%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP078^1 : 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 : n008.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 10:24:01 AM UTC 2026
% Result : Theorem 152.05s 25.65s
% Output : CNFRefutation 152.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 94
% Syntax : Number of formulae : 1654 ( 541 unt; 0 typ; 0 def)
% Number of atoms : 11755 (5523 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 16343 (3733 ~;3316 |; 30 &;9141 @)
% ( 0 <=>; 123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 775 ( 775 >; 0 *; 0 +; 0 <<)
% Number of symbols : 126 ( 123 usr; 9 con; 0-4 aty)
% Number of variables : 3480 ( 39 ^;3420 !; 21 ?;3480 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_int,type,
int: $tType ).
thf(tp_list_a,type,
list_a: $tType ).
thf(tp_list_nat,type,
list_nat: $tType ).
thf(tp_multiset_a,type,
multiset_a: $tType ).
thf(tp_multiset_int,type,
multiset_int: $tType ).
thf(tp_multiset_nat,type,
multiset_nat: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_set_int,type,
set_int: $tType ).
thf(tp_set_list_a,type,
set_list_a: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_real,type,
set_real: $tType ).
thf(tp_bij_betw_nat_a,type,
bij_betw_nat_a: ( nat > a ) > set_nat > set_a > $o ).
thf(tp_bij_betw_nat_int,type,
bij_betw_nat_int: ( nat > int ) > set_nat > set_int > $o ).
thf(tp_bij_betw_nat_nat,type,
bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
thf(tp_bij_betw_nat_real,type,
bij_betw_nat_real: ( nat > real ) > set_nat > set_real > $o ).
thf(tp_comp_a_a_nat,type,
comp_a_a_nat: ( a > a ) > ( nat > a ) > nat > a ).
thf(tp_comp_a_nat_nat,type,
comp_a_nat_nat: ( a > nat ) > ( nat > a ) > nat > nat ).
thf(tp_comp_int_int_nat,type,
comp_int_int_nat: ( int > int ) > ( nat > int ) > nat > int ).
thf(tp_comp_int_nat_nat,type,
comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
thf(tp_comp_l1234327363st_nat,type,
comp_l1234327363st_nat: ( list_a > list_a ) > ( list_nat > list_a ) > list_nat > list_a ).
thf(tp_comp_l728830689st_nat,type,
comp_l728830689st_nat: ( list_nat > list_a ) > ( list_nat > list_nat ) > list_nat > list_a ).
thf(tp_comp_m1386984005et_nat,type,
comp_m1386984005et_nat: ( multiset_nat > multiset_nat ) > ( multiset_nat > multiset_nat ) > multiset_nat > multiset_nat ).
thf(tp_comp_m1512105363et_nat,type,
comp_m1512105363et_nat: ( multiset_a > nat ) > ( multiset_nat > multiset_a ) > multiset_nat > nat ).
thf(tp_comp_m1844659105et_nat,type,
comp_m1844659105et_nat: ( multiset_nat > multiset_a ) > ( multiset_nat > multiset_nat ) > multiset_nat > multiset_a ).
thf(tp_comp_m1962190563et_nat,type,
comp_m1962190563et_nat: ( multiset_a > multiset_nat ) > ( multiset_nat > multiset_a ) > multiset_nat > multiset_nat ).
thf(tp_comp_m346803701et_nat,type,
comp_m346803701et_nat: ( multiset_nat > nat ) > ( multiset_nat > multiset_nat ) > multiset_nat > nat ).
thf(tp_comp_m540523139et_nat,type,
comp_m540523139et_nat: ( multiset_a > multiset_a ) > ( multiset_nat > multiset_a ) > multiset_nat > multiset_a ).
thf(tp_comp_nat_a_nat,type,
comp_nat_a_nat: ( nat > a ) > ( nat > nat ) > nat > a ).
thf(tp_comp_nat_int_nat,type,
comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
thf(tp_comp_nat_nat_nat,type,
comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(tp_f,type,
f: nat > nat ).
thf(tp_gen_length_a,type,
gen_length_a: nat > list_a > nat ).
thf(tp_if_int,type,
if_int: $o > int > int > int ).
thf(tp_if_nat,type,
if_nat: $o > nat > nat > nat ).
thf(tp_if_real,type,
if_real: $o > real > real > real ).
thf(tp_image_int_int,type,
image_int_int: ( int > int ) > set_int > set_int ).
thf(tp_image_int_nat,type,
image_int_nat: ( int > nat ) > set_int > set_nat ).
thf(tp_image_mset_a_a,type,
image_mset_a_a: ( a > a ) > multiset_a > multiset_a ).
thf(tp_image_mset_a_nat,type,
image_mset_a_nat: ( a > nat ) > multiset_a > multiset_nat ).
thf(tp_image_mset_nat_a,type,
image_mset_nat_a: ( nat > a ) > multiset_nat > multiset_a ).
thf(tp_image_mset_nat_int,type,
image_mset_nat_int: ( nat > int ) > multiset_nat > multiset_int ).
thf(tp_image_mset_nat_nat,type,
image_mset_nat_nat: ( nat > nat ) > multiset_nat > multiset_nat ).
thf(tp_image_nat_a,type,
image_nat_a: ( nat > a ) > set_nat > set_a ).
thf(tp_image_nat_int,type,
image_nat_int: ( nat > int ) > set_nat > set_int ).
thf(tp_image_nat_nat,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(tp_image_nat_real,type,
image_nat_real: ( nat > real ) > set_nat > set_real ).
thf(tp_inj_on_int_int,type,
inj_on_int_int: ( int > int ) > set_int > $o ).
thf(tp_inj_on_int_nat,type,
inj_on_int_nat: ( int > nat ) > set_int > $o ).
thf(tp_inj_on_nat_a,type,
inj_on_nat_a: ( nat > a ) > set_nat > $o ).
thf(tp_inj_on_nat_int,type,
inj_on_nat_int: ( nat > int ) > set_nat > $o ).
thf(tp_inj_on_nat_nat,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(tp_inj_on_nat_real,type,
inj_on_nat_real: ( nat > real ) > set_nat > $o ).
thf(tp_inverse_inverse_real,type,
inverse_inverse_real: real > real ).
thf(tp_list_ex_a,type,
list_ex_a: ( a > $o ) > list_a > $o ).
thf(tp_map_a_a,type,
map_a_a: ( a > a ) > list_a > list_a ).
thf(tp_map_a_nat,type,
map_a_nat: ( a > nat ) > list_a > list_nat ).
thf(tp_map_nat_a,type,
map_nat_a: ( nat > a ) > list_nat > list_a ).
thf(tp_map_nat_nat,type,
map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
thf(tp_map_tailrec_nat_a,type,
map_tailrec_nat_a: ( nat > a ) > list_nat > list_a ).
thf(tp_member_int,type,
member_int: int > set_int > $o ).
thf(tp_member_list_a,type,
member_list_a: list_a > set_list_a > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_real,type,
member_real: real > set_real > $o ).
thf(tp_mset_a,type,
mset_a: list_a > multiset_a ).
thf(tp_mset_nat,type,
mset_nat: list_nat > multiset_nat ).
thf(tp_mset_set_a,type,
mset_set_a: set_a > multiset_a ).
thf(tp_mset_set_int,type,
mset_set_int: set_int > multiset_int ).
thf(tp_mset_set_nat,type,
mset_set_nat: set_nat > multiset_nat ).
thf(tp_nat2,type,
nat2: int > nat ).
thf(tp_nth_a,type,
nth_a: list_a > nat > a ).
thf(tp_nth_nat,type,
nth_nat: list_nat > nat > nat ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(tp_ord_less_eq_set_int,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(tp_ord_less_set_int,type,
ord_less_set_int: set_int > set_int > $o ).
thf(tp_ord_less_set_nat,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_set_real,type,
ord_less_set_real: set_real > set_real > $o ).
thf(tp_ring_1_of_int_int,type,
ring_1_of_int_int: int > int ).
thf(tp_ring_1_of_int_real,type,
ring_1_of_int_real: int > real ).
thf(tp_sK10_SY310,type,
sK10_SY310: list_a > list_a > nat ).
thf(tp_sK11_SY311,type,
sK11_SY311: ( a > $o ) > list_a > nat ).
thf(tp_sK12_SY297,type,
sK12_SY297: ( nat > a > $o ) > nat > list_a ).
thf(tp_sK13_SY315,type,
sK13_SY315: list_a > ( nat > a > $o ) > nat > nat ).
thf(tp_sK14_SY297,type,
sK14_SY297: a > ( nat > a > $o ) > nat > list_a ).
thf(tp_sK15_SY316,type,
sK15_SY316: nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK16_SY292,type,
sK16_SY292: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK17_SY293,type,
sK17_SY293: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK18_SY292,type,
sK18_SY292: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK19_SY293,type,
sK19_SY293: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK1_SY255,type,
sK1_SY255: nat > list_a ).
thf(tp_sK20_SY318,type,
sK20_SY318: a > nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK21_SY311,type,
sK21_SY311: nat > ( a > $o ) > list_a > nat ).
thf(tp_sK22_SY297,type,
sK22_SY297: list_a > ( nat > a > $o ) > nat > list_a ).
thf(tp_sK23_SY297,type,
sK23_SY297: list_a > ( nat > a > $o ) > nat > list_a ).
thf(tp_sK24_SY320,type,
sK24_SY320: list_a > nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK25_SY321,type,
sK25_SY321: list_a > nat > nat > ( nat > a > $o ) > a ).
thf(tp_sK2_SY224,type,
sK2_SY224: int > nat ).
thf(tp_sK3_SY230,type,
sK3_SY230: list_a > ( list_a > $o ) > list_a ).
thf(tp_sK4_SY221,type,
sK4_SY221: nat > ( nat > $o ) > nat ).
thf(tp_sK5_SY225,type,
sK5_SY225: int > nat ).
thf(tp_sK6_SY295,type,
sK6_SY295: ( nat > a > $o ) > nat > nat ).
thf(tp_sK7_SY299,type,
sK7_SY299: ( nat > $o ) > nat > nat ).
thf(tp_sK8_SY300,type,
sK8_SY300: ( nat > $o ) > nat > nat ).
thf(tp_sK9_SY301,type,
sK9_SY301: list_a > list_a > nat ).
thf(tp_semiri1382578993at_nat,type,
semiri1382578993at_nat: nat > nat ).
thf(tp_semiri2019852685at_int,type,
semiri2019852685at_int: nat > int ).
thf(tp_semiri2110766477t_real,type,
semiri2110766477t_real: nat > real ).
thf(tp_set_or1199280219an_int,type,
set_or1199280219an_int: int > int > set_int ).
thf(tp_set_or1211449801n_real,type,
set_or1211449801n_real: real > set_real ).
thf(tp_set_or2075149659n_real,type,
set_or2075149659n_real: real > real > set_real ).
thf(tp_set_or562006527an_nat,type,
set_or562006527an_nat: nat > nat > set_nat ).
thf(tp_set_ord_lessThan_int,type,
set_ord_lessThan_int: int > set_int ).
thf(tp_set_ord_lessThan_nat,type,
set_ord_lessThan_nat: nat > set_nat ).
thf(tp_size_multiset_a,type,
size_multiset_a: ( a > nat ) > multiset_a > nat ).
thf(tp_size_multiset_nat,type,
size_multiset_nat: ( nat > nat ) > multiset_nat > nat ).
thf(tp_size_s1679505588et_nat,type,
size_s1679505588et_nat: multiset_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_multiset_a,type,
size_size_multiset_a: multiset_a > nat ).
thf(tp_uminus_uminus_int,type,
uminus_uminus_int: int > int ).
thf(tp_uminus_uminus_real,type,
uminus_uminus_real: real > real ).
thf(tp_upt,type,
upt: nat > nat > list_nat ).
thf(tp_xs,type,
xs: list_a ).
thf(tp_ys,type,
ys: list_a ).
thf(tp_zero_z2005226153et_nat,type,
zero_z2005226153et_nat: multiset_nat ).
thf(tp_zero_zero_int,type,
zero_zero_int: int ).
thf(tp_zero_zero_multiset_a,type,
zero_zero_multiset_a: multiset_a ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(3,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Real__Oreal_T) ).
thf(9,axiom,
! [I: int] :
( ( ( nat2 @ I )
= zero_zero_nat )
= ( ord_less_eq_int @ I @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_nat__0__iff) ).
thf(10,axiom,
! [Z2: int] :
( ( ord_less_eq_int @ Z2 @ zero_zero_int )
=> ( ( nat2 @ Z2 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_nat__le__0) ).
thf(14,axiom,
! [I: nat,L: nat,U: nat] :
( ( member_nat @ I @ ( set_or562006527an_nat @ L @ U ) )
= ( ( ord_less_eq_nat @ L @ I )
& ( ord_less_nat @ I @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_atLeastLessThan__iff) ).
thf(29,axiom,
! [I: nat,J: nat,M: nat,N: nat] :
( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ I @ J ) @ ( set_or562006527an_nat @ M @ N ) )
= ( ( ord_less_eq_nat @ J @ I )
| ( ( ord_less_eq_nat @ M @ I )
& ( ord_less_eq_nat @ J @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_ivl__subset) ).
thf(33,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_le__zero__eq) ).
thf(64,axiom,
( zero_zero_nat
= ( nat2 @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_nat__zero__as__int) ).
thf(65,axiom,
! [N: nat] :
( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_nat__zminus__int) ).
thf(77,axiom,
! [M: int] :
( ! [N2: nat] :
( M
!= ( semiri2019852685at_int @ N2 ) )
=> ~ ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( M
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ N2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_int__cases4) ).
thf(89,axiom,
! [N: nat,M: nat] :
( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) )
= ( semiri2019852685at_int @ M ) )
= ( ( N = zero_zero_nat )
& ( M = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_negative__eq__positive) ).
thf(114,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_int__ops_I1_J) ).
thf(116,axiom,
! [G: nat > nat,F: nat > nat] :
( ( comp_m346803701et_nat @ ( size_multiset_nat @ G ) @ ( image_mset_nat_nat @ F ) )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ G @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_size__multiset__o__map) ).
thf(131,axiom,
! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_of__nat__less__0__iff) ).
thf(135,axiom,
! [A: nat,B3: nat] :
( ( image_nat_int @ semiri2019852685at_int @ ( set_or562006527an_nat @ A @ B3 ) )
= ( set_or1199280219an_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_image__int__atLeastLessThan) ).
thf(142,axiom,
! [M: nat] :
( ( ( semiri2110766477t_real @ M )
= zero_zero_real )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_of__nat__eq__0__iff) ).
thf(143,axiom,
! [M: nat] :
( ( ( semiri2019852685at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_of__nat__eq__0__iff) ).
thf(144,axiom,
! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_of__nat__eq__0__iff) ).
thf(145,axiom,
! [N: nat] :
( ( zero_zero_real
= ( semiri2110766477t_real @ N ) )
= ( zero_zero_nat = N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_of__nat__0__eq__iff) ).
thf(146,axiom,
! [N: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ N ) )
= ( zero_zero_nat = N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_of__nat__0__eq__iff) ).
thf(147,axiom,
! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_of__nat__0__eq__iff) ).
thf(148,axiom,
( ( semiri2110766477t_real @ zero_zero_nat )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_of__nat__0) ).
thf(149,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_of__nat__0) ).
thf(150,axiom,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_of__nat__0) ).
thf(155,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_of__nat__0__less__iff) ).
thf(156,axiom,
( list_ex_a
= ( ^ [P2: a > $o,Xs3: list_a] :
? [N4: nat] :
( ( ord_less_nat @ N4 @ ( size_size_list_a @ Xs3 ) )
& ( P2 @ ( nth_a @ Xs3 @ N4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_list__ex__length) ).
thf(174,axiom,
( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_length__code) ).
thf(178,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_less__numeral__extra_I3_J) ).
thf(189,axiom,
! [X: list_a,A2: set_list_a,Y: list_a] :
( ( member_list_a @ X @ A2 )
=> ( ( ord_less_nat @ ( size_size_list_a @ X ) @ ( size_size_list_a @ Y ) )
=> ( X != Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mbs_Oless__not__eq) ).
thf(192,axiom,
! [Xs2: list_a,Ys: list_a] :
( ( ( mset_a @ Xs2 )
= ( mset_a @ Ys ) )
=> ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_mset__eq__length) ).
thf(195,axiom,
! [F: nat > nat,G: nat > nat] :
( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ F ) @ ( image_mset_nat_nat @ G ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_image__mset_Ocomp) ).
thf(196,axiom,
! [F: nat > a,G: nat > nat] :
( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ F ) @ ( image_mset_nat_nat @ G ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_image__mset_Ocomp) ).
thf(197,axiom,
! [F: a > nat,G: nat > a] :
( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ F ) @ ( image_mset_nat_a @ G ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_image__mset_Ocomp) ).
thf(198,axiom,
! [F: a > a,G: nat > a] :
( ( comp_m540523139et_nat @ ( image_mset_a_a @ F ) @ ( image_mset_nat_a @ G ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_image__mset_Ocomp) ).
thf(199,axiom,
! [F: nat > nat,G: nat > nat,Multiset: multiset_nat] :
( ( image_mset_nat_nat @ F @ ( image_mset_nat_nat @ G @ Multiset ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ Multiset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_image__mset_Ocompositionality) ).
thf(200,axiom,
! [F: nat > a,G: nat > nat,Multiset: multiset_nat] :
( ( image_mset_nat_a @ F @ ( image_mset_nat_nat @ G @ Multiset ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ F @ G ) @ Multiset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_image__mset_Ocompositionality) ).
thf(201,axiom,
! [F: a > nat,G: nat > a,Multiset: multiset_nat] :
( ( image_mset_a_nat @ F @ ( image_mset_nat_a @ G @ Multiset ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ F @ G ) @ Multiset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_image__mset_Ocompositionality) ).
thf(202,axiom,
! [F: a > a,G: nat > a,Multiset: multiset_nat] :
( ( image_mset_a_a @ F @ ( image_mset_nat_a @ G @ Multiset ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ F @ G ) @ Multiset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_image__mset_Ocompositionality) ).
thf(203,axiom,
! [G: nat > nat,F: nat > nat,V: multiset_nat] :
( ( image_mset_nat_nat @ G @ ( image_mset_nat_nat @ F @ V ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_multiset_Omap__comp) ).
thf(204,axiom,
! [G: nat > a,F: nat > nat,V: multiset_nat] :
( ( image_mset_nat_a @ G @ ( image_mset_nat_nat @ F @ V ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ G @ F ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_multiset_Omap__comp) ).
thf(205,axiom,
! [G: a > nat,F: nat > a,V: multiset_nat] :
( ( image_mset_a_nat @ G @ ( image_mset_nat_a @ F @ V ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ G @ F ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_multiset_Omap__comp) ).
thf(206,axiom,
! [G: a > a,F: nat > a,V: multiset_nat] :
( ( image_mset_a_a @ G @ ( image_mset_nat_a @ F @ V ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ G @ F ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_multiset_Omap__comp) ).
