord_less_nat @ SV111 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ~ ( ( SV100 != SV111 ) )
| ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SV111 ) ) )
= $true )
| ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1035,plain,
! [SV44: list_a,SV106: nat] :
( ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ! [SY239: nat] :
( ~ ( ord_less_nat @ SY239 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV106 != SY239 ) )
| ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SY239 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1036,plain,
! [SV44: list_a,SV115: nat] :
( ( ( ~ ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
| ! [SY247: nat] :
( ~ ( ord_less_nat @ SY247 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV115 != SY247 ) )
| ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SY247 ) ) ) )
= $true )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1037,plain,
! [SV44: list_a,SV112: nat] :
( ( ( ~ ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ! [SY243: nat] :
( ~ ( ord_less_nat @ SY243 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV112 != SY243 ) )
| ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SY243 ) ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1038,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( ord_less_nat @ ( sK12_SY221 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
= $true )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1039,plain,
! [SV87: list_a,SV47: a > $o] :
( ( ( SV47 @ ( nth_a @ SV87 @ ( sK12_SY221 @ SV47 @ SV87 ) ) )
= $true )
| ( ( list_ex_a @ SV47 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1040,plain,
! [SV94: nat,SV87: list_a,SV47: a > $o] :
( ( ( ~ ( list_ex_a @ SV47 @ SV87 ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1041,plain,
! [SV94: nat,SV47: a > $o,SV87: list_a] :
( ( ( ~ ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1042,plain,
! [SV48: list_list_a,SV101: nat,SV95: nat] :
( ( ( SV95 != SV101 )
= $false )
| ( ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SV101 ) )
= $true )
| ( ( ord_less_nat @ SV101 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1043,plain,
! [SV102: nat,SV48: list_list_a,SV113: nat] :
( ( ( ~ ( ord_less_nat @ SV113 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ~ ( ( SV102 != SV113 ) )
| ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SV113 ) ) )
= $true )
| ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1044,plain,
! [SV48: list_list_a,SV107: nat] :
( ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ! [SY240: nat] :
( ~ ( ord_less_nat @ SY240 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV107 != SY240 ) )
| ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SY240 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1045,plain,
! [SV48: list_list_a,SV116: nat] :
( ( ( ~ ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
| ! [SY248: nat] :
( ~ ( ord_less_nat @ SY248 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV116 != SY248 ) )
| ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SY248 ) ) ) )
= $true )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1046,plain,
! [SV48: list_list_a,SV114: nat] :
( ( ( ~ ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ! [SY244: nat] :
( ~ ( ord_less_nat @ SY244 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV114 != SY244 ) )
| ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SY244 ) ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1047,plain,
! [SV20: nat,SV103: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( SV51 @ SV103 @ ( sK21_SY235 @ SV20 @ SV103 @ SV51 ) ) )
= $false )
| ( ( ord_less_nat @ SV103 @ SV20 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1001]) ).
thf(1048,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ( size_s1427607542list_a @ ( sK15_SY195 @ SV51 @ SV20 ) )
!= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1049,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY237: nat] :
( ~ ( ord_less_nat @ SY237 @ SV20 )
| ( SV51 @ SY237 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SY237 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1050,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat,SV108: nat] :
( ( ( ord_less_nat @ SV108 @ SV20 )
= $false )
| ( ( ~ ! [SY241: list_a] :
~ ( SV51 @ SV108 @ SY241 ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1051,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV96: list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY245: nat] :
( ~ ( ord_less_nat @ SY245 @ SV20 )
| ( SV51 @ SY245 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SY245 ) ) ) ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1052,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) )
| ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1053,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1054,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1055,plain,
! [SV30: nat,SV104: nat,SV61: nat > a > $o] :
( ( ( ~ ( SV61 @ SV104 @ ( sK22_SY236 @ SV30 @ SV104 @ SV61 ) ) )
= $false )
| ( ( ord_less_nat @ SV104 @ SV30 )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1015]) ).
thf(1056,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ( size_size_list_a @ ( sK17_SY206 @ SV61 @ SV30 ) )
!= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1057,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY238: nat] :
( ~ ( ord_less_nat @ SY238 @ SV30 )
| ( SV61 @ SY238 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SY238 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1058,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat,SV109: nat] :
( ( ( ord_less_nat @ SV109 @ SV30 )
= $false )
| ( ( ~ ! [SY242: a] :
~ ( SV61 @ SV109 @ SY242 ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1059,plain,
! [SV30: nat,SV61: nat > a > $o,SV97: a] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY246: nat] :
( ~ ( ord_less_nat @ SY246 @ SV30 )
| ( SV61 @ SY246 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SY246 ) ) ) ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1060,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) )
| ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1061,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1062,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1063,plain,
! [SV88: list_list_a,SV62: list_list_a,SV110: nat] :
( ( ( ord_less_nat @ SV110 @ ( size_s1427607542list_a @ SV62 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ SV110 )
= ( nth_list_a @ SV88 @ SV110 ) )
= $true )
| ( ( SV62 = SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1064,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 != SV88 )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1065,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1066,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 = SV88 )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1067,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1068,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( ord_less_nat @ ( sK14_SY223 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
= $true )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1069,plain,
! [SV89: list_list_a,SV63: list_a > $o] :
( ( ( SV63 @ ( nth_list_a @ SV89 @ ( sK14_SY223 @ SV63 @ SV89 ) ) )
= $true )
| ( ( list_ex_list_a @ SV63 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1070,plain,
! [SV98: nat,SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( list_ex_list_a @ SV63 @ SV89 ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1071,plain,
! [SV98: nat,SV63: list_a > $o,SV89: list_list_a] :
( ( ( ~ ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1072,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( SV39 = SV84 )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1073,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1074,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1075,plain,
! [SV44: list_a,SV99: nat,SV93: nat] :
( ( ( SV93 = SV99 )
= $true )
| ( ( ( nth_a @ SV44 @ SV93 )
!= ( nth_a @ SV44 @ SV99 ) )
= $true )
| ( ( ord_less_nat @ SV99 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1076,plain,
! [SV100: nat,SV44: list_a,SV111: nat] :
( ( ( ord_less_nat @ SV111 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ~ ( ( SV100 != SV111 ) )
| ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SV111 ) ) )
= $true )
| ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1077,plain,
! [SV106: nat,SV44: list_a,SV117: nat] :
( ( ( ~ ( ord_less_nat @ SV117 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV106 != SV117 ) )
| ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SV117 ) ) )
= $true )
| ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1078,plain,
! [SV44: list_a,SV115: nat] :
( ( ( ~ ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ! [SY247: nat] :
( ~ ( ord_less_nat @ SY247 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV115 != SY247 ) )
| ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SY247 ) ) ) )
= $true )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1079,plain,
! [SV44: list_a,SV112: nat] :
( ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ! [SY243: nat] :
( ~ ( ord_less_nat @ SY243 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV112 != SY243 ) )
| ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SY243 ) ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1080,plain,
! [SV94: nat,SV87: list_a,SV47: a > $o] :
( ( ( list_ex_a @ SV47 @ SV87 )
= $true )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1081,plain,
! [SV94: nat,SV47: a > $o,SV87: list_a] :
( ( ( ~ ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1082,plain,
! [SV48: list_list_a,SV101: nat,SV95: nat] :
( ( ( SV95 = SV101 )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV95 )
!= ( nth_list_a @ SV48 @ SV101 ) )
= $true )
| ( ( ord_less_nat @ SV101 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1083,plain,
! [SV102: nat,SV48: list_list_a,SV113: nat] :
( ( ( ord_less_nat @ SV113 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ~ ( ( SV102 != SV113 ) )
| ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SV113 ) ) )
= $true )
| ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1084,plain,
! [SV107: nat,SV48: list_list_a,SV118: nat] :
( ( ( ~ ( ord_less_nat @ SV118 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV107 != SV118 ) )
| ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SV118 ) ) )
= $true )
| ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1085,plain,
! [SV48: list_list_a,SV116: nat] :
( ( ( ~ ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ! [SY248: nat] :
( ~ ( ord_less_nat @ SY248 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV116 != SY248 ) )
| ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SY248 ) ) ) )
= $true )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1086,plain,
! [SV48: list_list_a,SV114: nat] :
( ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ! [SY244: nat] :
( ~ ( ord_less_nat @ SY244 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV114 != SY244 ) )
| ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SY244 ) ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1087,plain,
! [SV20: nat,SV103: nat,SV51: nat > list_a > $o] :
( ( ( SV51 @ SV103 @ ( sK21_SY235 @ SV20 @ SV103 @ SV51 ) )
= $true )
| ( ( ord_less_nat @ SV103 @ SV20 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1088,plain,
! [SV20: nat,SV51: nat > list_a > $o] :
( ( ( ( size_s1427607542list_a @ ( sK15_SY195 @ SV51 @ SV20 ) )
= SV20 )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1089,plain,
! [SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY237: nat] :
( ~ ( ord_less_nat @ SY237 @ SV20 )
| ( SV51 @ SY237 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SY237 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1090,plain,
! [SV96: list_a,SV20: nat,SV108: nat,SV51: nat > list_a > $o] :
( ( ( ! [SY241: list_a] :
~ ( SV51 @ SV108 @ SY241 ) )
= $false )
| ( ( ord_less_nat @ SV108 @ SV20 )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1091,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV96: list_a] :
( ( ( ( ( size_s1427607542list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY245: nat] :
( ~ ( ord_less_nat @ SY245 @ SV20 )
| ( SV51 @ SY245 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SY245 ) ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1092,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1093,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1094,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1095,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1096,plain,
! [SV30: nat,SV104: nat,SV61: nat > a > $o] :
( ( ( SV61 @ SV104 @ ( sK22_SY236 @ SV30 @ SV104 @ SV61 ) )
= $true )
| ( ( ord_less_nat @ SV104 @ SV30 )
= $false )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1097,plain,
! [SV30: nat,SV61: nat > a > $o] :
( ( ( ( size_size_list_a @ ( sK17_SY206 @ SV61 @ SV30 ) )
= SV30 )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1098,plain,
! [SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY238: nat] :
( ~ ( ord_less_nat @ SY238 @ SV30 )
| ( SV61 @ SY238 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SY238 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1099,plain,
! [SV97: a,SV30: nat,SV109: nat,SV61: nat > a > $o] :
( ( ( ! [SY242: a] :
~ ( SV61 @ SV109 @ SY242 ) )
= $false )
| ( ( ord_less_nat @ SV109 @ SV30 )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1100,plain,
! [SV30: nat,SV61: nat > a > $o,SV97: a] :
( ( ( ( ( size_size_list_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY246: nat] :
( ~ ( ord_less_nat @ SY246 @ SV30 )
| ( SV61 @ SY246 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SY246 ) ) ) )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1101,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1102,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1103,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1104,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1105,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( SV62 = SV88 )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1106,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1107,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1108,plain,
! [SV98: nat,SV89: list_list_a,SV63: list_a > $o] :
( ( ( list_ex_list_a @ SV63 @ SV89 )
= $true )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1109,plain,
! [SV98: nat,SV63: list_a > $o,SV89: list_list_a] :
( ( ( ~ ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1110,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
| ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1111,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1112,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1113,plain,
! [SV99: nat,SV93: nat,SV44: list_a] :
( ( ( ( nth_a @ SV44 @ SV93 )
= ( nth_a @ SV44 @ SV99 ) )
= $false )
| ( ( SV93 = SV99 )
= $true )
| ( ( ord_less_nat @ SV99 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV93 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( distinct_a @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1114,plain,
! [SV44: list_a,SV111: nat,SV100: nat] :
( ( ( ~ ( ( SV100 != SV111 ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SV111 ) )
= $true )
| ( ( ord_less_nat @ SV111 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1115,plain,
! [SV106: nat,SV44: list_a,SV117: nat] :
( ( ( ~ ( ord_less_nat @ SV117 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ~ ( ( SV106 != SV117 ) )
| ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SV117 ) ) )
= $true )
| ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1116,plain,
! [SV44: list_a,SV115: nat] :
( ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ! [SY247: nat] :
( ~ ( ord_less_nat @ SY247 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV115 != SY247 ) )
| ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SY247 ) ) ) )
= $true )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1117,plain,
! [SV112: nat,SV44: list_a,SV119: nat] :
( ( ( ~ ( ord_less_nat @ SV119 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV112 != SV119 ) )
| ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SV119 ) ) )
= $true )
| ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1118,plain,
! [SV94: nat,SV47: a > $o,SV87: list_a] :
( ( ( ! [SY221: nat] :
~ ~ ( ~ ( ord_less_nat @ SY221 @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ SY221 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1119,plain,
! [SV101: nat,SV95: nat,SV48: list_list_a] :
( ( ( ( nth_list_a @ SV48 @ SV95 )
= ( nth_list_a @ SV48 @ SV101 ) )
= $false )
| ( ( SV95 = SV101 )
= $true )
| ( ( ord_less_nat @ SV101 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV95 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( distinct_list_a @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1120,plain,
! [SV48: list_list_a,SV113: nat,SV102: nat] :
( ( ( ~ ( ( SV102 != SV113 ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SV113 ) )
= $true )
| ( ( ord_less_nat @ SV113 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1121,plain,
! [SV107: nat,SV48: list_list_a,SV118: nat] :
( ( ( ~ ( ord_less_nat @ SV118 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ~ ( ( SV107 != SV118 ) )
| ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SV118 ) ) )
= $true )
| ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1122,plain,
! [SV48: list_list_a,SV116: nat] :
( ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ! [SY248: nat] :
( ~ ( ord_less_nat @ SY248 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV116 != SY248 ) )
| ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SY248 ) ) ) )
= $true )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1123,plain,
! [SV114: nat,SV48: list_list_a,SV120: nat] :
( ( ( ~ ( ord_less_nat @ SV120 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV114 != SV120 ) )
| ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SV120 ) ) )
= $true )
| ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1124,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV121: nat] :
( ( ( ~ ( ord_less_nat @ SV121 @ SV20 )
| ( SV51 @ SV121 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SV121 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1125,plain,
! [SV20: nat,SV96: list_a,SV108: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( SV51 @ SV108 @ ( sK23_SY241 @ SV96 @ SV20 @ SV108 @ SV51 ) ) )
= $false )
| ( ( ord_less_nat @ SV108 @ SV20 )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1090]) ).