thf(220,axiom,
! [A: nat,B3: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
= ( ( A = C )
& ( B3 = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_atLeastLessThan__eq__iff) ).
thf(223,axiom,
! [A: nat,B3: nat,C: nat,D: nat] :
( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_atLeastLessThan__inj_I1_J) ).
thf(226,axiom,
! [A: nat,B3: nat,C: nat,D: nat] :
( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( B3 = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_atLeastLessThan__inj_I2_J) ).
thf(260,axiom,
! [M: nat,N: nat] :
( ( mset_nat @ ( upt @ M @ N ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_mset__upt) ).
thf(261,axiom,
! [F: nat > nat,M4: multiset_nat] :
( ( size_s1679505588et_nat @ ( image_mset_nat_nat @ F @ M4 ) )
= ( size_s1679505588et_nat @ M4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_size__image__mset) ).
thf(262,axiom,
! [F: nat > a,M4: multiset_nat] :
( ( size_size_multiset_a @ ( image_mset_nat_a @ F @ M4 ) )
= ( size_s1679505588et_nat @ M4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_size__image__mset) ).
thf(263,axiom,
! [F: nat > nat,M4: multiset_nat] :
( ( ( image_mset_nat_nat @ F @ M4 )
= zero_z2005226153et_nat )
= ( M4 = zero_z2005226153et_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_image__mset__is__empty__iff) ).
thf(264,axiom,
! [F: nat > a,M4: multiset_nat] :
( ( ( image_mset_nat_a @ F @ M4 )
= zero_zero_multiset_a )
= ( M4 = zero_z2005226153et_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_image__mset__is__empty__iff) ).
thf(265,axiom,
! [F: nat > nat] :
( ( image_mset_nat_nat @ F @ zero_z2005226153et_nat )
= zero_z2005226153et_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_image__mset__empty) ).
thf(266,axiom,
! [F: nat > a] :
( ( image_mset_nat_a @ F @ zero_z2005226153et_nat )
= zero_zero_multiset_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_image__mset__empty) ).
thf(284,axiom,
( set_ord_lessThan_nat
= ( set_or562006527an_nat @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_lessThan__atLeast0) ).
thf(285,axiom,
! [F: nat > nat,A2: set_nat] :
( ( inj_on_nat_nat @ F @ A2 )
=> ( ( image_mset_nat_nat @ F @ ( mset_set_nat @ A2 ) )
= ( mset_set_nat @ ( image_nat_nat @ F @ A2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_image__mset__mset__set) ).
thf(286,axiom,
! [F: nat > a,A2: set_nat] :
( ( inj_on_nat_a @ F @ A2 )
=> ( ( image_mset_nat_a @ F @ ( mset_set_nat @ A2 ) )
= ( mset_set_a @ ( image_nat_a @ F @ A2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_image__mset__mset__set) ).
thf(291,axiom,
! [Xs2: list_a] :
( ( size_size_multiset_a @ ( mset_a @ Xs2 ) )
= ( size_size_list_a @ Xs2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_size__mset) ).
thf(293,axiom,
! [F: nat > nat,Xs2: list_nat] :
( ( mset_nat @ ( map_nat_nat @ F @ Xs2 ) )
= ( image_mset_nat_nat @ F @ ( mset_nat @ Xs2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mset__map) ).
thf(294,axiom,
! [F: nat > a,Xs2: list_nat] :
( ( mset_a @ ( map_nat_a @ F @ Xs2 ) )
= ( image_mset_nat_a @ F @ ( mset_nat @ Xs2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mset__map) ).
thf(299,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_zero__reorient) ).
thf(300,axiom,
! [Xs2: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ Xs2 @ I3 )
= ( nth_a @ Ys @ I3 ) ) )
=> ( Xs2 = Ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nth__equalityI) ).
thf(301,axiom,
! [K: nat,P: nat > a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X3: a] : ( P @ I2 @ X3 ) ) )
= ( ? [Xs3: list_a] :
( ( ( size_size_list_a @ Xs3 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_a @ Xs3 @ I2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Skolem__list__nth) ).
thf(302,axiom,
( ( ^ [Y2: list_a,Z: list_a] : ( Y2 = Z ) )
= ( ^ [Xs3: list_a,Ys3: list_a] :
( ( ( size_size_list_a @ Xs3 )
= ( size_size_list_a @ Ys3 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs3 ) )
=> ( ( nth_a @ Xs3 @ I2 )
= ( nth_a @ Ys3 @ I2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_list__eq__iff__nth__eq) ).
thf(303,axiom,
! [N: nat,P: nat > $o] :
( ( ? [M3: nat] :
( ( ord_less_nat @ M3 @ N )
& ( P @ M3 ) ) )
= ( ? [X2: nat] :
( ( member_nat @ X2 @ ( set_or562006527an_nat @ zero_zero_nat @ N ) )
& ( P @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_ex__nat__less__eq) ).
thf(304,axiom,
! [N: nat,P: nat > $o] :
( ( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N )
=> ( P @ M3 ) ) )
= ( ! [X2: nat] :
( ( member_nat @ X2 @ ( set_or562006527an_nat @ zero_zero_nat @ N ) )
=> ( P @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_all__nat__less__eq) ).
thf(305,axiom,
! [P: list_a > $o,Xs2: list_a] :
( ! [Xs: list_a] :
( ! [Ys2: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys2 ) @ ( size_size_list_a @ Xs ) )
=> ( P @ Ys2 ) )
=> ( P @ Xs ) )
=> ( P @ Xs2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_length__induct) ).
thf(306,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_gr0I) ).
thf(307,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_not__gr0) ).
thf(308,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_not__less0) ).
thf(309,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_less__zeroE) ).
thf(310,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_gr__implies__not0) ).
thf(311,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_infinite__descent0) ).
thf(312,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_bot__nat__0_Oextremum__strict) ).
thf(313,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_gr__zeroI) ).
thf(314,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_not__less__zero) ).
thf(315,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_gr__implies__not__zero) ).
thf(316,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zero__less__iff__neq__zero) ).
thf(317,axiom,
! [F: a > a,Xs2: list_a,G: nat > a,Ys: list_nat] :
( ( ( map_a_a @ F @ Xs2 )
= ( map_nat_a @ G @ Ys ) )
=> ( ( size_size_list_a @ Xs2 )
= ( size_size_list_nat @ Ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_map__eq__imp__length__eq) ).
thf(318,axiom,
! [F: nat > a,Xs2: list_nat,G: a > a,Ys: list_a] :
( ( ( map_nat_a @ F @ Xs2 )
= ( map_a_a @ G @ Ys ) )
=> ( ( size_size_list_nat @ Xs2 )
= ( size_size_list_a @ Ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_map__eq__imp__length__eq) ).
thf(329,axiom,
! [N: nat,Xs2: list_a,F: a > a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ ( map_a_a @ F @ Xs2 ) @ N )
= ( F @ ( nth_a @ Xs2 @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_nth__map) ).
thf(331,axiom,
! [F: a > a,Xs2: list_a] :
( ( size_size_list_a @ ( map_a_a @ F @ Xs2 ) )
= ( size_size_list_a @ Xs2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_length__map) ).
thf(332,axiom,
! [F: nat > a,Xs2: list_nat] :
( ( size_size_list_a @ ( map_nat_a @ F @ Xs2 ) )
= ( size_size_list_nat @ Xs2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_length__map) ).
thf(343,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_neq0__conv) ).
thf(344,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_less__nat__zero__code) ).
thf(345,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_bot__nat__0_Onot__eq__extremum) ).
thf(346,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_not__gr__zero) ).
thf(347,axiom,
! [X: list_a,Y: list_a] :
( ( ( size_size_list_a @ X )
!= ( size_size_list_a @ Y ) )
=> ( X != Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_size__neq__size__imp__neq) ).
thf(348,axiom,
! [Xs2: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs2 )
!= ( size_size_list_a @ Ys ) )
=> ( Xs2 != Ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_neq__if__length__neq) ).
thf(349,axiom,
! [N: nat] :
? [Xs: list_a] :
( ( size_size_list_a @ Xs )
= N ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Ex__list__of__length) ).
thf(350,axiom,
( xs
= ( map_nat_a @ ( comp_nat_a_nat @ ( nth_a @ ys ) @ f ) @ ( upt @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062xs_A_061_Amap_A_I_I_B_J_Ays_A_092_060circ_062_Af_J_A_0910_O_O_060length_Axs_093_092_060close_062) ).
thf(352,axiom,
bij_betw_nat_nat @ f @ ( set_ord_lessThan_nat @ ( size_size_list_a @ xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_a @ ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(353,axiom,
( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C2_C) ).
thf(354,axiom,
! [I: nat] :
( ( ord_less_nat @ I @ ( size_size_list_a @ xs ) )
=> ( ( nth_a @ xs @ I )
= ( nth_a @ ys @ ( f @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).
thf(355,axiom,
( ( mset_a @ xs )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation) ).
thf(356,axiom,
inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__C1_C) ).
thf(357,conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(358,negated_conjecture,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[357]) ).
thf(359,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[358]) ).
thf(360,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(361,plain,
( ( ! [I: int] :
( ( ( nat2 @ I )
= zero_zero_nat )
= ( ord_less_eq_int @ I @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(362,plain,
( ( ! [Z2: int] :
( ( ord_less_eq_int @ Z2 @ zero_zero_int )
=> ( ( nat2 @ Z2 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(363,plain,
( ( ! [I: nat,L: nat,U: nat] :
( ( member_nat @ I @ ( set_or562006527an_nat @ L @ U ) )
= ( ( ord_less_eq_nat @ L @ I )
& ( ord_less_nat @ I @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(364,plain,
( ( ! [I: nat,J: nat,M: nat,N: nat] :
( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ I @ J ) @ ( set_or562006527an_nat @ M @ N ) )
= ( ( ord_less_eq_nat @ J @ I )
| ( ( ord_less_eq_nat @ M @ I )
& ( ord_less_eq_nat @ J @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(365,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(366,plain,
( ( zero_zero_nat
= ( nat2 @ zero_zero_int ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(367,plain,
( ( ! [N: nat] :
( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(368,plain,
( ( ! [M: int] :
( ! [N2: nat] :
( M
!= ( semiri2019852685at_int @ N2 ) )
=> ~ ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( M
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ N2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(369,plain,
( ( ! [N: nat,M: nat] :
( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) )
= ( semiri2019852685at_int @ M ) )
= ( ( N = zero_zero_nat )
& ( M = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(370,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(371,plain,
( ( ! [G: nat > nat,F: nat > nat] :
( ( comp_m346803701et_nat @ ( size_multiset_nat @ G ) @ ( image_mset_nat_nat @ F ) )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ G @ F ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(372,plain,
( ( ! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(373,plain,
( ( ! [A: nat,B3: nat] :
( ( image_nat_int @ semiri2019852685at_int @ ( set_or562006527an_nat @ A @ B3 ) )
= ( set_or1199280219an_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(374,plain,
( ( ! [M: nat] :
( ( ( semiri2110766477t_real @ M )
= zero_zero_real )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(375,plain,
( ( ! [M: nat] :
( ( ( semiri2019852685at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(376,plain,
( ( ! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(377,plain,
( ( ! [N: nat] :
( ( zero_zero_real
= ( semiri2110766477t_real @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(378,plain,
( ( ! [N: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(379,plain,
( ( ! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(380,plain,
( ( ( semiri2110766477t_real @ zero_zero_nat )
= zero_zero_real )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(381,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(382,plain,
( ( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(383,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(384,plain,
( ( list_ex_a
= ( ^ [P2: a > $o,Xs3: list_a] :
? [N4: nat] :
( ( ord_less_nat @ N4 @ ( size_size_list_a @ Xs3 ) )
& ( P2 @ ( nth_a @ Xs3 @ N4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(385,plain,
( ( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(386,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(387,plain,
( ( ! [X: list_a,A2: set_list_a,Y: list_a] :
( ( member_list_a @ X @ A2 )
=> ( ( ord_less_nat @ ( size_size_list_a @ X ) @ ( size_size_list_a @ Y ) )
=> ( X != Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(388,plain,
( ( ! [Xs2: list_a,Ys: list_a] :
( ( ( mset_a @ Xs2 )
= ( mset_a @ Ys ) )
=> ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(389,plain,
( ( ! [F: nat > nat,G: nat > nat] :
( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ F ) @ ( image_mset_nat_nat @ G ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ F @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(390,plain,
( ( ! [F: nat > a,G: nat > nat] :
( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ F ) @ ( image_mset_nat_nat @ G ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ F @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(391,plain,
( ( ! [F: a > nat,G: nat > a] :
( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ F ) @ ( image_mset_nat_a @ G ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ F @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(392,plain,
( ( ! [F: a > a,G: nat > a] :
( ( comp_m540523139et_nat @ ( image_mset_a_a @ F ) @ ( image_mset_nat_a @ G ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ F @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(393,plain,
( ( ! [F: nat > nat,G: nat > nat,Multiset: multiset_nat] :
( ( image_mset_nat_nat @ F @ ( image_mset_nat_nat @ G @ Multiset ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(394,plain,
( ( ! [F: nat > a,G: nat > nat,Multiset: multiset_nat] :
( ( image_mset_nat_a @ F @ ( image_mset_nat_nat @ G @ Multiset ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(395,plain,
( ( ! [F: a > nat,G: nat > a,Multiset: multiset_nat] :
( ( image_mset_a_nat @ F @ ( image_mset_nat_a @ G @ Multiset ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(396,plain,
( ( ! [F: a > a,G: nat > a,Multiset: multiset_nat] :
( ( image_mset_a_a @ F @ ( image_mset_nat_a @ G @ Multiset ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(397,plain,
( ( ! [G: nat > nat,F: nat > nat,V: multiset_nat] :
( ( image_mset_nat_nat @ G @ ( image_mset_nat_nat @ F @ V ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(398,plain,
( ( ! [G: nat > a,F: nat > nat,V: multiset_nat] :
( ( image_mset_nat_a @ G @ ( image_mset_nat_nat @ F @ V ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ G @ F ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(399,plain,
( ( ! [G: a > nat,F: nat > a,V: multiset_nat] :
( ( image_mset_a_nat @ G @ ( image_mset_nat_a @ F @ V ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ G @ F ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(400,plain,
( ( ! [G: a > a,F: nat > a,V: multiset_nat] :
( ( image_mset_a_a @ G @ ( image_mset_nat_a @ F @ V ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ G @ F ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(401,plain,
( ( ! [A: nat,B3: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
= ( ( A = C )
& ( B3 = D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(402,plain,
( ( ! [A: nat,B3: nat,C: nat,D: nat] :
( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( A = C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(403,plain,
( ( ! [A: nat,B3: nat,C: nat,D: nat] :
( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( B3 = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(404,plain,
( ( ! [M: nat,N: nat] :
( ( mset_nat @ ( upt @ M @ N ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(405,plain,
( ( ! [F: nat > nat,M4: multiset_nat] :
( ( size_s1679505588et_nat @ ( image_mset_nat_nat @ F @ M4 ) )
= ( size_s1679505588et_nat @ M4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(406,plain,
( ( ! [F: nat > a,M4: multiset_nat] :
( ( size_size_multiset_a @ ( image_mset_nat_a @ F @ M4 ) )
= ( size_s1679505588et_nat @ M4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(407,plain,
( ( ! [F: nat > nat,M4: multiset_nat] :
( ( ( image_mset_nat_nat @ F @ M4 )
= zero_z2005226153et_nat )
= ( M4 = zero_z2005226153et_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(408,plain,
( ( ! [F: nat > a,M4: multiset_nat] :
( ( ( image_mset_nat_a @ F @ M4 )
= zero_zero_multiset_a )
= ( M4 = zero_z2005226153et_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(409,plain,
( ( ! [F: nat > nat] :
( ( image_mset_nat_nat @ F @ zero_z2005226153et_nat )
= zero_z2005226153et_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(410,plain,
( ( ! [F: nat > a] :
( ( image_mset_nat_a @ F @ zero_z2005226153et_nat )
= zero_zero_multiset_a ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(411,plain,
( ( set_ord_lessThan_nat
= ( set_or562006527an_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(412,plain,
( ( ! [F: nat > nat,A2: set_nat] :
( ( inj_on_nat_nat @ F @ A2 )
=> ( ( image_mset_nat_nat @ F @ ( mset_set_nat @ A2 ) )
= ( mset_set_nat @ ( image_nat_nat @ F @ A2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(413,plain,
( ( ! [F: nat > a,A2: set_nat] :
( ( inj_on_nat_a @ F @ A2 )
=> ( ( image_mset_nat_a @ F @ ( mset_set_nat @ A2 ) )
= ( mset_set_a @ ( image_nat_a @ F @ A2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(414,plain,
( ( ! [Xs2: list_a] :
( ( size_size_multiset_a @ ( mset_a @ Xs2 ) )
= ( size_size_list_a @ Xs2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(415,plain,
( ( ! [F: nat > nat,Xs2: list_nat] :
( ( mset_nat @ ( map_nat_nat @ F @ Xs2 ) )
= ( image_mset_nat_nat @ F @ ( mset_nat @ Xs2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(416,plain,
( ( ! [F: nat > a,Xs2: list_nat] :
( ( mset_a @ ( map_nat_a @ F @ Xs2 ) )
= ( image_mset_nat_a @ F @ ( mset_nat @ Xs2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(417,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(418,plain,
( ( ! [Xs2: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ Xs2 @ I3 )
= ( nth_a @ Ys @ I3 ) ) )
=> ( Xs2 = Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(419,plain,
( ( ! [K: nat,P: nat > a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X3: a] : ( P @ I2 @ X3 ) ) )
= ( ? [Xs3: list_a] :
( ( ( size_size_list_a @ Xs3 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_a @ Xs3 @ I2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(420,plain,
( ( ( ^ [Y2: list_a,Z: list_a] : ( Y2 = Z ) )
= ( ^ [Xs3: list_a,Ys3: list_a] :
( ( ( size_size_list_a @ Xs3 )
= ( size_size_list_a @ Ys3 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs3 ) )
=> ( ( nth_a @ Xs3 @ I2 )
= ( nth_a @ Ys3 @ I2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(421,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [M3: nat] :
( ( ord_less_nat @ M3 @ N )
& ( P @ M3 ) ) )
= ( ? [X2: nat] :
( ( member_nat @ X2 @ ( set_or562006527an_nat @ zero_zero_nat @ N ) )
& ( P @ X2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(422,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N )
=> ( P @ M3 ) ) )
= ( ! [X2: nat] :
( ( member_nat @ X2 @ ( set_or562006527an_nat @ zero_zero_nat @ N ) )
=> ( P @ X2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(423,plain,
( ( ! [P: list_a > $o,Xs2: list_a] :
( ! [Xs: list_a] :
( ! [Ys2: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys2 ) @ ( size_size_list_a @ Xs ) )
=> ( P @ Ys2 ) )
=> ( P @ Xs ) )
=> ( P @ Xs2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(424,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(425,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(426,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(427,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(428,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(429,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(430,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(431,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(432,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(433,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(434,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(435,plain,
( ( ! [F: a > a,Xs2: list_a,G: nat > a,Ys: list_nat] :
( ( ( map_a_a @ F @ Xs2 )
= ( map_nat_a @ G @ Ys ) )
=> ( ( size_size_list_a @ Xs2 )
= ( size_size_list_nat @ Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(436,plain,
( ( ! [F: nat > a,Xs2: list_nat,G: a > a,Ys: list_a] :
( ( ( map_nat_a @ F @ Xs2 )
= ( map_a_a @ G @ Ys ) )
=> ( ( size_size_list_nat @ Xs2 )
= ( size_size_list_a @ Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(437,plain,
( ( ! [N: nat,Xs2: list_a,F: a > a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ ( map_a_a @ F @ Xs2 ) @ N )
= ( F @ ( nth_a @ Xs2 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(438,plain,
( ( ! [F: a > a,Xs2: list_a] :
( ( size_size_list_a @ ( map_a_a @ F @ Xs2 ) )
= ( size_size_list_a @ Xs2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(439,plain,
( ( ! [F: nat > a,Xs2: list_nat] :
( ( size_size_list_a @ ( map_nat_a @ F @ Xs2 ) )
= ( size_size_list_nat @ Xs2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(440,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(441,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(442,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(443,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(444,plain,
( ( ! [X: list_a,Y: list_a] :
( ( ( size_size_list_a @ X )
!= ( size_size_list_a @ Y ) )
=> ( X != Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(445,plain,
( ( ! [Xs2: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs2 )
!= ( size_size_list_a @ Ys ) )
=> ( Xs2 != Ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(446,plain,
( ( ! [N: nat] :
? [Xs: list_a] :
( ( size_size_list_a @ Xs )
= N ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(447,plain,
( ( xs
= ( map_nat_a @ ( comp_nat_a_nat @ ( nth_a @ ys ) @ f ) @ ( upt @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(448,plain,
( ( bij_betw_nat_nat @ f @ ( set_ord_lessThan_nat @ ( size_size_list_a @ xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_a @ ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(449,plain,
( ( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(450,plain,
( ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_size_list_a @ xs ) )
=> ( ( nth_a @ xs @ I )
= ( nth_a @ ys @ ( f @ I ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(451,plain,
( ( ( mset_a @ xs )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(452,plain,
( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(453,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[359]) ).