thf(1126,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV96: list_a] :
( ( ( ( size_s1427607542list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) )
!= SV20 )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1127,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY245: nat] :
( ~ ( ord_less_nat @ SY245 @ SV20 )
| ( SV51 @ SY245 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SY245 ) ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1128,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY193: nat] :
( ~ ( ord_less_nat @ SY193 @ SV20 )
| ~ ! [SY194: list_a] :
~ ( SV51 @ SY193 @ SY194 ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1129,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1130,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV122: nat] :
( ( ( ~ ( ord_less_nat @ SV122 @ SV20 )
| ~ ! [SY249: list_a] :
~ ( SV51 @ SV122 @ SY249 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1131,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1132,plain,
! [SV61: nat > a > $o,SV30: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ SV123 @ SV30 )
| ( SV61 @ SV123 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SV123 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1133,plain,
! [SV30: nat,SV97: a,SV109: nat,SV61: nat > a > $o] :
( ( ( ~ ( SV61 @ SV109 @ ( sK24_SY242 @ SV97 @ SV30 @ SV109 @ SV61 ) ) )
= $false )
| ( ( ord_less_nat @ SV109 @ SV30 )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1099]) ).
thf(1134,plain,
! [SV30: nat,SV61: nat > a > $o,SV97: a] :
( ( ( ( size_size_list_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) )
!= SV30 )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1135,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY246: nat] :
( ~ ( ord_less_nat @ SY246 @ SV30 )
| ( SV61 @ SY246 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SY246 ) ) ) )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1136,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY204: nat] :
( ~ ( ord_less_nat @ SY204 @ SV30 )
| ~ ! [SY205: a] :
~ ( SV61 @ SY204 @ SY205 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1137,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1138,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV124: nat] :
( ( ( ~ ( ord_less_nat @ SV124 @ SV30 )
| ~ ! [SY250: a] :
~ ( SV61 @ SV124 @ SY250 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1139,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1140,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
| ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1141,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1142,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1143,plain,
! [SV98: nat,SV63: list_a > $o,SV89: list_list_a] :
( ( ( ! [SY223: nat] :
~ ~ ( ~ ( ord_less_nat @ SY223 @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ SY223 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1144,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
!= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1145,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ~ ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1146,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1147,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1148,plain,
! [SV44: list_a,SV111: nat,SV100: nat] :
( ( ( SV100 != SV111 )
= $false )
| ( ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SV111 ) )
= $true )
| ( ( ord_less_nat @ SV111 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1149,plain,
! [SV106: nat,SV44: list_a,SV117: nat] :
( ( ( ord_less_nat @ SV117 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ~ ( ( SV106 != SV117 ) )
| ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SV117 ) ) )
= $true )
| ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1150,plain,
! [SV115: nat,SV44: list_a,SV125: nat] :
( ( ( ~ ( ord_less_nat @ SV125 @ ( size_size_list_a @ SV44 ) )
| ~ ( ( SV115 != SV125 ) )
| ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SV125 ) ) )
= $true )
| ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1151,plain,
! [SV112: nat,SV44: list_a,SV119: nat] :
( ( ( ~ ( ord_less_nat @ SV119 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ~ ( ( SV112 != SV119 ) )
| ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SV119 ) ) )
= $true )
| ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1152,plain,
! [SV87: list_a,SV47: a > $o,SV94: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1118]) ).
thf(1153,plain,
! [SV48: list_list_a,SV113: nat,SV102: nat] :
( ( ( SV102 != SV113 )
= $false )
| ( ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SV113 ) )
= $true )
| ( ( ord_less_nat @ SV113 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1154,plain,
! [SV107: nat,SV48: list_list_a,SV118: nat] :
( ( ( ord_less_nat @ SV118 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ~ ( ( SV107 != SV118 ) )
| ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SV118 ) ) )
= $true )
| ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1155,plain,
! [SV116: nat,SV48: list_list_a,SV126: nat] :
( ( ( ~ ( ord_less_nat @ SV126 @ ( size_s1427607542list_a @ SV48 ) )
| ~ ( ( SV116 != SV126 ) )
| ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SV126 ) ) )
= $true )
| ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1156,plain,
! [SV114: nat,SV48: list_list_a,SV120: nat] :
( ( ( ~ ( ord_less_nat @ SV120 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ~ ( ( SV114 != SV120 ) )
| ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SV120 ) ) )
= $true )
| ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1157,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV121: nat] :
( ( ( ~ ( ord_less_nat @ SV121 @ SV20 ) )
= $true )
| ( ( SV51 @ SV121 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SV121 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1158,plain,
! [SV20: nat,SV96: list_a,SV108: nat,SV51: nat > list_a > $o] :
( ( ( SV51 @ SV108 @ ( sK23_SY241 @ SV96 @ SV20 @ SV108 @ SV51 ) )
= $true )
| ( ( ord_less_nat @ SV108 @ SV20 )
= $false )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1159,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV96: list_a] :
( ( ( ( size_s1427607542list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) )
= SV20 )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1160,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY245: nat] :
( ~ ( ord_less_nat @ SY245 @ SV20 )
| ( SV51 @ SY245 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SY245 ) ) ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1161,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ SV127 @ SV20 )
| ~ ! [SY251: list_a] :
~ ( SV51 @ SV127 @ SY251 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1162,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY195: list_list_a] :
~ ~ ( ( ( size_s1427607542list_a @ SY195 )
!= SV20 )
| ~ ! [SY196: nat] :
( ~ ( ord_less_nat @ SY196 @ SV20 )
| ( SV51 @ SY196 @ ( nth_list_a @ SY195 @ SY196 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1163,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV122: nat] :
( ( ( ~ ( ord_less_nat @ SV122 @ SV20 ) )
= $true )
| ( ( ~ ! [SY249: list_a] :
~ ( SV51 @ SV122 @ SY249 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1164,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ SV20 )
| ( SV51 @ SY252 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SY252 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1131]) ).