thf(454,plain,
( ( inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(455,plain,
( ( ( mset_a @ xs )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(456,plain,
( ( ! [I: nat] :
( ( ord_less_nat @ I @ ( size_size_list_a @ xs ) )
=> ( ( nth_a @ xs @ I )
= ( nth_a @ ys @ ( f @ I ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(457,plain,
( ( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(458,plain,
( ( bij_betw_nat_nat @ f @ ( set_ord_lessThan_nat @ ( size_size_list_a @ xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_a @ ys ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(459,plain,
( ( xs
= ( map_nat_a @ ( comp_nat_a_nat @ ( nth_a @ ys ) @ f ) @ ( upt @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(460,plain,
( ( ! [N: nat] :
? [Xs: list_a] :
( ( size_size_list_a @ Xs )
= N ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(461,plain,
( ( ! [Xs2: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs2 )
!= ( size_size_list_a @ Ys ) )
=> ( Xs2 != Ys ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(462,plain,
( ( ! [X: list_a,Y: list_a] :
( ( ( size_size_list_a @ X )
!= ( size_size_list_a @ Y ) )
=> ( X != Y ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(463,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(464,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(465,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(466,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(467,plain,
( ( ! [F: nat > a,Xs2: list_nat] :
( ( size_size_list_a @ ( map_nat_a @ F @ Xs2 ) )
= ( size_size_list_nat @ Xs2 ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(468,plain,
( ( ! [F: a > a,Xs2: list_a] :
( ( size_size_list_a @ ( map_a_a @ F @ Xs2 ) )
= ( size_size_list_a @ Xs2 ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(469,plain,
( ( ! [N: nat,Xs2: list_a,F: a > a] :
( ( ord_less_nat @ N @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ ( map_a_a @ F @ Xs2 ) @ N )
= ( F @ ( nth_a @ Xs2 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(470,plain,
( ( ! [F: nat > a,Xs2: list_nat,G: a > a,Ys: list_a] :
( ( ( map_nat_a @ F @ Xs2 )
= ( map_a_a @ G @ Ys ) )
=> ( ( size_size_list_nat @ Xs2 )
= ( size_size_list_a @ Ys ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(471,plain,
( ( ! [F: a > a,Xs2: list_a,G: nat > a,Ys: list_nat] :
( ( ( map_a_a @ F @ Xs2 )
= ( map_nat_a @ G @ Ys ) )
=> ( ( size_size_list_a @ Xs2 )
= ( size_size_list_nat @ Ys ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(472,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(473,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(474,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(475,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(476,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(477,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(478,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(479,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(480,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(481,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(482,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(483,plain,
( ( ! [P: list_a > $o,Xs2: list_a] :
( ! [Xs: list_a] :
( ! [Ys2: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ Ys2 ) @ ( size_size_list_a @ Xs ) )
=> ( P @ Ys2 ) )
=> ( P @ Xs ) )
=> ( P @ Xs2 ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(484,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N )
=> ( P @ M3 ) ) )
= ( ! [X2: nat] :
( ( member_nat @ X2 @ ( set_or562006527an_nat @ zero_zero_nat @ N ) )
=> ( P @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(485,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [M3: nat] :
( ( ord_less_nat @ M3 @ N )
& ( P @ M3 ) ) )
= ( ? [X2: nat] :
( ( member_nat @ X2 @ ( set_or562006527an_nat @ zero_zero_nat @ N ) )
& ( P @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(486,plain,
( ( ( ^ [Y2: list_a,Z: list_a] : ( Y2 = Z ) )
= ( ^ [Xs3: list_a,Ys3: list_a] :
( ( ( size_size_list_a @ Xs3 )
= ( size_size_list_a @ Ys3 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs3 ) )
=> ( ( nth_a @ Xs3 @ I2 )
= ( nth_a @ Ys3 @ I2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(487,plain,
( ( ! [K: nat,P: nat > a > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X3: a] : ( P @ I2 @ X3 ) ) )
= ( ? [Xs3: list_a] :
( ( ( size_size_list_a @ Xs3 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_a @ Xs3 @ I2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(488,plain,
( ( ! [Xs2: list_a,Ys: list_a] :
( ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs2 ) )
=> ( ( nth_a @ Xs2 @ I3 )
= ( nth_a @ Ys @ I3 ) ) )
=> ( Xs2 = Ys ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(489,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(490,plain,
( ( ! [F: nat > a,Xs2: list_nat] :
( ( mset_a @ ( map_nat_a @ F @ Xs2 ) )
= ( image_mset_nat_a @ F @ ( mset_nat @ Xs2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(491,plain,
( ( ! [F: nat > nat,Xs2: list_nat] :
( ( mset_nat @ ( map_nat_nat @ F @ Xs2 ) )
= ( image_mset_nat_nat @ F @ ( mset_nat @ Xs2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(492,plain,
( ( ! [Xs2: list_a] :
( ( size_size_multiset_a @ ( mset_a @ Xs2 ) )
= ( size_size_list_a @ Xs2 ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(493,plain,
( ( ! [F: nat > a,A2: set_nat] :
( ( inj_on_nat_a @ F @ A2 )
=> ( ( image_mset_nat_a @ F @ ( mset_set_nat @ A2 ) )
= ( mset_set_a @ ( image_nat_a @ F @ A2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(494,plain,
( ( ! [F: nat > nat,A2: set_nat] :
( ( inj_on_nat_nat @ F @ A2 )
=> ( ( image_mset_nat_nat @ F @ ( mset_set_nat @ A2 ) )
= ( mset_set_nat @ ( image_nat_nat @ F @ A2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(495,plain,
( ( set_ord_lessThan_nat
= ( set_or562006527an_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(496,plain,
( ( ! [F: nat > a] :
( ( image_mset_nat_a @ F @ zero_z2005226153et_nat )
= zero_zero_multiset_a ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(497,plain,
( ( ! [F: nat > nat] :
( ( image_mset_nat_nat @ F @ zero_z2005226153et_nat )
= zero_z2005226153et_nat ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(498,plain,
( ( ! [F: nat > a,M4: multiset_nat] :
( ( ( image_mset_nat_a @ F @ M4 )
= zero_zero_multiset_a )
= ( M4 = zero_z2005226153et_nat ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(499,plain,
( ( ! [F: nat > nat,M4: multiset_nat] :
( ( ( image_mset_nat_nat @ F @ M4 )
= zero_z2005226153et_nat )
= ( M4 = zero_z2005226153et_nat ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(500,plain,
( ( ! [F: nat > a,M4: multiset_nat] :
( ( size_size_multiset_a @ ( image_mset_nat_a @ F @ M4 ) )
= ( size_s1679505588et_nat @ M4 ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(501,plain,
( ( ! [F: nat > nat,M4: multiset_nat] :
( ( size_s1679505588et_nat @ ( image_mset_nat_nat @ F @ M4 ) )
= ( size_s1679505588et_nat @ M4 ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(502,plain,
( ( ! [M: nat,N: nat] :
( ( mset_nat @ ( upt @ M @ N ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(503,plain,
( ( ! [A: nat,B3: nat,C: nat,D: nat] :
( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( B3 = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(504,plain,
( ( ! [A: nat,B3: nat,C: nat,D: nat] :
( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( A = C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(505,plain,
( ( ! [A: nat,B3: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B3 )
=> ( ( ord_less_nat @ C @ D )
=> ( ( ( set_or562006527an_nat @ A @ B3 )
= ( set_or562006527an_nat @ C @ D ) )
= ( ( A = C )
& ( B3 = D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(506,plain,
( ( ! [G: a > a,F: nat > a,V: multiset_nat] :
( ( image_mset_a_a @ G @ ( image_mset_nat_a @ F @ V ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ G @ F ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(507,plain,
( ( ! [G: a > nat,F: nat > a,V: multiset_nat] :
( ( image_mset_a_nat @ G @ ( image_mset_nat_a @ F @ V ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ G @ F ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(508,plain,
( ( ! [G: nat > a,F: nat > nat,V: multiset_nat] :
( ( image_mset_nat_a @ G @ ( image_mset_nat_nat @ F @ V ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ G @ F ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(509,plain,
( ( ! [G: nat > nat,F: nat > nat,V: multiset_nat] :
( ( image_mset_nat_nat @ G @ ( image_mset_nat_nat @ F @ V ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(510,plain,
( ( ! [F: a > a,G: nat > a,Multiset: multiset_nat] :
( ( image_mset_a_a @ F @ ( image_mset_nat_a @ G @ Multiset ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(511,plain,
( ( ! [F: a > nat,G: nat > a,Multiset: multiset_nat] :
( ( image_mset_a_nat @ F @ ( image_mset_nat_a @ G @ Multiset ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(512,plain,
( ( ! [F: nat > a,G: nat > nat,Multiset: multiset_nat] :
( ( image_mset_nat_a @ F @ ( image_mset_nat_nat @ G @ Multiset ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(513,plain,
( ( ! [F: nat > nat,G: nat > nat,Multiset: multiset_nat] :
( ( image_mset_nat_nat @ F @ ( image_mset_nat_nat @ G @ Multiset ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ Multiset ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(514,plain,
( ( ! [F: a > a,G: nat > a] :
( ( comp_m540523139et_nat @ ( image_mset_a_a @ F ) @ ( image_mset_nat_a @ G ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ F @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(515,plain,
( ( ! [F: a > nat,G: nat > a] :
( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ F ) @ ( image_mset_nat_a @ G ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ F @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(516,plain,
( ( ! [F: nat > a,G: nat > nat] :
( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ F ) @ ( image_mset_nat_nat @ G ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ F @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(517,plain,
( ( ! [F: nat > nat,G: nat > nat] :
( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ F ) @ ( image_mset_nat_nat @ G ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ F @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(518,plain,
( ( ! [Xs2: list_a,Ys: list_a] :
( ( ( mset_a @ Xs2 )
= ( mset_a @ Ys ) )
=> ( ( size_size_list_a @ Xs2 )
= ( size_size_list_a @ Ys ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(519,plain,
( ( ! [X: list_a,A2: set_list_a,Y: list_a] :
( ( member_list_a @ X @ A2 )
=> ( ( ord_less_nat @ ( size_size_list_a @ X ) @ ( size_size_list_a @ Y ) )
=> ( X != Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(520,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(521,plain,
( ( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(522,plain,
( ( list_ex_a
= ( ^ [P2: a > $o,Xs3: list_a] :
? [N4: nat] :
( ( ord_less_nat @ N4 @ ( size_size_list_a @ Xs3 ) )
& ( P2 @ ( nth_a @ Xs3 @ N4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(523,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(524,plain,
( ( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(525,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(526,plain,
( ( ( semiri2110766477t_real @ zero_zero_nat )
= zero_zero_real )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(527,plain,
( ( ! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(528,plain,
( ( ! [N: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(529,plain,
( ( ! [N: nat] :
( ( zero_zero_real
= ( semiri2110766477t_real @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(530,plain,
( ( ! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(531,plain,
( ( ! [M: nat] :
( ( ( semiri2019852685at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(532,plain,
( ( ! [M: nat] :
( ( ( semiri2110766477t_real @ M )
= zero_zero_real )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(533,plain,
( ( ! [A: nat,B3: nat] :
( ( image_nat_int @ semiri2019852685at_int @ ( set_or562006527an_nat @ A @ B3 ) )
= ( set_or1199280219an_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(534,plain,
( ( ! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(535,plain,
( ( ! [G: nat > nat,F: nat > nat] :
( ( comp_m346803701et_nat @ ( size_multiset_nat @ G ) @ ( image_mset_nat_nat @ F ) )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ G @ F ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(536,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(537,plain,
( ( ! [N: nat,M: nat] :
( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) )
= ( semiri2019852685at_int @ M ) )
= ( ( N = zero_zero_nat )
& ( M = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(538,plain,
( ( ! [M: int] :
( ! [N2: nat] :
( M
!= ( semiri2019852685at_int @ N2 ) )
=> ~ ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( M
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ N2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(539,plain,
( ( ! [N: nat] :
( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(540,plain,
( ( zero_zero_nat
= ( nat2 @ zero_zero_int ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(541,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(542,plain,
( ( ! [I: nat,J: nat,M: nat,N: nat] :
( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ I @ J ) @ ( set_or562006527an_nat @ M @ N ) )
= ( ( ord_less_eq_nat @ J @ I )
| ( ( ord_less_eq_nat @ M @ I )
& ( ord_less_eq_nat @ J @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(543,plain,
( ( ! [I: nat,L: nat,U: nat] :
( ( member_nat @ I @ ( set_or562006527an_nat @ L @ U ) )
= ( ( ord_less_eq_nat @ L @ I )
& ( ord_less_nat @ I @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(544,plain,
( ( ! [Z2: int] :
( ( ord_less_eq_int @ Z2 @ zero_zero_int )
=> ( ( nat2 @ Z2 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(545,plain,
( ( ! [I: int] :
( ( ( nat2 @ I )
= zero_zero_nat )
= ( ord_less_eq_int @ I @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(546,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(547,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(548,plain,
( ( ! [SX0: nat,SX1: list_a,SX2: a > a] :
( ~ ( ord_less_nat @ SX0 @ ( size_size_list_a @ SX1 ) )
| ( ( nth_a @ ( map_a_a @ SX2 @ SX1 ) @ SX0 )
= ( SX2 @ ( nth_a @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(549,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)],[486]) ).
thf(550,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)],[462]) ).
thf(551,plain,
( ( ! [SX0: nat > nat,SX1: set_nat] :
( ~ ( inj_on_nat_nat @ SX0 @ SX1 )
| ( ( image_mset_nat_nat @ SX0 @ ( mset_set_nat @ SX1 ) )
= ( mset_set_nat @ ( image_nat_nat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(552,plain,
( ( ! [SX0: a > a,SX1: list_a,SX2: nat > a,SX3: list_nat] :
( ( ( map_a_a @ SX0 @ SX1 )
!= ( map_nat_a @ SX2 @ SX3 ) )
| ( ( size_size_list_a @ SX1 )
= ( size_size_list_nat @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(553,plain,
( ( ! [SX0: nat] :
( ( ord_less_nat @ zero_zero_nat @ SX0 )
= ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(554,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(555,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SX0 @ SX1 ) @ ( set_or562006527an_nat @ SX2 @ SX3 ) )
= ( ( ord_less_eq_nat @ SX1 @ SX0 )
| ~ ( ~ ( ord_less_eq_nat @ SX2 @ SX0 )
| ~ ( ord_less_eq_nat @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(556,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( ( set_or562006527an_nat @ SX0 @ SX1 )
!= ( set_or562006527an_nat @ SX2 @ SX3 ) )
| ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(557,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(558,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(559,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX2 )
| ~ ~ ( SX0 @ SX2 )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ~ ( SX0 @ SX3 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(560,plain,
( ( ! [SX0: int] :
( ~ ( ord_less_eq_int @ SX0 @ zero_zero_int )
| ( ( nat2 @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(561,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SX0 ) )
= ( semiri2019852685at_int @ SX1 ) )
= ( ~ ( ( SX0 != zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(562,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(563,plain,
( ( ! [SX0: int] :
( ~ ! [SX1: nat] :
( SX0
!= ( semiri2019852685at_int @ SX1 ) )
| ~ ! [SX1: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX1 )
| ( SX0
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(564,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( ( ( set_or562006527an_nat @ SX0 @ SX1 )
= ( set_or562006527an_nat @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(565,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)],[483]) ).
thf(566,plain,
( ( ! [SX0: list_a,SX1: list_a] :
( ( ( mset_a @ SX0 )
!= ( mset_a @ SX1 ) )
| ( ( size_size_list_a @ SX0 )
= ( size_size_list_a @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(567,plain,
( ( ! [SX0: nat > a,SX1: list_nat,SX2: a > a,SX3: list_a] :
( ( ( map_nat_a @ SX0 @ SX1 )
!= ( map_a_a @ SX2 @ SX3 ) )
| ( ( size_size_list_nat @ SX1 )
= ( size_size_list_a @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(568,plain,
( ( ! [SX0: list_a,SX1: set_list_a,SX2: list_a] :
( ~ ( member_list_a @ SX0 @ SX1 )
| ~ ( ord_less_nat @ ( size_size_list_a @ SX0 ) @ ( size_size_list_a @ SX2 ) )
| ( SX0 != SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(569,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(570,plain,
( ( ! [SX0: nat > a,SX1: set_nat] :
( ~ ( inj_on_nat_a @ SX0 @ SX1 )
| ( ( image_mset_nat_a @ SX0 @ ( mset_set_nat @ SX1 ) )
= ( mset_set_a @ ( image_nat_a @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(571,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ SX0 @ ( size_size_list_a @ xs ) )
| ( ( nth_a @ xs @ SX0 )
= ( nth_a @ ys @ ( f @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(572,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
( ( ( set_or562006527an_nat @ SX0 @ SX1 )
!= ( set_or562006527an_nat @ SX2 @ SX3 ) )
| ~ ( ord_less_nat @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX3 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(573,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)],[461]) ).