thf(1165,plain,
! [SV61: nat > a > $o,SV30: nat,SV123: nat] :
( ( ( ~ ( ord_less_nat @ SV123 @ SV30 ) )
= $true )
| ( ( SV61 @ SV123 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SV123 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1166,plain,
! [SV30: nat,SV97: a,SV109: nat,SV61: nat > a > $o] :
( ( ( SV61 @ SV109 @ ( sK24_SY242 @ SV97 @ SV30 @ SV109 @ SV61 ) )
= $true )
| ( ( ord_less_nat @ SV109 @ SV30 )
= $false )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1167,plain,
! [SV30: nat,SV61: nat > a > $o,SV97: a] :
( ( ( ( size_size_list_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) )
= SV30 )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1168,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY246: nat] :
( ~ ( ord_less_nat @ SY246 @ SV30 )
| ( SV61 @ SY246 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SY246 ) ) ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1169,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV128: nat] :
( ( ( ~ ( ord_less_nat @ SV128 @ SV30 )
| ~ ! [SY253: a] :
~ ( SV61 @ SV128 @ SY253 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1170,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY206: list_a] :
~ ~ ( ( ( size_size_list_a @ SY206 )
!= SV30 )
| ~ ! [SY207: nat] :
( ~ ( ord_less_nat @ SY207 @ SV30 )
| ( SV61 @ SY207 @ ( nth_a @ SY206 @ SY207 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1171,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV124: nat] :
( ( ( ~ ( ord_less_nat @ SV124 @ SV30 ) )
= $true )
| ( ( ~ ! [SY250: a] :
~ ( SV61 @ SV124 @ SY250 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1172,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY254: nat] :
( ~ ( ord_less_nat @ SY254 @ SV30 )
| ( SV61 @ SY254 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SY254 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1139]) ).
thf(1173,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
!= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1174,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ~ ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1175,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1176,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1177,plain,
! [SV89: list_list_a,SV63: list_a > $o,SV98: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1143]) ).
thf(1178,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1179,plain,
! [SV84: list_a,SV39: list_a] :
( ( ( ! [SY220: nat] :
( ~ ( ord_less_nat @ SY220 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SY220 )
= ( nth_a @ SV84 @ SY220 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1180,plain,
! [SV84: list_a,SV39: list_a,SV129: nat] :
( ( ( ~ ( ord_less_nat @ SV129 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SV129 )
= ( nth_a @ SV84 @ SV129 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1181,plain,
! [SV44: list_a,SV111: nat,SV100: nat] :
( ( ( SV100 = SV111 )
= $true )
| ( ( ( nth_a @ SV44 @ SV100 )
!= ( nth_a @ SV44 @ SV111 ) )
= $true )
| ( ( ord_less_nat @ SV111 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1182,plain,
! [SV44: list_a,SV117: nat,SV106: nat] :
( ( ( ~ ( ( SV106 != SV117 ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SV117 ) )
= $true )
| ( ( ord_less_nat @ SV117 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1183,plain,
! [SV115: nat,SV44: list_a,SV125: nat] :
( ( ( ~ ( ord_less_nat @ SV125 @ ( size_size_list_a @ SV44 ) ) )
= $true )
| ( ( ~ ( ( SV115 != SV125 ) )
| ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SV125 ) ) )
= $true )
| ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1184,plain,
! [SV112: nat,SV44: list_a,SV119: nat] :
( ( ( ord_less_nat @ SV119 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ~ ( ( SV112 != SV119 ) )
| ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SV119 ) ) )
= $true )
| ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1185,plain,
! [SV87: list_a,SV47: a > $o,SV94: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1186,plain,
! [SV48: list_list_a,SV113: nat,SV102: nat] :
( ( ( SV102 = SV113 )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV102 )
!= ( nth_list_a @ SV48 @ SV113 ) )
= $true )
| ( ( ord_less_nat @ SV113 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1187,plain,
! [SV48: list_list_a,SV118: nat,SV107: nat] :
( ( ( ~ ( ( SV107 != SV118 ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SV118 ) )
= $true )
| ( ( ord_less_nat @ SV118 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1188,plain,
! [SV116: nat,SV48: list_list_a,SV126: nat] :
( ( ( ~ ( ord_less_nat @ SV126 @ ( size_s1427607542list_a @ SV48 ) ) )
= $true )
| ( ( ~ ( ( SV116 != SV126 ) )
| ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SV126 ) ) )
= $true )
| ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1189,plain,
! [SV114: nat,SV48: list_list_a,SV120: nat] :
( ( ( ord_less_nat @ SV120 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ~ ( ( SV114 != SV120 ) )
| ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SV120 ) ) )
= $true )
| ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1190,plain,
! [SV51: nat > list_a > $o,SV20: nat,SV121: nat] :
( ( ( ord_less_nat @ SV121 @ SV20 )
= $false )
| ( ( SV51 @ SV121 @ ( nth_list_a @ ( sK15_SY195 @ SV51 @ SV20 ) @ SV121 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1191,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat,SV130: nat] :
( ( ( ~ ( ord_less_nat @ SV130 @ SV20 )
| ( SV51 @ SV130 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SV130 ) ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1192,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ SV127 @ SV20 ) )
= $true )
| ( ( ~ ! [SY251: list_a] :
~ ( SV51 @ SV127 @ SY251 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1193,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ~ ~ ( ( ( size_s1427607542list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY255: nat] :
( ~ ( ord_less_nat @ SY255 @ SV20 )
| ( SV51 @ SY255 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SY255 ) ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1162]) ).
thf(1194,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV122: nat] :
( ( ( ord_less_nat @ SV122 @ SV20 )
= $false )
| ( ( ~ ! [SY249: list_a] :
~ ( SV51 @ SV122 @ SY249 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1195,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ SV20 )
| ( SV51 @ SY252 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SY252 ) ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1196,plain,
! [SV61: nat > a > $o,SV30: nat,SV123: nat] :
( ( ( ord_less_nat @ SV123 @ SV30 )
= $false )
| ( ( SV61 @ SV123 @ ( nth_a @ ( sK17_SY206 @ SV61 @ SV30 ) @ SV123 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1197,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat,SV131: nat] :
( ( ( ~ ( ord_less_nat @ SV131 @ SV30 )
| ( SV61 @ SV131 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SV131 ) ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1198,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV128: nat] :
( ( ( ~ ( ord_less_nat @ SV128 @ SV30 ) )
= $true )
| ( ( ~ ! [SY253: a] :
~ ( SV61 @ SV128 @ SY253 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1199,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY256: nat] :
( ~ ( ord_less_nat @ SY256 @ SV30 )
| ( SV61 @ SY256 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SY256 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1170]) ).