thf(574,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)],[522]) ).
thf(575,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) )
= ( ~ ! [SX2: nat] :
~ ~ ( ~ ( member_nat @ SX2 @ ( set_or562006527an_nat @ zero_zero_nat @ SX0 ) )
| ~ ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(576,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( member_nat @ SX0 @ ( set_or562006527an_nat @ SX1 @ SX2 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SX1 @ SX0 )
| ~ ( ord_less_nat @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(577,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)],[487]) ).
thf(578,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(579,plain,
( ( ! [SX0: nat] :
~ ! [SX1: list_a] :
( ( size_size_list_a @ SX1 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(580,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) )
= ( ! [SX2: nat] :
( ~ ( member_nat @ SX2 @ ( set_or562006527an_nat @ zero_zero_nat @ SX0 ) )
| ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(581,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)],[488]) ).
thf(582,plain,
! [SV1: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 ) )
= ( SV1 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(583,plain,
! [SV2: nat] :
( ( ~ ( ord_less_nat @ SV2 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(584,plain,
! [SV3: nat > a] :
( ( ! [SY171: list_nat] :
( ( size_size_list_a @ ( map_nat_a @ SV3 @ SY171 ) )
= ( size_size_list_nat @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(585,plain,
! [SV4: a > a] :
( ( ! [SY172: list_a] :
( ( size_size_list_a @ ( map_a_a @ SV4 @ SY172 ) )
= ( size_size_list_a @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(586,plain,
! [SV5: nat] :
( ( ~ ( ord_less_nat @ SV5 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(587,plain,
! [SV6: nat] :
( ( ~ ( ord_less_nat @ SV6 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(588,plain,
! [SV7: nat] :
( ( ~ ( ord_less_nat @ SV7 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(589,plain,
! [SV8: nat] :
( ( ~ ( ord_less_nat @ SV8 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(590,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 ) )
= ( SV9 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(591,plain,
! [SV10: nat] :
( ( ( zero_zero_nat = SV10 )
= ( SV10 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(592,plain,
! [SV11: nat > a] :
( ( ! [SY173: list_nat] :
( ( mset_a @ ( map_nat_a @ SV11 @ SY173 ) )
= ( image_mset_nat_a @ SV11 @ ( mset_nat @ SY173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(593,plain,
! [SV12: nat > nat] :
( ( ! [SY174: list_nat] :
( ( mset_nat @ ( map_nat_nat @ SV12 @ SY174 ) )
= ( image_mset_nat_nat @ SV12 @ ( mset_nat @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(594,plain,
! [SV13: list_a] :
( ( ( size_size_multiset_a @ ( mset_a @ SV13 ) )
= ( size_size_list_a @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(595,plain,
( ( ! [SV14: nat] :
( ( set_ord_lessThan_nat @ SV14 )
= ( set_or562006527an_nat @ zero_zero_nat @ SV14 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[495]) ).
thf(596,plain,
( ( set_ord_lessThan_nat
= ( set_or562006527an_nat @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[495]) ).
thf(597,plain,
! [SV15: nat > a] :
( ( ( image_mset_nat_a @ SV15 @ zero_z2005226153et_nat )
= zero_zero_multiset_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(598,plain,
! [SV16: nat > nat] :
( ( ( image_mset_nat_nat @ SV16 @ zero_z2005226153et_nat )
= zero_z2005226153et_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(599,plain,
! [SV17: nat > a] :
( ( ! [SY175: multiset_nat] :
( ( ( image_mset_nat_a @ SV17 @ SY175 )
= zero_zero_multiset_a )
= ( SY175 = zero_z2005226153et_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(600,plain,
! [SV18: nat > nat] :
( ( ! [SY176: multiset_nat] :
( ( ( image_mset_nat_nat @ SV18 @ SY176 )
= zero_z2005226153et_nat )
= ( SY176 = zero_z2005226153et_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(601,plain,
! [SV19: nat > a] :
( ( ! [SY177: multiset_nat] :
( ( size_size_multiset_a @ ( image_mset_nat_a @ SV19 @ SY177 ) )
= ( size_s1679505588et_nat @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(602,plain,
! [SV20: nat > nat] :
( ( ! [SY178: multiset_nat] :
( ( size_s1679505588et_nat @ ( image_mset_nat_nat @ SV20 @ SY178 ) )
= ( size_s1679505588et_nat @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(603,plain,
! [SV21: nat] :
( ( ! [SY179: nat] :
( ( mset_nat @ ( upt @ SV21 @ SY179 ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ SV21 @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(604,plain,
! [SV22: a > a] :
( ( ! [SY180: nat > a,SY181: multiset_nat] :
( ( image_mset_a_a @ SV22 @ ( image_mset_nat_a @ SY180 @ SY181 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV22 @ SY180 ) @ SY181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(605,plain,
! [SV23: a > nat] :
( ( ! [SY182: nat > a,SY183: multiset_nat] :
( ( image_mset_a_nat @ SV23 @ ( image_mset_nat_a @ SY182 @ SY183 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV23 @ SY182 ) @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(606,plain,
! [SV24: nat > a] :
( ( ! [SY184: nat > nat,SY185: multiset_nat] :
( ( image_mset_nat_a @ SV24 @ ( image_mset_nat_nat @ SY184 @ SY185 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV24 @ SY184 ) @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(607,plain,
! [SV25: nat > nat] :
( ( ! [SY186: nat > nat,SY187: multiset_nat] :
( ( image_mset_nat_nat @ SV25 @ ( image_mset_nat_nat @ SY186 @ SY187 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV25 @ SY186 ) @ SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(608,plain,
! [SV26: a > a] :
( ( ! [SY188: nat > a,SY189: multiset_nat] :
( ( image_mset_a_a @ SV26 @ ( image_mset_nat_a @ SY188 @ SY189 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV26 @ SY188 ) @ SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(609,plain,
! [SV27: a > nat] :
( ( ! [SY190: nat > a,SY191: multiset_nat] :
( ( image_mset_a_nat @ SV27 @ ( image_mset_nat_a @ SY190 @ SY191 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV27 @ SY190 ) @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(610,plain,
! [SV28: nat > a] :
( ( ! [SY192: nat > nat,SY193: multiset_nat] :
( ( image_mset_nat_a @ SV28 @ ( image_mset_nat_nat @ SY192 @ SY193 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV28 @ SY192 ) @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(611,plain,
! [SV29: nat > nat] :
( ( ! [SY194: nat > nat,SY195: multiset_nat] :
( ( image_mset_nat_nat @ SV29 @ ( image_mset_nat_nat @ SY194 @ SY195 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV29 @ SY194 ) @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(612,plain,
! [SV30: a > a] :
( ( ! [SY196: nat > a] :
( ( comp_m540523139et_nat @ ( image_mset_a_a @ SV30 ) @ ( image_mset_nat_a @ SY196 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV30 @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(613,plain,
! [SV31: a > nat] :
( ( ! [SY197: nat > a] :
( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ SV31 ) @ ( image_mset_nat_a @ SY197 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV31 @ SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(614,plain,
! [SV32: nat > a] :
( ( ! [SY198: nat > nat] :
( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ SV32 ) @ ( image_mset_nat_nat @ SY198 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV32 @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(615,plain,
! [SV33: nat > nat] :
( ( ! [SY199: nat > nat] :
( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ SV33 ) @ ( image_mset_nat_nat @ SY199 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV33 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(616,plain,
( ( ord_less_nat @ zero_zero_nat @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(617,plain,
( ( ! [SV34: list_a] :
( ( size_size_list_a @ SV34 )
= ( gen_length_a @ zero_zero_nat @ SV34 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[521]) ).
thf(618,plain,
( ( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[521]) ).
thf(619,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= ( ord_less_nat @ zero_zero_nat @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(620,plain,
! [SV36: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= ( zero_zero_nat = SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(621,plain,
! [SV37: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= ( zero_zero_nat = SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(622,plain,
! [SV38: nat] :
( ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= ( zero_zero_nat = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(623,plain,
! [SV39: nat] :
( ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= ( SV39 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(624,plain,
! [SV40: nat] :
( ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= ( SV40 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(625,plain,
! [SV41: nat] :
( ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= ( SV41 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(626,plain,
! [SV42: nat] :
( ( ! [SY200: nat] :
( ( image_nat_int @ semiri2019852685at_int @ ( set_or562006527an_nat @ SV42 @ SY200 ) )
= ( set_or1199280219an_int @ ( semiri2019852685at_int @ SV42 ) @ ( semiri2019852685at_int @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(627,plain,
! [SV43: nat] :
( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV43 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(628,plain,
! [SV44: nat > nat] :
( ( ! [SY201: nat > nat] :
( ( comp_m346803701et_nat @ ( size_multiset_nat @ SV44 ) @ ( image_mset_nat_nat @ SY201 ) )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ SV44 @ SY201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(629,plain,
! [SV45: nat] :
( ( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ SV45 ) ) )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(630,plain,
! [SV46: nat] :
( ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= ( SV46 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(631,plain,
! [SV47: int] :
( ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(632,plain,
! [SV48: $o] :
( ( ( SV48 = $true )
| ( SV48 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[546]) ).
thf(633,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[546]) ).
thf(634,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[546]) ).
thf(635,plain,
( ( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(636,plain,
! [SV49: nat] :
( ( ! [SY202: list_a,SY203: a > a] :
( ~ ( ord_less_nat @ SV49 @ ( size_size_list_a @ SY202 ) )
| ( ( nth_a @ ( map_a_a @ SY203 @ SY202 ) @ SV49 )
= ( SY203 @ ( nth_a @ SY202 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(637,plain,
( ( ! [SV50: list_a] :
( ( ^ [SY204: list_a] : ( SV50 = SY204 ) )
= ( ^ [SY205: list_a] :
~ ( ( ( size_size_list_a @ SV50 )
!= ( size_size_list_a @ SY205 ) )
| ~ ! [SY206: nat] :
( ~ ( ord_less_nat @ SY206 @ ( size_size_list_a @ SV50 ) )
| ( ( nth_a @ SV50 @ SY206 )
= ( nth_a @ SY205 @ SY206 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[549]) ).
thf(638,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)],[549]) ).
thf(639,plain,
! [SV51: list_a] :
( ( ! [SY207: list_a] :
( ~ ( ( ( size_size_list_a @ SV51 )
!= ( size_size_list_a @ SY207 ) ) )
| ( SV51 != SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(640,plain,
! [SV52: nat > nat] :
( ( ! [SY208: set_nat] :
( ~ ( inj_on_nat_nat @ SV52 @ SY208 )
| ( ( image_mset_nat_nat @ SV52 @ ( mset_set_nat @ SY208 ) )
= ( mset_set_nat @ ( image_nat_nat @ SV52 @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(641,plain,
! [SV53: a > a] :
( ( ! [SY209: list_a,SY210: nat > a,SY211: list_nat] :
( ( ( map_a_a @ SV53 @ SY209 )
!= ( map_nat_a @ SY210 @ SY211 ) )
| ( ( size_size_list_a @ SY209 )
= ( size_size_list_nat @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(642,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= ( SV54 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(643,plain,
! [SV55: nat] :
( ( ! [SY212: nat] :
( ~ ( ord_less_nat @ SV55 @ SY212 )
| ( SY212 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(644,plain,
! [SV56: nat] :
( ( ! [SY213: nat,SY214: nat,SY215: nat] :
( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SY213 ) @ ( set_or562006527an_nat @ SY214 @ SY215 ) )
= ( ( ord_less_eq_nat @ SY213 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SY214 @ SV56 )
| ~ ( ord_less_eq_nat @ SY213 @ SY215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(645,plain,
! [SV57: nat] :
( ( ! [SY216: nat,SY217: nat,SY218: nat] :
( ( ( set_or562006527an_nat @ SV57 @ SY216 )
!= ( set_or562006527an_nat @ SY217 @ SY218 ) )
| ~ ( ord_less_nat @ SV57 @ SY216 )
| ~ ( ord_less_nat @ SY217 @ SY218 )
| ( SV57 = SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(646,plain,
! [SV58: nat] :
( ( ~ ( ( SV58 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(647,plain,
! [SV59: nat] :
( ( ! [SY219: nat] :
( ~ ( ord_less_nat @ SV59 @ SY219 )
| ( SY219 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(648,plain,
! [SV60: nat > $o] :
( ( ! [SY220: nat] :
( ~ ( SV60 @ zero_zero_nat )
| ~ ! [SY221: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY221 )
| ~ ~ ( SV60 @ SY221 )
| ~ ! [SY222: nat] :
~ ~ ( ~ ( ord_less_nat @ SY222 @ SY221 )
| ~ ~ ( SV60 @ SY222 ) ) )
| ( SV60 @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(649,plain,
! [SV61: int] :
( ( ~ ( ord_less_eq_int @ SV61 @ zero_zero_int )
| ( ( nat2 @ SV61 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(650,plain,
! [SV62: nat] :
( ( ! [SY223: nat] :
( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SY223 ) )
= ( ~ ( ( SV62 != zero_zero_nat )
| ( SY223 != zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(651,plain,
! [SV63: nat] :
( ( ( SV63 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(652,plain,
! [SV64: int] :
( ( ~ ! [SY224: nat] :
( SV64
!= ( semiri2019852685at_int @ SY224 ) )
| ~ ! [SY225: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY225 )
| ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ SY225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(653,plain,
! [SV65: nat] :
( ( ! [SY226: nat,SY227: nat,SY228: nat] :
( ~ ( ord_less_nat @ SV65 @ SY226 )
| ~ ( ord_less_nat @ SY227 @ SY228 )
| ( ( ( set_or562006527an_nat @ SV65 @ SY226 )
= ( set_or562006527an_nat @ SY227 @ SY228 ) )
= ( ~ ( ( SV65 != SY227 )
| ( SY226 != SY228 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(654,plain,
! [SV66: list_a > $o] :
( ( ! [SY229: list_a] :
( ~ ! [SY230: list_a] :
( ~ ! [SY231: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY231 ) @ ( size_size_list_a @ SY230 ) )
| ( SV66 @ SY231 ) )
| ( SV66 @ SY230 ) )
| ( SV66 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(655,plain,
! [SV67: list_a] :
( ( ! [SY232: list_a] :
( ( ( mset_a @ SV67 )
!= ( mset_a @ SY232 ) )
| ( ( size_size_list_a @ SV67 )
= ( size_size_list_a @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(656,plain,
! [SV68: nat > a] :
( ( ! [SY233: list_nat,SY234: a > a,SY235: list_a] :
( ( ( map_nat_a @ SV68 @ SY233 )
!= ( map_a_a @ SY234 @ SY235 ) )
| ( ( size_size_list_nat @ SY233 )
= ( size_size_list_a @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(657,plain,
! [SV69: list_a] :
( ( ! [SY236: set_list_a,SY237: list_a] :
( ~ ( member_list_a @ SV69 @ SY236 )
| ~ ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SY237 ) )
| ( SV69 != SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(658,plain,
! [SV70: nat] :
( ( ( SV70 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(659,plain,
! [SV71: nat > a] :
( ( ! [SY238: set_nat] :
( ~ ( inj_on_nat_a @ SV71 @ SY238 )
| ( ( image_mset_nat_a @ SV71 @ ( mset_set_nat @ SY238 ) )
= ( mset_set_a @ ( image_nat_a @ SV71 @ SY238 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(660,plain,
! [SV72: nat] :
( ( ~ ( ord_less_nat @ SV72 @ ( size_size_list_a @ xs ) )
| ( ( nth_a @ xs @ SV72 )
= ( nth_a @ ys @ ( f @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(661,plain,
! [SV73: nat] :
( ( ! [SY239: nat,SY240: nat,SY241: nat] :
( ( ( set_or562006527an_nat @ SV73 @ SY239 )
!= ( set_or562006527an_nat @ SY240 @ SY241 ) )
| ~ ( ord_less_nat @ SV73 @ SY239 )
| ~ ( ord_less_nat @ SY240 @ SY241 )
| ( SY239 = SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(662,plain,
! [SV74: list_a] :
( ( ! [SY242: list_a] :
( ~ ( ( ( size_size_list_a @ SV74 )
!= ( size_size_list_a @ SY242 ) ) )
| ( SV74 != SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(663,plain,
( ( ! [SV75: a > $o] :
( ( list_ex_a @ SV75 )
= ( ^ [SY243: list_a] :
~ ! [SY244: nat] :
~ ~ ( ~ ( ord_less_nat @ SY244 @ ( size_size_list_a @ SY243 ) )
| ~ ( SV75 @ ( nth_a @ SY243 @ SY244 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[574]) ).
thf(664,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)],[574]) ).
thf(665,plain,
! [SV76: nat] :
( ( ! [SY245: nat > $o] :
( ( ~ ! [SY246: nat] :
~ ~ ( ~ ( ord_less_nat @ SY246 @ SV76 )
| ~ ( SY245 @ SY246 ) ) )
= ( ~ ! [SY247: nat] :
~ ~ ( ~ ( member_nat @ SY247 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SY245 @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(666,plain,
! [SV77: nat] :
( ( ! [SY248: nat,SY249: nat] :
( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SY248 @ SY249 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SY248 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SY249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(667,plain,
! [SV78: nat] :
( ( ! [SY250: nat > a > $o] :
( ( ! [SY251: nat] :
( ~ ( ord_less_nat @ SY251 @ SV78 )
| ~ ! [SX3: a] :
~ ( SY250 @ SY251 @ SX3 ) ) )
= ( ~ ! [SY253: list_a] :
~ ~ ( ( ( size_size_list_a @ SY253 )
!= SV78 )
| ~ ! [SY254: nat] :
( ~ ( ord_less_nat @ SY254 @ SV78 )
| ( SY250 @ SY254 @ ( nth_a @ SY253 @ SY254 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(668,plain,
! [SV79: nat] :
( ( ~ ( ( SV79 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(669,plain,
! [SV80: nat] :
( ( ~ ! [SY255: list_a] :
( ( size_size_list_a @ SY255 )
!= SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(670,plain,
! [SV81: nat] :
( ( ! [SY256: nat > $o] :
( ( ! [SY257: nat] :
( ~ ( ord_less_nat @ SY257 @ SV81 )
| ( SY256 @ SY257 ) ) )
= ( ! [SY258: nat] :
( ~ ( member_nat @ SY258 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SY256 @ SY258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(671,plain,
! [SV82: list_a] :
( ( ! [SY259: list_a] :
( ( ( size_size_list_a @ SV82 )
!= ( size_size_list_a @ SY259 ) )
| ~ ! [SY260: nat] :
( ~ ( ord_less_nat @ SY260 @ ( size_size_list_a @ SV82 ) )
| ( ( nth_a @ SV82 @ SY260 )
= ( nth_a @ SY259 @ SY260 ) ) )
| ( SV82 = SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(672,plain,
! [SV1: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[582]) ).