thf(1200,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV124: nat] :
( ( ( ord_less_nat @ SV124 @ SV30 )
= $false )
| ( ( ~ ! [SY250: a] :
~ ( SV61 @ SV124 @ SY250 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1201,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY254: nat] :
( ~ ( ord_less_nat @ SY254 @ SV30 )
| ( SV61 @ SY254 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SY254 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1202,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1203,plain,
! [SV88: list_list_a,SV62: list_list_a] :
( ( ( ! [SY222: nat] :
( ~ ( ord_less_nat @ SY222 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SY222 )
= ( nth_list_a @ SV88 @ SY222 ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1204,plain,
! [SV88: list_list_a,SV62: list_list_a,SV132: nat] :
( ( ( ~ ( ord_less_nat @ SV132 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SV132 )
= ( nth_list_a @ SV88 @ SV132 ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1205,plain,
! [SV89: list_list_a,SV63: list_a > $o,SV98: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1206,plain,
! [SV84: list_a,SV39: list_a,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( size_size_list_a @ SV39 ) )
| ( ( nth_a @ SV39 @ SV133 )
= ( nth_a @ SV84 @ SV133 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1207,plain,
! [SV84: list_a,SV39: list_a,SV129: nat] :
( ( ( ~ ( ord_less_nat @ SV129 @ ( size_size_list_a @ SV39 ) ) )
= $true )
| ( ( ( nth_a @ SV39 @ SV129 )
= ( nth_a @ SV84 @ SV129 ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1208,plain,
! [SV111: nat,SV100: nat,SV44: list_a] :
( ( ( ( nth_a @ SV44 @ SV100 )
= ( nth_a @ SV44 @ SV111 ) )
= $false )
| ( ( SV100 = SV111 )
= $true )
| ( ( ord_less_nat @ SV111 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV100 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK3_SY182 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1209,plain,
! [SV44: list_a,SV117: nat,SV106: nat] :
( ( ( SV106 != SV117 )
= $false )
| ( ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SV117 ) )
= $true )
| ( ( ord_less_nat @ SV117 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1210,plain,
! [SV115: nat,SV44: list_a,SV125: nat] :
( ( ( ord_less_nat @ SV125 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ~ ( ( SV115 != SV125 ) )
| ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SV125 ) ) )
= $true )
| ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1211,plain,
! [SV44: list_a,SV119: nat,SV112: nat] :
( ( ( ~ ( ( SV112 != SV119 ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SV119 ) )
= $true )
| ( ( ord_less_nat @ SV119 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1212,plain,
! [SV87: list_a,SV47: a > $o,SV94: nat] :
( ( ( ~ ( ord_less_nat @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
| ~ ( SV47 @ ( nth_a @ SV87 @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1213,plain,
! [SV113: nat,SV102: nat,SV48: list_list_a] :
( ( ( ( nth_list_a @ SV48 @ SV102 )
= ( nth_list_a @ SV48 @ SV113 ) )
= $false )
| ( ( SV102 = SV113 )
= $true )
| ( ( ord_less_nat @ SV113 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV102 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK4_SY189 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1214,plain,
! [SV48: list_list_a,SV118: nat,SV107: nat] :
( ( ( SV107 != SV118 )
= $false )
| ( ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SV118 ) )
= $true )
| ( ( ord_less_nat @ SV118 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1215,plain,
! [SV116: nat,SV48: list_list_a,SV126: nat] :
( ( ( ord_less_nat @ SV126 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ~ ( ( SV116 != SV126 ) )
| ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SV126 ) ) )
= $true )
| ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1216,plain,
! [SV48: list_list_a,SV120: nat,SV114: nat] :
( ( ( ~ ( ( SV114 != SV120 ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SV120 ) )
= $true )
| ( ( ord_less_nat @ SV120 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1217,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat,SV130: nat] :
( ( ( ~ ( ord_less_nat @ SV130 @ SV20 ) )
= $true )
| ( ( SV51 @ SV130 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SV130 ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1218,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV127: nat] :
( ( ( ord_less_nat @ SV127 @ SV20 )
= $false )
| ( ( ~ ! [SY251: list_a] :
~ ( SV51 @ SV127 @ SY251 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1219,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ~ ( ( ( size_s1427607542list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY255: nat] :
( ~ ( ord_less_nat @ SY255 @ SV20 )
| ( SV51 @ SY255 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SY255 ) ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1220,plain,
! [SV90: list_list_a,SV20: nat,SV122: nat,SV51: nat > list_a > $o] :
( ( ( ! [SY249: list_a] :
~ ( SV51 @ SV122 @ SY249 ) )
= $false )
| ( ( ord_less_nat @ SV122 @ SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1221,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ SV20 )
| ( SV51 @ SY252 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SY252 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1222,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat,SV131: nat] :
( ( ( ~ ( ord_less_nat @ SV131 @ SV30 ) )
= $true )
| ( ( SV61 @ SV131 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SV131 ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1223,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV128: nat] :
( ( ( ord_less_nat @ SV128 @ SV30 )
= $false )
| ( ( ~ ! [SY253: a] :
~ ( SV61 @ SV128 @ SY253 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1224,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY256: nat] :
( ~ ( ord_less_nat @ SY256 @ SV30 )
| ( SV61 @ SY256 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SY256 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1225,plain,
! [SV92: list_a,SV30: nat,SV124: nat,SV61: nat > a > $o] :
( ( ( ! [SY250: a] :
~ ( SV61 @ SV124 @ SY250 ) )
= $false )
| ( ( ord_less_nat @ SV124 @ SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1226,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ( ( size_size_list_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY254: nat] :
( ~ ( ord_less_nat @ SY254 @ SV30 )
| ( SV61 @ SY254 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SY254 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1227,plain,
! [SV88: list_list_a,SV62: list_list_a,SV134: nat] :
( ( ( ~ ( ord_less_nat @ SV134 @ ( size_s1427607542list_a @ SV62 ) )
| ( ( nth_list_a @ SV62 @ SV134 )
= ( nth_list_a @ SV88 @ SV134 ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1228,plain,
! [SV88: list_list_a,SV62: list_list_a,SV132: nat] :
( ( ( ~ ( ord_less_nat @ SV132 @ ( size_s1427607542list_a @ SV62 ) ) )
= $true )
| ( ( ( nth_list_a @ SV62 @ SV132 )
= ( nth_list_a @ SV88 @ SV132 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1229,plain,
! [SV89: list_list_a,SV63: list_a > $o,SV98: nat] :
( ( ( ~ ( ord_less_nat @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
| ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1230,plain,
! [SV84: list_a,SV39: list_a,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( size_size_list_a @ SV39 ) ) )
= $true )
| ( ( ( nth_a @ SV39 @ SV133 )
= ( nth_a @ SV84 @ SV133 ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1231,plain,
! [SV84: list_a,SV39: list_a,SV129: nat] :
( ( ( ord_less_nat @ SV129 @ ( size_size_list_a @ SV39 ) )
= $false )
| ( ( ( nth_a @ SV39 @ SV129 )
= ( nth_a @ SV84 @ SV129 ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ( nth_a @ SV39 @ ( sK11_SY220 @ SV84 @ SV39 ) )
= ( nth_a @ SV84 @ ( sK11_SY220 @ SV84 @ SV39 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1232,plain,
! [SV44: list_a,SV117: nat,SV106: nat] :
( ( ( SV106 = SV117 )
= $true )
| ( ( ( nth_a @ SV44 @ SV106 )
!= ( nth_a @ SV44 @ SV117 ) )
= $true )
| ( ( ord_less_nat @ SV117 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1233,plain,
! [SV44: list_a,SV125: nat,SV115: nat] :
( ( ( ~ ( ( SV115 != SV125 ) ) )
= $true )
| ( ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SV125 ) )
= $true )
| ( ( ord_less_nat @ SV125 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1234,plain,
! [SV44: list_a,SV119: nat,SV112: nat] :
( ( ( SV112 != SV119 )
= $false )
| ( ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SV119 ) )
= $true )
| ( ( ord_less_nat @ SV119 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1235,plain,
! [SV87: list_a,SV47: a > $o,SV94: nat] :
( ( ( ~ ( ord_less_nat @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1236,plain,
! [SV94: nat,SV87: list_a,SV47: a > $o] :
( ( ( ~ ( SV47 @ ( nth_a @ SV87 @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1237,plain,
! [SV48: list_list_a,SV118: nat,SV107: nat] :
( ( ( SV107 = SV118 )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV107 )
!= ( nth_list_a @ SV48 @ SV118 ) )
= $true )
| ( ( ord_less_nat @ SV118 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1238,plain,
! [SV48: list_list_a,SV126: nat,SV116: nat] :
( ( ( ~ ( ( SV116 != SV126 ) ) )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SV126 ) )
= $true )
| ( ( ord_less_nat @ SV126 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1239,plain,
! [SV48: list_list_a,SV120: nat,SV114: nat] :
( ( ( SV114 != SV120 )
= $false )
| ( ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SV120 ) )
= $true )
| ( ( ord_less_nat @ SV120 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1240,plain,
! [SV96: list_a,SV51: nat > list_a > $o,SV20: nat,SV130: nat] :
( ( ( ord_less_nat @ SV130 @ SV20 )
= $false )
| ( ( SV51 @ SV130 @ ( nth_list_a @ ( sK19_SY195 @ SV96 @ SV51 @ SV20 ) @ SV130 ) )
= $true )
| ( ( SV51 @ ( sK6_SY193 @ SV51 @ SV20 ) @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1241,plain,
! [SV90: list_list_a,SV20: nat,SV127: nat,SV51: nat > list_a > $o] :
( ( ( ! [SY251: list_a] :
~ ( SV51 @ SV127 @ SY251 ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1242,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ( ( size_s1427607542list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
| ~ ! [SY255: nat] :
( ~ ( ord_less_nat @ SY255 @ SV20 )
| ( SV51 @ SY255 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SY255 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1243,plain,
! [SV20: nat,SV90: list_list_a,SV122: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( SV51 @ SV122 @ ( sK31_SY249 @ SV90 @ SV20 @ SV122 @ SV51 ) ) )
= $false )
| ( ( ord_less_nat @ SV122 @ SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1220]) ).
thf(1244,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ( size_s1427607542list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1245,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ SV20 )
| ( SV51 @ SY252 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SY252 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1246,plain,
! [SV97: a,SV61: nat > a > $o,SV30: nat,SV131: nat] :
( ( ( ord_less_nat @ SV131 @ SV30 )
= $false )
| ( ( SV61 @ SV131 @ ( nth_a @ ( sK20_SY206 @ SV97 @ SV61 @ SV30 ) @ SV131 ) )
= $true )
| ( ( SV61 @ ( sK8_SY204 @ SV61 @ SV30 ) @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1247,plain,
! [SV92: list_a,SV30: nat,SV128: nat,SV61: nat > a > $o] :
( ( ( ! [SY253: a] :
~ ( SV61 @ SV128 @ SY253 ) )
= $false )
| ( ( ord_less_nat @ SV128 @ SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1248,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ( ( size_size_list_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
| ~ ! [SY256: nat] :
( ~ ( ord_less_nat @ SY256 @ SV30 )
| ( SV61 @ SY256 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SY256 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1249,plain,
! [SV30: nat,SV92: list_a,SV124: nat,SV61: nat > a > $o] :
( ( ( ~ ( SV61 @ SV124 @ ( sK32_SY250 @ SV92 @ SV30 @ SV124 @ SV61 ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1225]) ).
thf(1250,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ( size_size_list_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1251,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY254: nat] :
( ~ ( ord_less_nat @ SY254 @ SV30 )
| ( SV61 @ SY254 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SY254 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1252,plain,
! [SV88: list_list_a,SV62: list_list_a,SV134: nat] :
( ( ( ~ ( ord_less_nat @ SV134 @ ( size_s1427607542list_a @ SV62 ) ) )
= $true )
| ( ( ( nth_list_a @ SV62 @ SV134 )
= ( nth_list_a @ SV88 @ SV134 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1253,plain,
! [SV88: list_list_a,SV62: list_list_a,SV132: nat] :
( ( ( ord_less_nat @ SV132 @ ( size_s1427607542list_a @ SV62 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ SV132 )
= ( nth_list_a @ SV88 @ SV132 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ ( sK13_SY222 @ SV88 @ SV62 ) )
= ( nth_list_a @ SV88 @ ( sK13_SY222 @ SV88 @ SV62 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1254,plain,
! [SV89: list_list_a,SV63: list_a > $o,SV98: nat] :
( ( ( ~ ( ord_less_nat @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1255,plain,
! [SV98: nat,SV89: list_list_a,SV63: list_a > $o] :
( ( ( ~ ( SV63 @ ( nth_list_a @ SV89 @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1256,plain,
! [SV84: list_a,SV39: list_a,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( size_size_list_a @ SV39 ) )
= $false )
| ( ( ( nth_a @ SV39 @ SV133 )
= ( nth_a @ SV84 @ SV133 ) )
= $true )
| ( ( ( size_size_list_a @ SV39 )
= ( size_size_list_a @ SV84 ) )
= $false )
| ( ( ord_less_nat @ ( sK11_SY220 @ SV84 @ SV39 ) @ ( size_size_list_a @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1257,plain,
! [SV117: nat,SV106: nat,SV44: list_a] :
( ( ( ( nth_a @ SV44 @ SV106 )
= ( nth_a @ SV44 @ SV117 ) )
= $false )
| ( ( SV106 = SV117 )
= $true )
| ( ( ord_less_nat @ SV117 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV106 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ ( sK9_SY225 @ SV44 ) @ ( size_size_list_a @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1258,plain,
! [SV44: list_a,SV125: nat,SV115: nat] :
( ( ( SV115 != SV125 )
= $false )
| ( ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SV125 ) )
= $true )
| ( ( ord_less_nat @ SV125 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1259,plain,
! [SV44: list_a,SV119: nat,SV112: nat] :
( ( ( SV112 = SV119 )
= $true )
| ( ( ( nth_a @ SV44 @ SV112 )
!= ( nth_a @ SV44 @ SV119 ) )
= $true )
| ( ( ord_less_nat @ SV119 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1260,plain,
! [SV87: list_a,SV47: a > $o,SV94: nat] :
( ( ( ord_less_nat @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) @ ( size_size_list_a @ SV87 ) )
= $true )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1261,plain,
! [SV94: nat,SV87: list_a,SV47: a > $o] :
( ( ( SV47 @ ( nth_a @ SV87 @ ( sK25_SY221 @ SV94 @ SV47 @ SV87 ) ) )
= $true )
| ( ( ord_less_nat @ SV94 @ ( size_size_list_a @ SV87 ) )
= $false )
| ( ( SV47 @ ( nth_a @ SV87 @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1262,plain,
! [SV118: nat,SV107: nat,SV48: list_list_a] :
( ( ( ( nth_list_a @ SV48 @ SV107 )
= ( nth_list_a @ SV48 @ SV118 ) )
= $false )
| ( ( SV107 = SV118 )
= $true )
| ( ( ord_less_nat @ SV118 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV107 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY226 @ SV48 ) @ ( size_s1427607542list_a @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1263,plain,
! [SV48: list_list_a,SV126: nat,SV116: nat] :
( ( ( SV116 != SV126 )
= $false )
| ( ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SV126 ) )
= $true )
| ( ( ord_less_nat @ SV126 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1264,plain,
! [SV48: list_list_a,SV120: nat,SV114: nat] :
( ( ( SV114 = SV120 )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV114 )
!= ( nth_list_a @ SV48 @ SV120 ) )
= $true )
| ( ( ord_less_nat @ SV120 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1239]) ).