thf(673,plain,
! [SV1: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 ) )
= ( SV1 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[582]) ).
thf(674,plain,
! [SV2: nat] :
( ( ord_less_nat @ SV2 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(675,plain,
! [SV83: list_nat,SV3: nat > a] :
( ( ( size_size_list_a @ ( map_nat_a @ SV3 @ SV83 ) )
= ( size_size_list_nat @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(676,plain,
! [SV84: list_a,SV4: a > a] :
( ( ( size_size_list_a @ ( map_a_a @ SV4 @ SV84 ) )
= ( size_size_list_a @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(677,plain,
! [SV5: nat] :
( ( ord_less_nat @ SV5 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(678,plain,
! [SV6: nat] :
( ( ord_less_nat @ SV6 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(679,plain,
! [SV7: nat] :
( ( ord_less_nat @ SV7 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(680,plain,
! [SV8: nat] :
( ( ord_less_nat @ SV8 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(681,plain,
! [SV9: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[590]) ).
thf(682,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 ) )
= ( SV9 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[590]) ).
thf(683,plain,
! [SV10: nat] :
( ( ~ ( ( zero_zero_nat = SV10 )
| ( SV10 = zero_zero_nat ) )
| ~ ( ( zero_zero_nat != SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[591]) ).
thf(684,plain,
! [SV10: nat] :
( ( ( zero_zero_nat = SV10 )
= ( SV10 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[591]) ).
thf(685,plain,
! [SV85: list_nat,SV11: nat > a] :
( ( ( mset_a @ ( map_nat_a @ SV11 @ SV85 ) )
= ( image_mset_nat_a @ SV11 @ ( mset_nat @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(686,plain,
! [SV86: list_nat,SV12: nat > nat] :
( ( ( mset_nat @ ( map_nat_nat @ SV12 @ SV86 ) )
= ( image_mset_nat_nat @ SV12 @ ( mset_nat @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(687,plain,
! [SV87: nat] :
( ( ( set_ord_lessThan_nat @ SV87 )
= ( set_or562006527an_nat @ zero_zero_nat @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(688,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= ( SV88 = zero_z2005226153et_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(689,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= ( SV89 = zero_z2005226153et_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(690,plain,
! [SV90: multiset_nat,SV19: nat > a] :
( ( ( size_size_multiset_a @ ( image_mset_nat_a @ SV19 @ SV90 ) )
= ( size_s1679505588et_nat @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(691,plain,
! [SV91: multiset_nat,SV20: nat > nat] :
( ( ( size_s1679505588et_nat @ ( image_mset_nat_nat @ SV20 @ SV91 ) )
= ( size_s1679505588et_nat @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(692,plain,
! [SV92: nat,SV21: nat] :
( ( ( mset_nat @ ( upt @ SV21 @ SV92 ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ SV21 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(693,plain,
! [SV93: nat > a,SV22: a > a] :
( ( ! [SY261: multiset_nat] :
( ( image_mset_a_a @ SV22 @ ( image_mset_nat_a @ SV93 @ SY261 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV22 @ SV93 ) @ SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(694,plain,
! [SV94: nat > a,SV23: a > nat] :
( ( ! [SY262: multiset_nat] :
( ( image_mset_a_nat @ SV23 @ ( image_mset_nat_a @ SV94 @ SY262 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV23 @ SV94 ) @ SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(695,plain,
! [SV95: nat > nat,SV24: nat > a] :
( ( ! [SY263: multiset_nat] :
( ( image_mset_nat_a @ SV24 @ ( image_mset_nat_nat @ SV95 @ SY263 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV24 @ SV95 ) @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(696,plain,
! [SV96: nat > nat,SV25: nat > nat] :
( ( ! [SY264: multiset_nat] :
( ( image_mset_nat_nat @ SV25 @ ( image_mset_nat_nat @ SV96 @ SY264 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV25 @ SV96 ) @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(697,plain,
! [SV97: nat > a,SV26: a > a] :
( ( ! [SY265: multiset_nat] :
( ( image_mset_a_a @ SV26 @ ( image_mset_nat_a @ SV97 @ SY265 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV26 @ SV97 ) @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(698,plain,
! [SV98: nat > a,SV27: a > nat] :
( ( ! [SY266: multiset_nat] :
( ( image_mset_a_nat @ SV27 @ ( image_mset_nat_a @ SV98 @ SY266 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV27 @ SV98 ) @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(699,plain,
! [SV99: nat > nat,SV28: nat > a] :
( ( ! [SY267: multiset_nat] :
( ( image_mset_nat_a @ SV28 @ ( image_mset_nat_nat @ SV99 @ SY267 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV28 @ SV99 ) @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(700,plain,
! [SV100: nat > nat,SV29: nat > nat] :
( ( ! [SY268: multiset_nat] :
( ( image_mset_nat_nat @ SV29 @ ( image_mset_nat_nat @ SV100 @ SY268 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV29 @ SV100 ) @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(701,plain,
! [SV101: nat > a,SV30: a > a] :
( ( ( comp_m540523139et_nat @ ( image_mset_a_a @ SV30 ) @ ( image_mset_nat_a @ SV101 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV30 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(702,plain,
! [SV102: nat > a,SV31: a > nat] :
( ( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ SV31 ) @ ( image_mset_nat_a @ SV102 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV31 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(703,plain,
! [SV103: nat > nat,SV32: nat > a] :
( ( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ SV32 ) @ ( image_mset_nat_nat @ SV103 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV32 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(704,plain,
! [SV104: nat > nat,SV33: nat > nat] :
( ( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ SV33 ) @ ( image_mset_nat_nat @ SV104 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV33 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(705,plain,
! [SV105: list_a] :
( ( ( size_size_list_a @ SV105 )
= ( gen_length_a @ zero_zero_nat @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(706,plain,
! [SV35: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ( ord_less_nat @ zero_zero_nat @ SV35 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[619]) ).
thf(707,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= ( ord_less_nat @ zero_zero_nat @ SV35 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[619]) ).
thf(708,plain,
! [SV36: nat] :
( ( ~ ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat = SV36 ) )
| ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat != SV36 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[620]) ).
thf(709,plain,
! [SV36: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= ( zero_zero_nat = SV36 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[620]) ).
thf(710,plain,
! [SV37: nat] :
( ( ~ ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat = SV37 ) )
| ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat != SV37 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(711,plain,
! [SV37: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= ( zero_zero_nat = SV37 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(712,plain,
! [SV38: nat] :
( ( ~ ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat = SV38 ) )
| ~ ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat != SV38 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[622]) ).
thf(713,plain,
! [SV38: nat] :
( ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= ( zero_zero_nat = SV38 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[622]) ).
thf(714,plain,
! [SV39: nat] :
( ( ~ ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
| ( SV39 = zero_zero_nat ) )
| ~ ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
| ( SV39 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[623]) ).
thf(715,plain,
! [SV39: nat] :
( ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= ( SV39 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[623]) ).
thf(716,plain,
! [SV40: nat] :
( ( ~ ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
| ( SV40 = zero_zero_nat ) )
| ~ ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
| ( SV40 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[624]) ).
thf(717,plain,
! [SV40: nat] :
( ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= ( SV40 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[624]) ).
thf(718,plain,
! [SV41: nat] :
( ( ~ ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
| ( SV41 = zero_zero_nat ) )
| ~ ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
| ( SV41 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[625]) ).
thf(719,plain,
! [SV41: nat] :
( ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= ( SV41 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[625]) ).
thf(720,plain,
! [SV106: nat,SV42: nat] :
( ( ( image_nat_int @ semiri2019852685at_int @ ( set_or562006527an_nat @ SV42 @ SV106 ) )
= ( set_or1199280219an_int @ ( semiri2019852685at_int @ SV42 ) @ ( semiri2019852685at_int @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(721,plain,
! [SV43: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ SV43 ) @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(722,plain,
! [SV107: nat > nat,SV44: nat > nat] :
( ( ( comp_m346803701et_nat @ ( size_multiset_nat @ SV44 ) @ ( image_mset_nat_nat @ SV107 ) )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ SV44 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(723,plain,
! [SV46: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[630]) ).
thf(724,plain,
! [SV46: nat] :
( ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= ( SV46 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[630]) ).
thf(725,plain,
! [SV47: int] :
( ( ~ ( ( ( nat2 @ SV47 )
= zero_zero_nat )
| ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
| ~ ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
| ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[631]) ).
thf(726,plain,
! [SV47: int] :
( ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[631]) ).
thf(727,plain,
! [SV48: $o] :
( ( ( SV48 = $true )
= $true )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(728,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(729,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(730,plain,
! [SV108: list_a,SV49: nat] :
( ( ! [SY269: a > a] :
( ~ ( ord_less_nat @ SV49 @ ( size_size_list_a @ SV108 ) )
| ( ( nth_a @ ( map_a_a @ SY269 @ SV108 ) @ SV49 )
= ( SY269 @ ( nth_a @ SV108 @ SV49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(731,plain,
! [SV109: list_a] :
( ( ( ^ [SY270: list_a] : ( SV109 = SY270 ) )
= ( ^ [SY271: list_a] :
~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SY271 ) )
| ~ ! [SY272: nat] :
( ~ ( ord_less_nat @ SY272 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY272 )
= ( nth_a @ SY271 @ SY272 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(732,plain,
! [SV110: list_a,SV51: list_a] :
( ( ~ ( ( ( size_size_list_a @ SV51 )
!= ( size_size_list_a @ SV110 ) ) )
| ( SV51 != SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(733,plain,
! [SV111: set_nat,SV52: nat > nat] :
( ( ~ ( inj_on_nat_nat @ SV52 @ SV111 )
| ( ( image_mset_nat_nat @ SV52 @ ( mset_set_nat @ SV111 ) )
= ( mset_set_nat @ ( image_nat_nat @ SV52 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(734,plain,
! [SV112: list_a,SV53: a > a] :
( ( ! [SY273: nat > a,SY274: list_nat] :
( ( ( map_a_a @ SV53 @ SV112 )
!= ( map_nat_a @ SY273 @ SY274 ) )
| ( ( size_size_list_a @ SV112 )
= ( size_size_list_nat @ SY274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(735,plain,
! [SV54: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[642]) ).
thf(736,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= ( SV54 != zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[642]) ).
thf(737,plain,
! [SV113: nat,SV55: nat] :
( ( ~ ( ord_less_nat @ SV55 @ SV113 )
| ( SV113 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(738,plain,
! [SV114: nat,SV56: nat] :
( ( ! [SY275: nat,SY276: nat] :
( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SY275 @ SY276 ) )
= ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SY275 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(739,plain,
! [SV115: nat,SV57: nat] :
( ( ! [SY277: nat,SY278: nat] :
( ( ( set_or562006527an_nat @ SV57 @ SV115 )
!= ( set_or562006527an_nat @ SY277 @ SY278 ) )
| ~ ( ord_less_nat @ SV57 @ SV115 )
| ~ ( ord_less_nat @ SY277 @ SY278 )
| ( SV57 = SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(740,plain,
! [SV58: nat] :
( ( ( ~ ( ( SV58 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(741,plain,
! [SV116: nat,SV59: nat] :
( ( ~ ( ord_less_nat @ SV59 @ SV116 )
| ( SV116 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(742,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ~ ( SV60 @ zero_zero_nat )
| ~ ! [SY221: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY221 )
| ~ ~ ( SV60 @ SY221 )
| ~ ! [SY222: nat] :
~ ~ ( ~ ( ord_less_nat @ SY222 @ SY221 )
| ~ ~ ( SV60 @ SY222 ) ) )
| ( SV60 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(743,plain,
! [SV61: int] :
( ( ( ~ ( ord_less_eq_int @ SV61 @ zero_zero_int ) )
= $true )
| ( ( ( nat2 @ SV61 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(744,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= ( ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(745,plain,
! [SV63: nat] :
( ( ~ ( ( SV63 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV63 ) )
| ~ ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[651]) ).
thf(746,plain,
! [SV63: nat] :
( ( ( SV63 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[651]) ).
thf(747,plain,
! [SV64: int] :
( ( ( ~ ! [SY224: nat] :
( SV64
!= ( semiri2019852685at_int @ SY224 ) ) )
= $true )
| ( ( ~ ! [SY225: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY225 )
| ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ SY225 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(748,plain,
! [SV119: nat,SV65: nat] :
( ( ! [SY281: nat,SY282: nat] :
( ~ ( ord_less_nat @ SV65 @ SV119 )
| ~ ( ord_less_nat @ SY281 @ SY282 )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SY281 @ SY282 ) )
= ( ~ ( ( SV65 != SY281 )
| ( SV119 != SY282 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(749,plain,
! [SV120: list_a,SV66: list_a > $o] :
( ( ~ ! [SY230: list_a] :
( ~ ! [SY231: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY231 ) @ ( size_size_list_a @ SY230 ) )
| ( SV66 @ SY231 ) )
| ( SV66 @ SY230 ) )
| ( SV66 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(750,plain,
! [SV121: list_a,SV67: list_a] :
( ( ( ( mset_a @ SV67 )
!= ( mset_a @ SV121 ) )
| ( ( size_size_list_a @ SV67 )
= ( size_size_list_a @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(751,plain,
! [SV122: list_nat,SV68: nat > a] :
( ( ! [SY285: a > a,SY286: list_a] :
( ( ( map_nat_a @ SV68 @ SV122 )
!= ( map_a_a @ SY285 @ SY286 ) )
| ( ( size_size_list_nat @ SV122 )
= ( size_size_list_a @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(752,plain,
! [SV123: set_list_a,SV69: list_a] :
( ( ! [SY287: list_a] :
( ~ ( member_list_a @ SV69 @ SV123 )
| ~ ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SY287 ) )
| ( SV69 != SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(753,plain,
! [SV70: nat] :
( ( ~ ( ( SV70 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV70 ) )
| ~ ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[658]) ).
thf(754,plain,
! [SV70: nat] :
( ( ( SV70 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV70 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[658]) ).
thf(755,plain,
! [SV124: set_nat,SV71: nat > a] :
( ( ~ ( inj_on_nat_a @ SV71 @ SV124 )
| ( ( image_mset_nat_a @ SV71 @ ( mset_set_nat @ SV124 ) )
= ( mset_set_a @ ( image_nat_a @ SV71 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(756,plain,
! [SV72: nat] :
( ( ( ~ ( ord_less_nat @ SV72 @ ( size_size_list_a @ xs ) ) )
= $true )
| ( ( ( nth_a @ xs @ SV72 )
= ( nth_a @ ys @ ( f @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(757,plain,
! [SV125: nat,SV73: nat] :
( ( ! [SY288: nat,SY289: nat] :
( ( ( set_or562006527an_nat @ SV73 @ SV125 )
!= ( set_or562006527an_nat @ SY288 @ SY289 ) )
| ~ ( ord_less_nat @ SV73 @ SV125 )
| ~ ( ord_less_nat @ SY288 @ SY289 )
| ( SV125 = SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(758,plain,
! [SV126: list_a,SV74: list_a] :
( ( ~ ( ( ( size_size_list_a @ SV74 )
!= ( size_size_list_a @ SV126 ) ) )
| ( SV74 != SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(759,plain,
! [SV127: a > $o] :
( ( ( list_ex_a @ SV127 )
= ( ^ [SY290: list_a] :
~ ! [SY291: nat] :
~ ~ ( ~ ( ord_less_nat @ SY291 @ ( size_size_list_a @ SY290 ) )
| ~ ( SV127 @ ( nth_a @ SY290 @ SY291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(760,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= ( ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(761,plain,
! [SV129: nat,SV77: nat] :
( ( ! [SY294: nat] :
( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SY294 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(762,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= ( ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(763,plain,
! [SV79: nat] :
( ( ( ~ ( ( SV79 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(764,plain,
! [SV80: nat] :
( ( ! [SY255: list_a] :
( ( size_size_list_a @ SY255 )
!= SV80 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(765,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= ( ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(766,plain,
! [SV132: list_a,SV82: list_a] :
( ( ( ( size_size_list_a @ SV82 )
!= ( size_size_list_a @ SV132 ) )
| ~ ! [SY301: nat] :
( ~ ( ord_less_nat @ SY301 @ ( size_size_list_a @ SV82 ) )
| ( ( nth_a @ SV82 @ SY301 )
= ( nth_a @ SV132 @ SY301 ) ) )
| ( SV82 = SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(767,plain,
! [SV1: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(768,plain,
! [SV9: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(769,plain,
! [SV10: nat] :
( ( ( ~ ( ( zero_zero_nat = SV10 )
| ( SV10 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat != SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(770,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ~ ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
| ( SV88 = zero_z2005226153et_nat ) )
| ~ ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
| ( SV88 != zero_z2005226153et_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[688]) ).
thf(771,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= ( SV88 = zero_z2005226153et_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[688]) ).
thf(772,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ~ ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
| ( SV89 = zero_z2005226153et_nat ) )
| ~ ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
| ( SV89 != zero_z2005226153et_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[689]) ).
thf(773,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= ( SV89 = zero_z2005226153et_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[689]) ).
thf(774,plain,
! [SV133: multiset_nat,SV93: nat > a,SV22: a > a] :
( ( ( image_mset_a_a @ SV22 @ ( image_mset_nat_a @ SV93 @ SV133 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV22 @ SV93 ) @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(775,plain,
! [SV134: multiset_nat,SV94: nat > a,SV23: a > nat] :
( ( ( image_mset_a_nat @ SV23 @ ( image_mset_nat_a @ SV94 @ SV134 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV23 @ SV94 ) @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(776,plain,
! [SV135: multiset_nat,SV95: nat > nat,SV24: nat > a] :
( ( ( image_mset_nat_a @ SV24 @ ( image_mset_nat_nat @ SV95 @ SV135 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV24 @ SV95 ) @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(777,plain,
! [SV136: multiset_nat,SV96: nat > nat,SV25: nat > nat] :
( ( ( image_mset_nat_nat @ SV25 @ ( image_mset_nat_nat @ SV96 @ SV136 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV25 @ SV96 ) @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(778,plain,
! [SV137: multiset_nat,SV97: nat > a,SV26: a > a] :
( ( ( image_mset_a_a @ SV26 @ ( image_mset_nat_a @ SV97 @ SV137 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV26 @ SV97 ) @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(779,plain,
! [SV138: multiset_nat,SV98: nat > a,SV27: a > nat] :
( ( ( image_mset_a_nat @ SV27 @ ( image_mset_nat_a @ SV98 @ SV138 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV27 @ SV98 ) @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(780,plain,
! [SV139: multiset_nat,SV99: nat > nat,SV28: nat > a] :
( ( ( image_mset_nat_a @ SV28 @ ( image_mset_nat_nat @ SV99 @ SV139 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV28 @ SV99 ) @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(781,plain,
! [SV140: multiset_nat,SV100: nat > nat,SV29: nat > nat] :
( ( ( image_mset_nat_nat @ SV29 @ ( image_mset_nat_nat @ SV100 @ SV140 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV29 @ SV100 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(782,plain,
! [SV101: nat > a,SV30: a > a] :
( ( ! [SV141: multiset_nat] :
( ( comp_m540523139et_nat @ ( image_mset_a_a @ SV30 ) @ ( image_mset_nat_a @ SV101 ) @ SV141 )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV30 @ SV101 ) @ SV141 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[701]) ).