thf(1265,plain,
! [SV20: nat,SV90: list_list_a,SV127: nat,SV51: nat > list_a > $o] :
( ( ( ~ ( SV51 @ SV127 @ ( sK33_SY251 @ SV90 @ SV20 @ SV127 @ SV51 ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1241]) ).
thf(1266,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ( size_s1427607542list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) )
!= SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1267,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ~ ! [SY255: nat] :
( ~ ( ord_less_nat @ SY255 @ SV20 )
| ( SV51 @ SY255 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SY255 ) ) ) )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1268,plain,
! [SV20: nat,SV90: list_list_a,SV122: nat,SV51: nat > list_a > $o] :
( ( ( SV51 @ SV122 @ ( sK31_SY249 @ SV90 @ SV20 @ SV122 @ SV51 ) )
= $true )
| ( ( ord_less_nat @ SV122 @ SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1269,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ( size_s1427607542list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) )
= SV20 )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1270,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY252: nat] :
( ~ ( ord_less_nat @ SY252 @ SV20 )
| ( SV51 @ SY252 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SY252 ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1271,plain,
! [SV30: nat,SV92: list_a,SV128: nat,SV61: nat > a > $o] :
( ( ( ~ ( SV61 @ SV128 @ ( sK34_SY253 @ SV92 @ SV30 @ SV128 @ SV61 ) ) )
= $false )
| ( ( ord_less_nat @ SV128 @ SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1247]) ).
thf(1272,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ( size_size_list_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) )
!= SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1273,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ~ ! [SY256: nat] :
( ~ ( ord_less_nat @ SY256 @ SV30 )
| ( SV61 @ SY256 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SY256 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1274,plain,
! [SV30: nat,SV92: list_a,SV124: nat,SV61: nat > a > $o] :
( ( ( SV61 @ SV124 @ ( sK32_SY250 @ SV92 @ SV30 @ SV124 @ SV61 ) )
= $true )
| ( ( ord_less_nat @ SV124 @ SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1275,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ( size_size_list_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) )
= SV30 )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1276,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY254: nat] :
( ~ ( ord_less_nat @ SY254 @ SV30 )
| ( SV61 @ SY254 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SY254 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1277,plain,
! [SV88: list_list_a,SV62: list_list_a,SV134: nat] :
( ( ( ord_less_nat @ SV134 @ ( size_s1427607542list_a @ SV62 ) )
= $false )
| ( ( ( nth_list_a @ SV62 @ SV134 )
= ( nth_list_a @ SV88 @ SV134 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV62 )
= ( size_s1427607542list_a @ SV88 ) )
= $false )
| ( ( ord_less_nat @ ( sK13_SY222 @ SV88 @ SV62 ) @ ( size_s1427607542list_a @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1278,plain,
! [SV89: list_list_a,SV63: list_a > $o,SV98: nat] :
( ( ( ord_less_nat @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) @ ( size_s1427607542list_a @ SV89 ) )
= $true )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1279,plain,
! [SV98: nat,SV89: list_list_a,SV63: list_a > $o] :
( ( ( SV63 @ ( nth_list_a @ SV89 @ ( sK28_SY223 @ SV98 @ SV63 @ SV89 ) ) )
= $true )
| ( ( ord_less_nat @ SV98 @ ( size_s1427607542list_a @ SV89 ) )
= $false )
| ( ( SV63 @ ( nth_list_a @ SV89 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1280,plain,
! [SV44: list_a,SV125: nat,SV115: nat] :
( ( ( SV115 = SV125 )
= $true )
| ( ( ( nth_a @ SV44 @ SV115 )
!= ( nth_a @ SV44 @ SV125 ) )
= $true )
| ( ( ord_less_nat @ SV125 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1281,plain,
! [SV119: nat,SV112: nat,SV44: list_a] :
( ( ( ( nth_a @ SV44 @ SV112 )
= ( nth_a @ SV44 @ SV119 ) )
= $false )
| ( ( SV112 = SV119 )
= $true )
| ( ( ord_less_nat @ SV119 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV112 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( nth_a @ SV44 @ ( sK3_SY182 @ SV44 ) )
= ( nth_a @ SV44 @ ( sK9_SY225 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1282,plain,
! [SV48: list_list_a,SV126: nat,SV116: nat] :
( ( ( SV116 = SV126 )
= $true )
| ( ( ( nth_list_a @ SV48 @ SV116 )
!= ( nth_list_a @ SV48 @ SV126 ) )
= $true )
| ( ( ord_less_nat @ SV126 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1283,plain,
! [SV120: nat,SV114: nat,SV48: list_list_a] :
( ( ( ( nth_list_a @ SV48 @ SV114 )
= ( nth_list_a @ SV48 @ SV120 ) )
= $false )
| ( ( SV114 = SV120 )
= $true )
| ( ( ord_less_nat @ SV120 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV114 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( nth_list_a @ SV48 @ ( sK4_SY189 @ SV48 ) )
= ( nth_list_a @ SV48 @ ( sK10_SY226 @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1284,plain,
! [SV20: nat,SV90: list_list_a,SV127: nat,SV51: nat > list_a > $o] :
( ( ( SV51 @ SV127 @ ( sK33_SY251 @ SV90 @ SV20 @ SV127 @ SV51 ) )
= $true )
| ( ( ord_less_nat @ SV127 @ SV20 )
= $false )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1285,plain,
! [SV20: nat,SV51: nat > list_a > $o,SV90: list_list_a] :
( ( ( ( size_s1427607542list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) )
= SV20 )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1286,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat] :
( ( ( ! [SY255: nat] :
( ~ ( ord_less_nat @ SY255 @ SV20 )
| ( SV51 @ SY255 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SY255 ) ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1287,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ SV135 @ SV20 )
| ( SV51 @ SV135 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SV135 ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1288,plain,
! [SV30: nat,SV92: list_a,SV128: nat,SV61: nat > a > $o] :
( ( ( SV61 @ SV128 @ ( sK34_SY253 @ SV92 @ SV30 @ SV128 @ SV61 ) )
= $true )
| ( ( ord_less_nat @ SV128 @ SV30 )
= $false )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1289,plain,
! [SV30: nat,SV61: nat > a > $o,SV92: list_a] :
( ( ( ( size_size_list_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) )
= SV30 )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1290,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat] :