thf(783,plain,
! [SV101: nat > a,SV30: a > a] :
( ( ( comp_m540523139et_nat @ ( image_mset_a_a @ SV30 ) @ ( image_mset_nat_a @ SV101 ) )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV30 @ SV101 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[701]) ).
thf(784,plain,
! [SV102: nat > a,SV31: a > nat] :
( ( ! [SV142: multiset_nat] :
( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ SV31 ) @ ( image_mset_nat_a @ SV102 ) @ SV142 )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV31 @ SV102 ) @ SV142 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[702]) ).
thf(785,plain,
! [SV102: nat > a,SV31: a > nat] :
( ( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ SV31 ) @ ( image_mset_nat_a @ SV102 ) )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV31 @ SV102 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[702]) ).
thf(786,plain,
! [SV103: nat > nat,SV32: nat > a] :
( ( ! [SV143: multiset_nat] :
( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ SV32 ) @ ( image_mset_nat_nat @ SV103 ) @ SV143 )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV32 @ SV103 ) @ SV143 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[703]) ).
thf(787,plain,
! [SV103: nat > nat,SV32: nat > a] :
( ( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ SV32 ) @ ( image_mset_nat_nat @ SV103 ) )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV32 @ SV103 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[703]) ).
thf(788,plain,
! [SV104: nat > nat,SV33: nat > nat] :
( ( ! [SV144: multiset_nat] :
( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ SV33 ) @ ( image_mset_nat_nat @ SV104 ) @ SV144 )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV33 @ SV104 ) @ SV144 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(789,plain,
! [SV104: nat > nat,SV33: nat > nat] :
( ( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ SV33 ) @ ( image_mset_nat_nat @ SV104 ) )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV33 @ SV104 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(790,plain,
! [SV35: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ( ord_less_nat @ zero_zero_nat @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(791,plain,
! [SV36: nat] :
( ( ( ~ ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat = SV36 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat != SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(792,plain,
! [SV37: nat] :
( ( ( ~ ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat = SV37 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat != SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(793,plain,
! [SV38: nat] :
( ( ( ~ ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat = SV38 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat != SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(794,plain,
! [SV39: nat] :
( ( ( ~ ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
| ( SV39 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
| ( SV39 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(795,plain,
! [SV40: nat] :
( ( ( ~ ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
| ( SV40 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
| ( SV40 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(796,plain,
! [SV41: nat] :
( ( ( ~ ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
| ( SV41 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
| ( SV41 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(797,plain,
! [SV107: nat > nat,SV44: nat > nat] :
( ( ! [SV145: multiset_nat] :
( ( comp_m346803701et_nat @ ( size_multiset_nat @ SV44 ) @ ( image_mset_nat_nat @ SV107 ) @ SV145 )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ SV44 @ SV107 ) @ SV145 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[722]) ).
thf(798,plain,
! [SV107: nat > nat,SV44: nat > nat] :
( ( ( comp_m346803701et_nat @ ( size_multiset_nat @ SV44 ) @ ( image_mset_nat_nat @ SV107 ) )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ SV44 @ SV107 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[722]) ).
thf(799,plain,
! [SV46: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(800,plain,
! [SV47: int] :
( ( ( ~ ( ( ( nat2 @ SV47 )
= zero_zero_nat )
| ( ord_less_eq_int @ SV47 @ zero_zero_int ) ) )
= $true )
| ( ( ~ ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
| ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(801,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $true )
| ~ ( ~ SV48
| ~ $true ) )
= $true )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[727]) ).
thf(802,plain,
! [SV48: $o] :
( ( ( SV48 = $true )
= $true )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[727]) ).
thf(803,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[728]) ).
thf(804,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[728]) ).
thf(805,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[729]) ).
thf(806,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[729]) ).
thf(807,plain,
! [SV146: a > a,SV108: list_a,SV49: nat] :
( ( ~ ( ord_less_nat @ SV49 @ ( size_size_list_a @ SV108 ) )
| ( ( nth_a @ ( map_a_a @ SV146 @ SV108 ) @ SV49 )
= ( SV146 @ ( nth_a @ SV108 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(808,plain,
! [SV109: list_a] :
( ( ! [SV147: list_a] :
( ( SV109 = SV147 )
= ( ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV147 ) )
| ~ ! [SY302: nat] :
( ~ ( ord_less_nat @ SY302 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY302 )
= ( nth_a @ SV147 @ SY302 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[731]) ).
thf(809,plain,
! [SV109: list_a] :
( ( ( ^ [SY270: list_a] : ( SV109 = SY270 ) )
= ( ^ [SY271: list_a] :
~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SY271 ) )
| ~ ! [SY272: nat] :
( ~ ( ord_less_nat @ SY272 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY272 )
= ( nth_a @ SY271 @ SY272 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[731]) ).
thf(810,plain,
! [SV110: list_a,SV51: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV51 )
!= ( size_size_list_a @ SV110 ) ) ) )
= $true )
| ( ( SV51 != SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(811,plain,
! [SV111: set_nat,SV52: nat > nat] :
( ( ( ~ ( inj_on_nat_nat @ SV52 @ SV111 ) )
= $true )
| ( ( ( image_mset_nat_nat @ SV52 @ ( mset_set_nat @ SV111 ) )
= ( mset_set_nat @ ( image_nat_nat @ SV52 @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(812,plain,
! [SV148: nat > a,SV112: list_a,SV53: a > a] :
( ( ! [SY303: list_nat] :
( ( ( map_a_a @ SV53 @ SV112 )
!= ( map_nat_a @ SV148 @ SY303 ) )
| ( ( size_size_list_a @ SV112 )
= ( size_size_list_nat @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(813,plain,
! [SV54: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(814,plain,
! [SV113: nat,SV55: nat] :
( ( ( ~ ( ord_less_nat @ SV55 @ SV113 ) )
= $true )
| ( ( SV113 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(815,plain,
! [SV149: nat,SV114: nat,SV56: nat] :
( ( ! [SY304: nat] :
( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SY304 ) )
= ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SY304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(816,plain,
! [SV150: nat,SV115: nat,SV57: nat] :
( ( ! [SY305: nat] :
( ( ( set_or562006527an_nat @ SV57 @ SV115 )
!= ( set_or562006527an_nat @ SV150 @ SY305 ) )
| ~ ( ord_less_nat @ SV57 @ SV115 )
| ~ ( ord_less_nat @ SV150 @ SY305 )
| ( SV57 = SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(817,plain,
! [SV58: nat] :
( ( ( SV58 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(818,plain,
! [SV116: nat,SV59: nat] :
( ( ( ~ ( ord_less_nat @ SV59 @ SV116 ) )
= $true )
| ( ( SV116 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(819,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( ~ ( SV60 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY221: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY221 )
| ~ ~ ( SV60 @ SY221 )
| ~ ! [SY222: nat] :
~ ~ ( ~ ( ord_less_nat @ SY222 @ SY221 )
| ~ ~ ( SV60 @ SY222 ) ) )
| ( SV60 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(820,plain,
! [SV61: int] :
( ( ( ord_less_eq_int @ SV61 @ zero_zero_int )
= $false )
| ( ( ( nat2 @ SV61 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(821,plain,
! [SV118: nat,SV62: nat] :
( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
| ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
| ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[744]) ).
thf(822,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= ( ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[744]) ).
thf(823,plain,
! [SV63: nat] :
( ( ( ~ ( ( SV63 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV63 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(824,plain,
! [SV64: int] :
( ( ( ! [SY224: nat] :
( SV64
!= ( semiri2019852685at_int @ SY224 ) ) )
= $false )
| ( ( ~ ! [SY225: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY225 )
| ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ SY225 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(825,plain,
! [SV151: nat,SV119: nat,SV65: nat] :
( ( ! [SY306: nat] :
( ~ ( ord_less_nat @ SV65 @ SV119 )
| ~ ( ord_less_nat @ SV151 @ SY306 )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SY306 ) )
= ( ~ ( ( SV65 != SV151 )
| ( SV119 != SY306 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(826,plain,
! [SV120: list_a,SV66: list_a > $o] :
( ( ( ~ ! [SY230: list_a] :
( ~ ! [SY231: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY231 ) @ ( size_size_list_a @ SY230 ) )
| ( SV66 @ SY231 ) )
| ( SV66 @ SY230 ) ) )
= $true )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(827,plain,
! [SV121: list_a,SV67: list_a] :
( ( ( ( mset_a @ SV67 )
!= ( mset_a @ SV121 ) )
= $true )
| ( ( ( size_size_list_a @ SV67 )
= ( size_size_list_a @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(828,plain,
! [SV152: a > a,SV122: list_nat,SV68: nat > a] :
( ( ! [SY307: list_a] :
( ( ( map_nat_a @ SV68 @ SV122 )
!= ( map_a_a @ SV152 @ SY307 ) )
| ( ( size_size_list_nat @ SV122 )
= ( size_size_list_a @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(829,plain,
! [SV153: list_a,SV123: set_list_a,SV69: list_a] :
( ( ~ ( member_list_a @ SV69 @ SV123 )
| ~ ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SV153 ) )
| ( SV69 != SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(830,plain,
! [SV70: nat] :
( ( ( ~ ( ( SV70 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV70 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(831,plain,
! [SV124: set_nat,SV71: nat > a] :
( ( ( ~ ( inj_on_nat_a @ SV71 @ SV124 ) )
= $true )
| ( ( ( image_mset_nat_a @ SV71 @ ( mset_set_nat @ SV124 ) )
= ( mset_set_a @ ( image_nat_a @ SV71 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(832,plain,
! [SV72: nat] :
( ( ( ord_less_nat @ SV72 @ ( size_size_list_a @ xs ) )
= $false )
| ( ( ( nth_a @ xs @ SV72 )
= ( nth_a @ ys @ ( f @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(833,plain,
! [SV154: nat,SV125: nat,SV73: nat] :
( ( ! [SY308: nat] :
( ( ( set_or562006527an_nat @ SV73 @ SV125 )
!= ( set_or562006527an_nat @ SV154 @ SY308 ) )
| ~ ( ord_less_nat @ SV73 @ SV125 )
| ~ ( ord_less_nat @ SV154 @ SY308 )
| ( SV125 = SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(834,plain,
! [SV126: list_a,SV74: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV74 )
!= ( size_size_list_a @ SV126 ) ) ) )
= $true )
| ( ( SV74 != SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(835,plain,
! [SV127: a > $o] :
( ( ! [SV155: list_a] :
( ( list_ex_a @ SV127 @ SV155 )
= ( ~ ! [SY309: nat] :
~ ~ ( ~ ( ord_less_nat @ SY309 @ ( size_size_list_a @ SV155 ) )
| ~ ( SV127 @ ( nth_a @ SV155 @ SY309 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[759]) ).
thf(836,plain,
! [SV127: a > $o] :
( ( ( list_ex_a @ SV127 )
= ( ^ [SY290: list_a] :
~ ! [SY291: nat] :
~ ~ ( ~ ( ord_less_nat @ SY291 @ ( size_size_list_a @ SY290 ) )
| ~ ( SV127 @ ( nth_a @ SY290 @ SY291 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[759]) ).
thf(837,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ~ ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
| ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[760]) ).
thf(838,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= ( ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[760]) ).
thf(839,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(840,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ~ ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
| ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[762]) ).
thf(841,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= ( ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[762]) ).
thf(842,plain,
! [SV79: nat] :
( ( ( SV79 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(843,plain,
! [SV80: nat] :
( ( ( size_size_list_a @ ( sK1_SY255 @ SV80 ) )
!= SV80 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[764]) ).
thf(844,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ~ ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
| ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[765]) ).
thf(845,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= ( ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[765]) ).
thf(846,plain,
! [SV132: list_a,SV82: list_a] :
( ( ( ( size_size_list_a @ SV82 )
!= ( size_size_list_a @ SV132 ) )
= $true )
| ( ( ~ ! [SY301: nat] :
( ~ ( ord_less_nat @ SY301 @ ( size_size_list_a @ SV82 ) )
| ( ( nth_a @ SV82 @ SY301 )
= ( nth_a @ SV132 @ SY301 ) ) )
| ( SV82 = SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(847,plain,
! [SV1: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(848,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(849,plain,
! [SV10: nat] :
( ( ( ( zero_zero_nat = SV10 )
| ( SV10 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(850,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ~ ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
| ( SV88 = zero_z2005226153et_nat ) ) )
= $true )
| ( ( ~ ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
| ( SV88 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(851,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ~ ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
| ( SV89 = zero_z2005226153et_nat ) ) )
= $true )
| ( ( ~ ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
| ( SV89 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(852,plain,
! [SV157: multiset_nat,SV101: nat > a,SV30: a > a] :
( ( ( comp_m540523139et_nat @ ( image_mset_a_a @ SV30 ) @ ( image_mset_nat_a @ SV101 ) @ SV157 )
= ( image_mset_nat_a @ ( comp_a_a_nat @ SV30 @ SV101 ) @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(853,plain,
! [SV158: multiset_nat,SV102: nat > a,SV31: a > nat] :
( ( ( comp_m1962190563et_nat @ ( image_mset_a_nat @ SV31 ) @ ( image_mset_nat_a @ SV102 ) @ SV158 )
= ( image_mset_nat_nat @ ( comp_a_nat_nat @ SV31 @ SV102 ) @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(854,plain,
! [SV159: multiset_nat,SV103: nat > nat,SV32: nat > a] :
( ( ( comp_m1844659105et_nat @ ( image_mset_nat_a @ SV32 ) @ ( image_mset_nat_nat @ SV103 ) @ SV159 )
= ( image_mset_nat_a @ ( comp_nat_a_nat @ SV32 @ SV103 ) @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(855,plain,
! [SV160: multiset_nat,SV104: nat > nat,SV33: nat > nat] :
( ( ( comp_m1386984005et_nat @ ( image_mset_nat_nat @ SV33 ) @ ( image_mset_nat_nat @ SV104 ) @ SV160 )
= ( image_mset_nat_nat @ ( comp_nat_nat_nat @ SV33 @ SV104 ) @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(856,plain,
! [SV35: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ( ord_less_nat @ zero_zero_nat @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(857,plain,
! [SV36: nat] :
( ( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat = SV36 ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat != SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(858,plain,
! [SV37: nat] :
( ( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat = SV37 ) )
= $false )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat != SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(859,plain,
! [SV38: nat] :
( ( ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat = SV38 ) )
= $false )
| ( ( ~ ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat != SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(860,plain,
! [SV39: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
| ( SV39 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
| ( SV39 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(861,plain,
! [SV40: nat] :
( ( ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
| ( SV40 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
| ( SV40 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(862,plain,
! [SV41: nat] :
( ( ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
| ( SV41 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
| ( SV41 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(863,plain,
! [SV161: multiset_nat,SV107: nat > nat,SV44: nat > nat] :
( ( ( comp_m346803701et_nat @ ( size_multiset_nat @ SV44 ) @ ( image_mset_nat_nat @ SV107 ) @ SV161 )
= ( size_multiset_nat @ ( comp_nat_nat_nat @ SV44 @ SV107 ) @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(864,plain,
! [SV46: nat] :
( ( ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(865,plain,
! [SV47: int] :
( ( ( ( ( nat2 @ SV47 )
= zero_zero_nat )
| ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
= $false )
| ( ( ~ ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
| ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(866,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $true ) )
= $true )
| ( ( ~ ( ~ SV48
| ~ $true ) )
= $true )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(867,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false )
| ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[802]) ).
thf(868,plain,
! [SV48: $o] :
( ( ( SV48 = $false )
= $true )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[802]) ).
thf(869,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(870,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[804]) ).
thf(871,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[804]) ).
thf(872,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(873,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[806]) ).
thf(874,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[806]) ).
thf(875,plain,
! [SV146: a > a,SV108: list_a,SV49: nat] :
( ( ( ~ ( ord_less_nat @ SV49 @ ( size_size_list_a @ SV108 ) ) )
= $true )
| ( ( ( nth_a @ ( map_a_a @ SV146 @ SV108 ) @ SV49 )
= ( SV146 @ ( nth_a @ SV108 @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(876,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 = SV162 )
= ( ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(877,plain,
! [SV110: list_a,SV51: list_a] :
( ( ( ( size_size_list_a @ SV51 )
!= ( size_size_list_a @ SV110 ) )
= $false )
| ( ( SV51 != SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(878,plain,
! [SV111: set_nat,SV52: nat > nat] :
( ( ( inj_on_nat_nat @ SV52 @ SV111 )
= $false )
| ( ( ( image_mset_nat_nat @ SV52 @ ( mset_set_nat @ SV111 ) )
= ( mset_set_nat @ ( image_nat_nat @ SV52 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(879,plain,
! [SV163: list_nat,SV148: nat > a,SV112: list_a,SV53: a > a] :
( ( ( ( map_a_a @ SV53 @ SV112 )
!= ( map_nat_a @ SV148 @ SV163 ) )
| ( ( size_size_list_a @ SV112 )
= ( size_size_list_nat @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(880,plain,
! [SV54: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
| ( SV54 != zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(881,plain,
! [SV113: nat,SV55: nat] :
( ( ( ord_less_nat @ SV55 @ SV113 )
= $false )
| ( ( SV113 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(882,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(883,plain,
! [SV165: nat,SV150: nat,SV115: nat,SV57: nat] :
( ( ( ( set_or562006527an_nat @ SV57 @ SV115 )
!= ( set_or562006527an_nat @ SV150 @ SV165 ) )
| ~ ( ord_less_nat @ SV57 @ SV115 )
| ~ ( ord_less_nat @ SV150 @ SV165 )
| ( SV57 = SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(884,plain,
! [SV58: nat] :
( ( ( SV58 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(885,plain,
! [SV116: nat,SV59: nat] :
( ( ( ord_less_nat @ SV59 @ SV116 )
= $false )
| ( ( SV116 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(886,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( SV60 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY221: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY221 )
| ~ ~ ( SV60 @ SY221 )
| ~ ! [SY222: nat] :
~ ~ ( ~ ( ord_less_nat @ SY222 @ SY221 )
| ~ ~ ( SV60 @ SY222 ) ) )
| ( SV60 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(887,plain,
! [SV118: nat,SV62: nat] :
( ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
| ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(888,plain,
! [SV63: nat] :
( ( ( ( SV63 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( ~ ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(889,plain,
! [SV64: int] :
( ( ( SV64
!= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $false )
| ( ( ~ ! [SY225: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY225 )
| ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ SY225 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[824]) ).
thf(890,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ~ ( ord_less_nat @ SV65 @ SV119 )
| ~ ( ord_less_nat @ SV151 @ SV166 )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(891,plain,
! [SV120: list_a,SV66: list_a > $o] :
( ( ( ! [SY230: list_a] :
( ~ ! [SY231: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY231 ) @ ( size_size_list_a @ SY230 ) )
| ( SV66 @ SY231 ) )
| ( SV66 @ SY230 ) ) )
= $false )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(892,plain,
! [SV121: list_a,SV67: list_a] :
( ( ( ( mset_a @ SV67 )
= ( mset_a @ SV121 ) )
= $false )
| ( ( ( size_size_list_a @ SV67 )
= ( size_size_list_a @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(893,plain,
! [SV167: list_a,SV152: a > a,SV122: list_nat,SV68: nat > a] :
( ( ( ( map_nat_a @ SV68 @ SV122 )
!= ( map_a_a @ SV152 @ SV167 ) )
| ( ( size_size_list_nat @ SV122 )
= ( size_size_list_a @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(894,plain,
! [SV153: list_a,SV123: set_list_a,SV69: list_a] :
( ( ( ~ ( member_list_a @ SV69 @ SV123 ) )
= $true )
| ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SV153 ) )
| ( SV69 != SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(895,plain,
! [SV70: nat] :
( ( ( ( SV70 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV70 ) )
= $false )
| ( ( ~ ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(896,plain,
! [SV124: set_nat,SV71: nat > a] :
( ( ( inj_on_nat_a @ SV71 @ SV124 )
= $false )
| ( ( ( image_mset_nat_a @ SV71 @ ( mset_set_nat @ SV124 ) )
= ( mset_set_a @ ( image_nat_a @ SV71 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(897,plain,
! [SV168: nat,SV154: nat,SV125: nat,SV73: nat] :
( ( ( ( set_or562006527an_nat @ SV73 @ SV125 )
!= ( set_or562006527an_nat @ SV154 @ SV168 ) )
| ~ ( ord_less_nat @ SV73 @ SV125 )
| ~ ( ord_less_nat @ SV154 @ SV168 )
| ( SV125 = SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(898,plain,
! [SV126: list_a,SV74: list_a] :
( ( ( ( size_size_list_a @ SV74 )
!= ( size_size_list_a @ SV126 ) )
= $false )
| ( ( SV74 != SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(899,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( list_ex_a @ SV127 @ SV169 )
= ( ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(900,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ~ ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(901,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ~ ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
| ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[839]) ).
thf(902,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= ( ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[839]) ).
thf(903,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(904,plain,
! [SV79: nat] :
( ( ( SV79 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(905,plain,
! [SV80: nat] :
( ( ( size_size_list_a @ ( sK1_SY255 @ SV80 ) )
= SV80 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(906,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(907,plain,
! [SV132: list_a,SV82: list_a] :
( ( ( ( size_size_list_a @ SV82 )
= ( size_size_list_a @ SV132 ) )
= $false )
| ( ( ~ ! [SY301: nat] :
( ~ ( ord_less_nat @ SY301 @ ( size_size_list_a @ SV82 ) )
| ( ( nth_a @ SV82 @ SY301 )
= ( nth_a @ SV132 @ SY301 ) ) )
| ( SV82 = SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(908,plain,
! [SV1: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(909,plain,
! [SV1: nat] :
( ( ( SV1 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(910,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(911,plain,
! [SV9: nat] :
( ( ( SV9 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(912,plain,
! [SV10: nat] :
( ( ( zero_zero_nat = SV10 )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(913,plain,
! [SV10: nat] :
( ( ( SV10 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV10 )
| ( SV10 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(914,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
| ( SV88 = zero_z2005226153et_nat ) )
= $false )
| ( ( ~ ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
| ( SV88 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(915,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
| ( SV89 = zero_z2005226153et_nat ) )
= $false )
| ( ( ~ ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
| ( SV89 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(916,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(917,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(918,plain,
! [SV36: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat != SV36 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(919,plain,
! [SV36: nat] :
( ( ( zero_zero_nat = SV36 )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat != SV36 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(920,plain,
! [SV37: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $false )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat != SV37 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(921,plain,
! [SV37: nat] :
( ( ( zero_zero_nat = SV37 )
= $false )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat != SV37 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(922,plain,
! [SV38: nat] :
( ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $false )
| ( ( ~ ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat != SV38 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(923,plain,
! [SV38: nat] :
( ( ( zero_zero_nat = SV38 )
= $false )
| ( ( ~ ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat != SV38 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(924,plain,
! [SV39: nat] :
( ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
| ( SV39 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(925,plain,
! [SV39: nat] :
( ( ( SV39 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
| ( SV39 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(926,plain,
! [SV40: nat] :
( ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $false )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
| ( SV40 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(927,plain,
! [SV40: nat] :
( ( ( SV40 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
| ( SV40 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(928,plain,
! [SV41: nat] :
( ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $false )
| ( ( ~ ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
| ( SV41 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(929,plain,
! [SV41: nat] :
( ( ( SV41 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
| ( SV41 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(930,plain,
! [SV46: nat] :
( ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(931,plain,
! [SV46: nat] :
( ( ( SV46 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(932,plain,
! [SV47: int] :
( ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
| ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(933,plain,
! [SV47: int] :
( ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $false )
| ( ( ~ ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
| ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(934,plain,
! [SV48: $o] :
( ( ( SV48
| $true )
= $false )
| ( ( ~ ( ~ SV48
| ~ $true ) )
= $true )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(935,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false ) )
= $true )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(936,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(937,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(938,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(939,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(940,plain,
! [SV146: a > a,SV108: list_a,SV49: nat] :
( ( ( ord_less_nat @ SV49 @ ( size_size_list_a @ SV108 ) )
= $false )
| ( ( ( nth_a @ ( map_a_a @ SV146 @ SV108 ) @ SV49 )
= ( SV146 @ ( nth_a @ SV108 @ SV49 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(941,plain,
! [SV162: list_a,SV109: list_a] :
( ( ~ ( ( SV109 = SV162 )
| ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
| ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[876]) ).
thf(942,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 = SV162 )
= ( ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[876]) ).
thf(943,plain,
! [SV110: list_a,SV51: list_a] :
( ( ( ( size_size_list_a @ SV51 )
= ( size_size_list_a @ SV110 ) )
= $true )
| ( ( SV51 != SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(944,plain,
! [SV163: list_nat,SV148: nat > a,SV112: list_a,SV53: a > a] :
( ( ( ( map_a_a @ SV53 @ SV112 )
!= ( map_nat_a @ SV148 @ SV163 ) )
= $true )
| ( ( ( size_size_list_a @ SV112 )
= ( size_size_list_nat @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(945,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(946,plain,
! [SV54: nat] :
( ( ( SV54 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[880]) ).
thf(947,plain,
! [SV55: nat,SV113: nat] :
( ( ( SV113 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV55 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(948,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ~ ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
| ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[882]) ).
thf(949,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[882]) ).
thf(950,plain,
! [SV165: nat,SV150: nat,SV115: nat,SV57: nat] :
( ( ( ( set_or562006527an_nat @ SV57 @ SV115 )
!= ( set_or562006527an_nat @ SV150 @ SV165 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV57 @ SV115 )
| ~ ( ord_less_nat @ SV150 @ SV165 )
| ( SV57 = SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(951,plain,
! [SV59: nat,SV116: nat] :
( ( ( SV116 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV59 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(952,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( ~ ! [SY221: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY221 )
| ~ ~ ( SV60 @ SY221 )
| ~ ! [SY222: nat] :
~ ~ ( ~ ( ord_less_nat @ SY222 @ SY221 )
| ~ ~ ( SV60 @ SY222 ) ) ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(953,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
| ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(954,plain,
! [SV63: nat] :
( ( ( SV63 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(955,plain,
! [SV63: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false )
| ( ( ~ ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(956,plain,
! [SV64: int] :
( ( ( SV64
= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $true )
| ( ( ~ ! [SY225: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY225 )
| ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ SY225 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(957,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ~ ( ord_less_nat @ SV65 @ SV119 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV151 @ SV166 )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(958,plain,
! [SV66: list_a > $o,SV120: list_a] :
( ( ( ~ ! [SY312: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY312 ) @ ( size_size_list_a @ ( sK3_SY230 @ SV120 @ SV66 ) ) )
| ( SV66 @ SY312 ) )
| ( SV66 @ ( sK3_SY230 @ SV120 @ SV66 ) ) )
= $false )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[891]) ).
thf(959,plain,
! [SV167: list_a,SV152: a > a,SV122: list_nat,SV68: nat > a] :
( ( ( ( map_nat_a @ SV68 @ SV122 )
!= ( map_a_a @ SV152 @ SV167 ) )
= $true )
| ( ( ( size_size_list_nat @ SV122 )
= ( size_size_list_a @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(960,plain,
! [SV153: list_a,SV123: set_list_a,SV69: list_a] :
( ( ( member_list_a @ SV69 @ SV123 )
= $false )
| ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SV153 ) )
| ( SV69 != SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(961,plain,
! [SV70: nat] :
( ( ( SV70 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(962,plain,
! [SV70: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $false )
| ( ( ~ ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(963,plain,
! [SV168: nat,SV154: nat,SV125: nat,SV73: nat] :
( ( ( ( set_or562006527an_nat @ SV73 @ SV125 )
!= ( set_or562006527an_nat @ SV154 @ SV168 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV73 @ SV125 )
| ~ ( ord_less_nat @ SV154 @ SV168 )
| ( SV125 = SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(964,plain,
! [SV126: list_a,SV74: list_a] :
( ( ( ( size_size_list_a @ SV74 )
= ( size_size_list_a @ SV126 ) )
= $true )
| ( ( SV74 != SV126 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(965,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ~ ( ( list_ex_a @ SV127 @ SV169 )
| ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
| ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[899]) ).
thf(966,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( list_ex_a @ SV127 @ SV169 )
= ( ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[899]) ).
thf(967,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(968,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( ~ ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(969,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(970,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(971,plain,
! [SV132: list_a,SV82: list_a] :
( ( ( ~ ! [SY301: nat] :
( ~ ( ord_less_nat @ SY301 @ ( size_size_list_a @ SV82 ) )
| ( ( nth_a @ SV82 @ SY301 )
= ( nth_a @ SV132 @ SY301 ) ) ) )
= $true )
| ( ( SV82 = SV132 )
= $true )
| ( ( ( size_size_list_a @ SV82 )
= ( size_size_list_a @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(972,plain,
! [SV1: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[908]) ).
thf(973,plain,
! [SV1: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) )
= $false )
| ( ( SV1 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(974,plain,
! [SV9: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(975,plain,
! [SV9: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) )
= $false )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(976,plain,
! [SV10: nat] :
( ( ( ( zero_zero_nat != SV10 )
| ( SV10 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat = SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(977,plain,
! [SV10: nat] :
( ( ( ( zero_zero_nat != SV10 )
| ( SV10 != zero_zero_nat ) )
= $false )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(978,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $false )
| ( ( ~ ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
| ( SV88 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(979,plain,
! [SV17: nat > a,SV88: multiset_nat] :
( ( ( SV88 = zero_z2005226153et_nat )
= $false )
| ( ( ~ ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
| ( SV88 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(980,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $false )
| ( ( ~ ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
| ( SV89 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(981,plain,
! [SV18: nat > nat,SV89: multiset_nat] :
( ( ( SV89 = zero_z2005226153et_nat )
= $false )
| ( ( ~ ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
| ( SV89 != zero_z2005226153et_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(982,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(983,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(984,plain,
! [SV36: nat] :
( ( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat != SV36 ) )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(985,plain,
! [SV36: nat] :
( ( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
| ( zero_zero_nat != SV36 ) )
= $false )
| ( ( zero_zero_nat = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(986,plain,
! [SV37: nat] :
( ( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat != SV37 ) )
= $false )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(987,plain,
! [SV37: nat] :
( ( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
| ( zero_zero_nat != SV37 ) )
= $false )
| ( ( zero_zero_nat = SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(988,plain,
! [SV38: nat] :
( ( ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat != SV38 ) )
= $false )
| ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(989,plain,
! [SV38: nat] :
( ( ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
| ( zero_zero_nat != SV38 ) )
= $false )
| ( ( zero_zero_nat = SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(990,plain,
! [SV39: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
| ( SV39 != zero_zero_nat ) )
= $false )
| ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(991,plain,
! [SV39: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
| ( SV39 != zero_zero_nat ) )
= $false )
| ( ( SV39 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(992,plain,
! [SV40: nat] :
( ( ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
| ( SV40 != zero_zero_nat ) )
= $false )
| ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(993,plain,
! [SV40: nat] :
( ( ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
| ( SV40 != zero_zero_nat ) )
= $false )
| ( ( SV40 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(994,plain,
! [SV41: nat] :
( ( ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
| ( SV41 != zero_zero_nat ) )
= $false )
| ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(995,plain,
! [SV41: nat] :
( ( ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
| ( SV41 != zero_zero_nat ) )
= $false )
| ( ( SV41 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(996,plain,
! [SV46: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(997,plain,
! [SV46: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
| ( SV46 != zero_zero_nat ) )
= $false )
| ( ( SV46 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(998,plain,
! [SV47: int] :
( ( ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
| ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
= $false )
| ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(999,plain,
! [SV47: int] :
( ( ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
| ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
= $false )
| ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1000,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( ~ ( ~ SV48
| ~ $true ) )
= $true )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(1001,plain,
! [SV48: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV48
| ~ $true ) )
= $true )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(1002,plain,
! [SV48: $o] :
( ( ( SV48
| $false )
= $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1003,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1004,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1005,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1006,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1007,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1008,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1009,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ( ( SV109 = SV162 )
| ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1010,plain,
! [SV110: list_a,SV51: list_a] :
( ( ( SV51 = SV110 )
= $false )
| ( ( ( size_size_list_a @ SV51 )
= ( size_size_list_a @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1011,plain,
! [SV163: list_nat,SV148: nat > a,SV112: list_a,SV53: a > a] :
( ( ( ( map_a_a @ SV53 @ SV112 )
= ( map_nat_a @ SV148 @ SV163 ) )
= $false )
| ( ( ( size_size_list_a @ SV112 )
= ( size_size_list_nat @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1012,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1013,plain,
! [SV54: nat] :
( ( ( SV54 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1014,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ~ ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1015,plain,
! [SV165: nat,SV150: nat,SV115: nat,SV57: nat] :
( ( ( ( set_or562006527an_nat @ SV57 @ SV115 )
= ( set_or562006527an_nat @ SV150 @ SV165 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV57 @ SV115 )
| ~ ( ord_less_nat @ SV150 @ SV165 )
| ( SV57 = SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1016,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( ! [SY221: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY221 )
| ~ ~ ( SV60 @ SY221 )
| ~ ! [SY222: nat] :
~ ~ ( ~ ( ord_less_nat @ SY222 @ SY221 )
| ~ ~ ( SV60 @ SY222 ) ) ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1017,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1018,plain,
! [SV118: nat,SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1019,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1020,plain,
! [SV63: nat] :
( ( ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1021,plain,
! [SV64: int] :
( ( ( ! [SY225: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY225 )
| ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ SY225 ) ) ) ) )
= $false )
| ( ( SV64
= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1022,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ord_less_nat @ SV65 @ SV119 )
= $false )
| ( ( ~ ( ord_less_nat @ SV151 @ SV166 )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1023,plain,
! [SV66: list_a > $o,SV120: list_a] :
( ( ( ~ ! [SY312: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY312 ) @ ( size_size_list_a @ ( sK3_SY230 @ SV120 @ SV66 ) ) )
| ( SV66 @ SY312 ) ) )
= $false )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1024,plain,
! [SV120: list_a,SV66: list_a > $o] :
( ( ( SV66 @ ( sK3_SY230 @ SV120 @ SV66 ) )
= $false )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1025,plain,
! [SV167: list_a,SV152: a > a,SV122: list_nat,SV68: nat > a] :
( ( ( ( map_nat_a @ SV68 @ SV122 )
= ( map_a_a @ SV152 @ SV167 ) )
= $false )
| ( ( ( size_size_list_nat @ SV122 )
= ( size_size_list_a @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1026,plain,
! [SV123: set_list_a,SV153: list_a,SV69: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SV153 ) ) )
= $true )
| ( ( SV69 != SV153 )
= $true )
| ( ( member_list_a @ SV69 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1027,plain,
! [SV70: nat] :
( ( ( SV70 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1028,plain,
! [SV70: nat] :
( ( ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1029,plain,
! [SV168: nat,SV154: nat,SV125: nat,SV73: nat] :
( ( ( ( set_or562006527an_nat @ SV73 @ SV125 )
= ( set_or562006527an_nat @ SV154 @ SV168 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV73 @ SV125 )
| ~ ( ord_less_nat @ SV154 @ SV168 )
| ( SV125 = SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1030,plain,
! [SV126: list_a,SV74: list_a] :
( ( ( SV74 = SV126 )
= $false )
| ( ( ( size_size_list_a @ SV74 )
= ( size_size_list_a @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1031,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ( ( list_ex_a @ SV127 @ SV169 )
| ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1032,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1033,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1034,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1035,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1036,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1037,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(1038,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(1039,plain,
! [SV132: list_a,SV82: list_a] :
( ( ( ! [SY301: nat] :
( ~ ( ord_less_nat @ SY301 @ ( size_size_list_a @ SV82 ) )
| ( ( nth_a @ SV82 @ SY301 )
= ( nth_a @ SV132 @ SY301 ) ) ) )
= $false )
| ( ( SV82 = SV132 )
= $true )
| ( ( ( size_size_list_a @ SV82 )
= ( size_size_list_a @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1040,plain,
! [SV1: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 )
| ( SV1 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1041,plain,
! [SV1: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 ) )
= $false )
| ( ( SV1 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1042,plain,
! [SV1: nat] :
( ( ( SV1 != zero_zero_nat )
= $false )
| ( ( SV1 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1043,plain,
! [SV9: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 )
| ( SV9 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1044,plain,
! [SV9: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 ) )
= $false )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1045,plain,
! [SV9: nat] :
( ( ( SV9 != zero_zero_nat )
= $false )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1046,plain,
! [SV10: nat] :
( ( ( zero_zero_nat != SV10 )
= $false )
| ( ( zero_zero_nat = SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1047,plain,
! [SV10: nat] :
( ( ( SV10 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1048,plain,
! [SV10: nat] :
( ( ( zero_zero_nat != SV10 )
= $false )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1049,plain,
! [SV10: nat] :
( ( ( SV10 != zero_zero_nat )
= $false )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1050,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
| ( SV88 != zero_z2005226153et_nat ) )
= $false )
| ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1051,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
| ( SV88 != zero_z2005226153et_nat ) )
= $false )
| ( ( SV88 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1052,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
| ( SV89 != zero_z2005226153et_nat ) )
= $false )
| ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1053,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
| ( SV89 != zero_z2005226153et_nat ) )
= $false )
| ( ( SV89 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1054,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1055,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1056,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1057,plain,
! [SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV35 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1058,plain,
! [SV36: nat] :
( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1059,plain,
! [SV36: nat] :
( ( ( zero_zero_nat != SV36 )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1060,plain,
! [SV36: nat] :
( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV36 ) )
= $false )
| ( ( zero_zero_nat = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1061,plain,
! [SV36: nat] :
( ( ( zero_zero_nat != SV36 )
= $false )
| ( ( zero_zero_nat = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1062,plain,
! [SV37: nat] :
( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
= $false )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1063,plain,
! [SV37: nat] :
( ( ( zero_zero_nat != SV37 )
= $false )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1064,plain,
! [SV37: nat] :
( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV37 ) )
= $false )
| ( ( zero_zero_nat = SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[987]) ).