( ( ( ! [SY256: nat] :
( ~ ( ord_less_nat @ SY256 @ SV30 )
| ( SV61 @ SY256 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SY256 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1291,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ SV136 @ SV30 )
| ( SV61 @ SV136 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SV136 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1292,plain,
! [SV125: nat,SV115: nat,SV44: list_a] :
( ( ( ( nth_a @ SV44 @ SV115 )
= ( nth_a @ SV44 @ SV125 ) )
= $false )
| ( ( SV115 = SV125 )
= $true )
| ( ( ord_less_nat @ SV125 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ord_less_nat @ SV115 @ ( size_size_list_a @ SV44 ) )
= $false )
| ( ( ( sK3_SY182 @ SV44 )
= ( sK9_SY225 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1293,plain,
! [SV126: nat,SV116: nat,SV48: list_list_a] :
( ( ( ( nth_list_a @ SV48 @ SV116 )
= ( nth_list_a @ SV48 @ SV126 ) )
= $false )
| ( ( SV116 = SV126 )
= $true )
| ( ( ord_less_nat @ SV126 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ord_less_nat @ SV116 @ ( size_s1427607542list_a @ SV48 ) )
= $false )
| ( ( ( sK4_SY189 @ SV48 )
= ( sK10_SY226 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1294,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV137: nat] :
( ( ( ~ ( ord_less_nat @ SV137 @ SV20 )
| ( SV51 @ SV137 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SV137 ) ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1295,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ SV135 @ SV20 ) )
= $true )
| ( ( SV51 @ SV135 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SV135 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1296,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV138: nat] :
( ( ( ~ ( ord_less_nat @ SV138 @ SV30 )
| ( SV61 @ SV138 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SV138 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1297,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ SV136 @ SV30 ) )
= $true )
| ( ( SV61 @ SV136 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SV136 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1298,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV137: nat] :
( ( ( ~ ( ord_less_nat @ SV137 @ SV20 ) )
= $true )
| ( ( SV51 @ SV137 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SV137 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1299,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV135: nat] :
( ( ( ord_less_nat @ SV135 @ SV20 )
= $false )
| ( ( SV51 @ SV135 @ ( nth_list_a @ ( sK26_SY195 @ SV90 @ SV51 @ SV20 ) @ SV135 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( SV51 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ ( nth_list_a @ SV90 @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1300,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV138: nat] :
( ( ( ~ ( ord_less_nat @ SV138 @ SV30 ) )
= $true )
| ( ( SV61 @ SV138 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SV138 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1301,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV136: nat] :
( ( ( ord_less_nat @ SV136 @ SV30 )
= $false )
| ( ( SV61 @ SV136 @ ( nth_a @ ( sK27_SY206 @ SV92 @ SV61 @ SV30 ) @ SV136 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( SV61 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ ( nth_a @ SV92 @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1302,plain,
! [SV90: list_list_a,SV51: nat > list_a > $o,SV20: nat,SV137: nat] :
( ( ( ord_less_nat @ SV137 @ SV20 )
= $false )
| ( ( SV51 @ SV137 @ ( nth_list_a @ ( sK29_SY195 @ SV90 @ SV51 @ SV20 ) @ SV137 ) )
= $true )
| ( ( ( size_s1427607542list_a @ SV90 )
= SV20 )
= $false )
| ( ( ord_less_nat @ ( sK16_SY229 @ SV90 @ SV51 @ SV20 ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1303,plain,
! [SV92: list_a,SV61: nat > a > $o,SV30: nat,SV138: nat] :
( ( ( ord_less_nat @ SV138 @ SV30 )
= $false )
| ( ( SV61 @ SV138 @ ( nth_a @ ( sK30_SY206 @ SV92 @ SV61 @ SV30 ) @ SV138 ) )
= $true )
| ( ( ( size_size_list_a @ SV92 )
= SV30 )
= $false )
| ( ( ord_less_nat @ ( sK18_SY230 @ SV92 @ SV61 @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1304,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[387,1303,1302,1301,1299,1293,1292,1289,1288,1285,1284,1283,1281,1279,1278,1277,1275,1274,1269,1268,1262,1261,1260,1257,1256,1253,1246,1240,1231,1213,1208,1202,1196,1190,1178,1175,1167,1166,1159,1158,1146,1119,1113,1108,1105,1097,1096,1088,1087,1080,1072,1069,1068,1066,1063,1039,1038,1031,1028,1014,1013,1012,1011,1010,1009,1008,1007,998,989,955,946,932,913,904,898,847,846,845,844,839,835,830,828,827,826,825,824,819,816,793,791,779,776,766,764,763,728,722,716,708,693,686,645,638,635,634,630,622,617,615,612,605,600,597,594,593,591,578,566,561,560,559,557,555,544,540,538,534,527,523,522,492,489,488,486,471,469,465,458,454,451]) ).
thf(1305,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP104^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.20 % Computer : n016.cluster.edu
% 0.13/0.20 % Model : x86_64 x86_64
% 0.13/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.20 % Memory : 8046.5625MB
% 0.13/0.20 % OS : Linux 6.8.0-71-generic
% 0.13/0.20 % CPULimit : 300
% 0.13/0.20 % WCLimit : 300
% 0.13/0.20 % DateTime : Tue Oct 6 11:22:29 UTC 2026
% 0.13/0.20 % CPUTime :
% 0.13/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.78/2.54 ..
% 13.78/2.54
% 13.78/2.54 No.of.Axioms: 33
% 13.78/2.54
% 13.78/2.54 Length.of.Defs: 0
% 13.78/2.54
% 13.78/2.54 Contains.Choice.Funs: false
% 13.78/2.54 .............................
% 13.78/2.54
% 13.78/2.54 ********************************
% 13.78/2.54 * All subproblems solved! *
% 13.78/2.54 ********************************
% 13.78/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:33,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1304,loop_count:0,foatp_calls:1,translation:fof_full)
% 13.78/2.54
% 13.78/2.54 %**** Beginning of derivation protocol ****
% 13.78/2.54 % SZS output start CNFRefutation
% See solution above
% 13.78/2.56
% 13.78/2.56 %**** End of derivation protocol ****
% 13.78/2.56 %**** no. of clauses in derivation: 989 ****
% 13.78/2.56 %**** clause counter: 1304 ****
% 13.78/2.56
% 13.78/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:33,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1304,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------