thf(1065,plain,
! [SV37: nat] :
( ( ( zero_zero_nat != SV37 )
= $false )
| ( ( zero_zero_nat = SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[987]) ).
thf(1066,plain,
! [SV38: nat] :
( ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
= $false )
| ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1067,plain,
! [SV38: nat] :
( ( ( zero_zero_nat != SV38 )
= $false )
| ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1068,plain,
! [SV38: nat] :
( ( ( zero_zero_real
!= ( semiri2110766477t_real @ SV38 ) )
= $false )
| ( ( zero_zero_nat = SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1069,plain,
! [SV38: nat] :
( ( ( zero_zero_nat != SV38 )
= $false )
| ( ( zero_zero_nat = SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1070,plain,
! [SV39: nat] :
( ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
= $false )
| ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1071,plain,
! [SV39: nat] :
( ( ( SV39 != zero_zero_nat )
= $false )
| ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1072,plain,
! [SV39: nat] :
( ( ( ( semiri1382578993at_nat @ SV39 )
!= zero_zero_nat )
= $false )
| ( ( SV39 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1073,plain,
! [SV39: nat] :
( ( ( SV39 != zero_zero_nat )
= $false )
| ( ( SV39 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1074,plain,
! [SV40: nat] :
( ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
= $false )
| ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1075,plain,
! [SV40: nat] :
( ( ( SV40 != zero_zero_nat )
= $false )
| ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1076,plain,
! [SV40: nat] :
( ( ( ( semiri2019852685at_int @ SV40 )
!= zero_zero_int )
= $false )
| ( ( SV40 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1077,plain,
! [SV40: nat] :
( ( ( SV40 != zero_zero_nat )
= $false )
| ( ( SV40 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1078,plain,
! [SV41: nat] :
( ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
= $false )
| ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1079,plain,
! [SV41: nat] :
( ( ( SV41 != zero_zero_nat )
= $false )
| ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1080,plain,
! [SV41: nat] :
( ( ( ( semiri2110766477t_real @ SV41 )
!= zero_zero_real )
= $false )
| ( ( SV41 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1081,plain,
! [SV41: nat] :
( ( ( SV41 != zero_zero_nat )
= $false )
| ( ( SV41 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1082,plain,
! [SV46: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1083,plain,
! [SV46: nat] :
( ( ( SV46 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1084,plain,
! [SV46: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV46 @ zero_zero_nat ) )
= $false )
| ( ( SV46 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1085,plain,
! [SV46: nat] :
( ( ( SV46 != zero_zero_nat )
= $false )
| ( ( SV46 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1086,plain,
! [SV47: int] :
( ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
= $false )
| ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[998]) ).
thf(1087,plain,
! [SV47: int] :
( ( ( ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
= $false )
| ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[998]) ).
thf(1088,plain,
! [SV47: int] :
( ( ( ( nat2 @ SV47 )
!= zero_zero_nat )
= $false )
| ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1089,plain,
! [SV47: int] :
( ( ( ~ ( ord_less_eq_int @ SV47 @ zero_zero_int ) )
= $false )
| ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1090,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $true )
= $false )
| ( SV48 = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1091,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1092,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1093,plain,
! [SV48: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1094,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1095,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1096,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1097,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1098,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1099,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1100,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1101,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1102,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( SV109 = SV162 )
| ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1103,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1104,plain,
! [SV54: nat] :
( ( ( ~ ( ( SV54 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1105,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 )
| ~ ( ( SV54 != zero_zero_nat ) ) )
= $false )
| ( ( SV54 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1106,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1107,plain,
! [SV165: nat,SV150: nat,SV115: nat,SV57: nat] :
( ( ( ~ ( ord_less_nat @ SV57 @ SV115 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV150 @ SV165 )
| ( SV57 = SV150 ) )
= $true )
| ( ( ( set_or562006527an_nat @ SV57 @ SV115 )
= ( set_or562006527an_nat @ SV150 @ SV165 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1108,plain,
! [SV60: nat > $o,SV117: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ! [SY313: nat] :
~ ~ ( ~ ( ord_less_nat @ SY313 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ SY313 ) ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1016]) ).
thf(1109,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $false )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1110,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) )
= $true )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1111,plain,
! [SV63: nat] :
( ( ( ~ ( ( SV63 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1112,plain,
! [SV63: nat] :
( ( ( ~ ( ( SV63 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1113,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1114,plain,
! [SV64: int] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK5_SY225 @ SV64 ) )
| ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ ( sK5_SY225 @ SV64 ) ) ) ) )
= $false )
| ( ( SV64
= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1021]) ).
thf(1115,plain,
! [SV119: nat,SV65: nat,SV166: nat,SV151: nat] :
( ( ( ~ ( ord_less_nat @ SV151 @ SV166 ) )
= $true )
| ( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1116,plain,
! [SV66: list_a > $o,SV120: list_a] :
( ( ( ! [SY312: list_a] :
( ~ ( ord_less_nat @ ( size_size_list_a @ SY312 ) @ ( size_size_list_a @ ( sK3_SY230 @ SV120 @ SV66 ) ) )
| ( SV66 @ SY312 ) ) )
= $true )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1117,plain,
! [SV123: set_list_a,SV153: list_a,SV69: list_a] :
( ( ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SV153 ) )
= $false )
| ( ( SV69 != SV153 )
= $true )
| ( ( member_list_a @ SV69 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1118,plain,
! [SV70: nat] :
( ( ( ~ ( ( SV70 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) )
= $false )
| ( ( SV70 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1119,plain,
! [SV70: nat] :
( ( ( ~ ( ( SV70 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1120,plain,
! [SV70: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1121,plain,
! [SV168: nat,SV154: nat,SV125: nat,SV73: nat] :
( ( ( ~ ( ord_less_nat @ SV73 @ SV125 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV154 @ SV168 )
| ( SV125 = SV168 ) )
= $true )
| ( ( ( set_or562006527an_nat @ SV73 @ SV125 )
= ( set_or562006527an_nat @ SV154 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1122,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ( list_ex_a @ SV127 @ SV169 )
| ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1123,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1124,plain,
! [SV128: nat > $o,SV76: nat] :
( ( ( ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1125,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1126,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1127,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
| ~ ! [SY314: a] :
~ ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SY314 ) )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1035]) ).
thf(1128,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1129,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
| ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1037]) ).
thf(1130,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( ~ ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1038]) ).
thf(1131,plain,
! [SV82: list_a,SV132: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK9_SY301 @ SV132 @ SV82 ) @ ( size_size_list_a @ SV82 ) )
| ( ( nth_a @ SV82 @ ( sK9_SY301 @ SV132 @ SV82 ) )
= ( nth_a @ SV132 @ ( sK9_SY301 @ SV132 @ SV82 ) ) ) )
= $false )
| ( ( SV82 = SV132 )
= $true )
| ( ( ( size_size_list_a @ SV82 )
= ( size_size_list_a @ SV132 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1039]) ).
thf(1132,plain,
! [SV1: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV1 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1133,plain,
! [SV1: nat] :
( ( ( SV1 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1134,plain,
! [SV1: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 ) )
= $true )
| ( ( SV1 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1135,plain,
! [SV1: nat] :
( ( ( SV1 = zero_zero_nat )
= $true )
| ( ( SV1 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1136,plain,
! [SV9: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV9 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1137,plain,
! [SV9: nat] :
( ( ( SV9 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1138,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 ) )
= $true )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1139,plain,
! [SV9: nat] :
( ( ( SV9 = zero_zero_nat )
= $true )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1140,plain,
! [SV10: nat] :
( ( ( zero_zero_nat = SV10 )
= $true )
| ( ( zero_zero_nat = SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1141,plain,
! [SV10: nat] :
( ( ( SV10 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat = SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1142,plain,
! [SV10: nat] :
( ( ( zero_zero_nat = SV10 )
= $true )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1143,plain,
! [SV10: nat] :
( ( ( SV10 = zero_zero_nat )
= $true )
| ( ( SV10 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1144,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
= $false )
| ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1145,plain,
! [SV17: nat > a,SV88: multiset_nat] :
( ( ( SV88 != zero_z2005226153et_nat )
= $false )
| ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1146,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
!= zero_zero_multiset_a )
= $false )
| ( ( SV88 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1147,plain,
! [SV88: multiset_nat] :
( ( ( SV88 != zero_z2005226153et_nat )
= $false )
| ( ( SV88 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1148,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
= $false )
| ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1149,plain,
! [SV18: nat > nat,SV89: multiset_nat] :
( ( ( SV89 != zero_z2005226153et_nat )
= $false )
| ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1150,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
!= zero_z2005226153et_nat )
= $false )
| ( ( SV89 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1151,plain,
! [SV89: multiset_nat] :
( ( ( SV89 != zero_z2005226153et_nat )
= $false )
| ( ( SV89 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1152,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1153,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1154,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV35 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1155,plain,
! [SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1156,plain,
! [SV36: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $true )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1157,plain,
! [SV36: nat] :
( ( ( zero_zero_nat = SV36 )
= $true )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1158,plain,
! [SV36: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV36 ) )
= $true )
| ( ( zero_zero_nat = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1159,plain,
! [SV36: nat] :
( ( ( zero_zero_nat = SV36 )
= $true )
| ( ( zero_zero_nat = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1160,plain,
! [SV37: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $true )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1161,plain,
! [SV37: nat] :
( ( ( zero_zero_nat = SV37 )
= $true )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1162,plain,
! [SV37: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV37 ) )
= $true )
| ( ( zero_zero_nat = SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1163,plain,
! [SV37: nat] :
( ( ( zero_zero_nat = SV37 )
= $true )
| ( ( zero_zero_nat = SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1164,plain,
! [SV38: nat] :
( ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $true )
| ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1165,plain,
! [SV38: nat] :
( ( ( zero_zero_nat = SV38 )
= $true )
| ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1166,plain,
! [SV38: nat] :
( ( ( zero_zero_real
= ( semiri2110766477t_real @ SV38 ) )
= $true )
| ( ( zero_zero_nat = SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1167,plain,
! [SV38: nat] :
( ( ( zero_zero_nat = SV38 )
= $true )
| ( ( zero_zero_nat = SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1168,plain,
! [SV39: nat] :
( ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $true )
| ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1169,plain,
! [SV39: nat] :
( ( ( SV39 = zero_zero_nat )
= $true )
| ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1170,plain,
! [SV39: nat] :
( ( ( ( semiri1382578993at_nat @ SV39 )
= zero_zero_nat )
= $true )
| ( ( SV39 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1171,plain,
! [SV39: nat] :
( ( ( SV39 = zero_zero_nat )
= $true )
| ( ( SV39 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1172,plain,
! [SV40: nat] :
( ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $true )
| ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1173,plain,
! [SV40: nat] :
( ( ( SV40 = zero_zero_nat )
= $true )
| ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1174,plain,
! [SV40: nat] :
( ( ( ( semiri2019852685at_int @ SV40 )
= zero_zero_int )
= $true )
| ( ( SV40 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1175,plain,
! [SV40: nat] :
( ( ( SV40 = zero_zero_nat )
= $true )
| ( ( SV40 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1176,plain,
! [SV41: nat] :
( ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $true )
| ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1177,plain,
! [SV41: nat] :
( ( ( SV41 = zero_zero_nat )
= $true )
| ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1178,plain,
! [SV41: nat] :
( ( ( ( semiri2110766477t_real @ SV41 )
= zero_zero_real )
= $true )
| ( ( SV41 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1179,plain,
! [SV41: nat] :
( ( ( SV41 = zero_zero_nat )
= $true )
| ( ( SV41 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1180,plain,
! [SV46: nat] :
( ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1181,plain,
! [SV46: nat] :
( ( ( SV46 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1182,plain,
! [SV46: nat] :
( ( ( ord_less_eq_nat @ SV46 @ zero_zero_nat )
= $true )
| ( ( SV46 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1183,plain,
! [SV46: nat] :
( ( ( SV46 = zero_zero_nat )
= $true )
| ( ( SV46 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1184,plain,
! [SV47: int] :
( ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $true )
| ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1185,plain,
! [SV47: int] :
( ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $true )
| ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1186,plain,
! [SV47: int] :
( ( ( ( nat2 @ SV47 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1187,plain,
! [SV47: int] :
( ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ SV47 @ zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1188,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( SV48 = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1189,plain,
! [SV48: $o] :
( ( ( ~ $true ) = $false )
| ( SV48 = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1190,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( $true = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1191,plain,
! [SV48: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1192,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( SV48 = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1193,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1194,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1195,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1196,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1197,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1198,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1199,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1200,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1201,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1202,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1203,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1204,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1205,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1206,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 = SV162 )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1207,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1208,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1209,plain,
! [SV54: nat] :
( ( ( SV54 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1210,plain,
! [SV54: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV54 ) )
= $false )
| ( ( SV54 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1211,plain,
! [SV54: nat] :
( ( ( ~ ( ( SV54 != zero_zero_nat ) ) )
= $false )
| ( ( SV54 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1212,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1213,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1214,plain,
! [SV165: nat,SV150: nat,SV115: nat,SV57: nat] :
( ( ( ord_less_nat @ SV57 @ SV115 )
= $false )
| ( ( ~ ( ord_less_nat @ SV150 @ SV165 )
| ( SV57 = SV150 ) )
= $true )
| ( ( ( set_or562006527an_nat @ SV57 @ SV115 )
= ( set_or562006527an_nat @ SV150 @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1215,plain,
! [SV60: nat > $o,SV117: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK4_SY221 @ SV117 @ SV60 ) ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1108]) ).
thf(1216,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( ~ ~ ( SV60 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ! [SY313: nat] :
~ ~ ( ~ ( ord_less_nat @ SY313 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ SY313 ) ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1108]) ).
thf(1217,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
= $false )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1218,plain,
! [SV118: nat,SV62: nat] :
( ( ( ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $false )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1219,plain,
! [SV118: nat,SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $true )
| ( ( SV118 != zero_zero_nat )
= $true )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1220,plain,
! [SV63: nat] :
( ( ( ~ ( ( SV63 != zero_zero_nat ) ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1111]) ).
thf(1221,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1111]) ).
thf(1222,plain,
! [SV63: nat] :
( ( ( SV63 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1223,plain,
! [SV63: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1224,plain,
! [SV64: int] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK5_SY225 @ SV64 ) ) )
= $false )
| ( ( SV64
= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1225,plain,
! [SV64: int] :
( ( ( SV64
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ ( sK5_SY225 @ SV64 ) ) ) )
= $false )
| ( ( SV64
= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1226,plain,
! [SV119: nat,SV65: nat,SV166: nat,SV151: nat] :
( ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1227,plain,
! [SV66: list_a > $o,SV120: list_a,SV170: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV170 ) @ ( size_size_list_a @ ( sK3_SY230 @ SV120 @ SV66 ) ) )
| ( SV66 @ SV170 ) )
= $true )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1228,plain,
! [SV123: set_list_a,SV153: list_a,SV69: list_a] :
( ( ( SV69 = SV153 )
= $false )
| ( ( ord_less_nat @ ( size_size_list_a @ SV69 ) @ ( size_size_list_a @ SV153 ) )
= $false )
| ( ( member_list_a @ SV69 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1229,plain,
! [SV70: nat] :
( ( ( ~ ( ( SV70 != zero_zero_nat ) ) )
= $false )
| ( ( SV70 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1230,plain,
! [SV70: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV70 ) )
= $false )
| ( ( SV70 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1231,plain,
! [SV70: nat] :
( ( ( SV70 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1232,plain,
! [SV70: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1233,plain,
! [SV168: nat,SV154: nat,SV125: nat,SV73: nat] :
( ( ( ord_less_nat @ SV73 @ SV125 )
= $false )
| ( ( ~ ( ord_less_nat @ SV154 @ SV168 )
| ( SV125 = SV168 ) )
= $true )
| ( ( ( set_or562006527an_nat @ SV73 @ SV125 )
= ( set_or562006527an_nat @ SV154 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1234,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( list_ex_a @ SV127 @ SV169 )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1235,plain,
! [SV127: a > $o,SV169: list_a] :
( ( ( ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1236,plain,
! [SV128: nat > $o,SV76: nat,SV171: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV171 @ SV76 )
| ~ ( SV128 @ SV171 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1237,plain,
! [SV128: nat > $o,SV76: nat,SV172: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1238,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $false )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1239,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1240,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 ) )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1127]) ).
thf(1241,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ~ ! [SY314: a] :
~ ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SY314 ) )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1127]) ).
thf(1242,plain,
! [SV130: nat > a > $o,SV78: nat,SV173: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV173 )
!= SV78 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_nat @ SY315 @ SV78 )
| ( SV130 @ SY315 @ ( nth_a @ SV173 @ SY315 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1243,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1244,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1245,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( ~ ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1246,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1247,plain,
! [SV82: list_a,SV132: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK9_SY301 @ SV132 @ SV82 ) @ ( size_size_list_a @ SV82 ) ) )
= $false )
| ( ( SV82 = SV132 )
= $true )
| ( ( ( size_size_list_a @ SV82 )
= ( size_size_list_a @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1248,plain,
! [SV132: list_a,SV82: list_a] :
( ( ( ( nth_a @ SV82 @ ( sK9_SY301 @ SV132 @ SV82 ) )
= ( nth_a @ SV132 @ ( sK9_SY301 @ SV132 @ SV82 ) ) )
= $false )
| ( ( SV82 = SV132 )
= $true )
| ( ( ( size_size_list_a @ SV82 )
= ( size_size_list_a @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1249,plain,
! [SV1: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV1 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1132]) ).
thf(1250,plain,
! [SV1: nat] :
( ( ( SV1 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1251,plain,
! [SV1: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $false )
| ( ( SV1 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1252,plain,
! [SV9: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV9 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1253,plain,
! [SV9: nat] :
( ( ( SV9 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1254,plain,
! [SV9: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $false )
| ( ( SV9 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1255,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $true )
| ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1256,plain,
! [SV17: nat > a,SV88: multiset_nat] :
( ( ( SV88 = zero_z2005226153et_nat )
= $true )
| ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1257,plain,
! [SV88: multiset_nat,SV17: nat > a] :
( ( ( ( image_mset_nat_a @ SV17 @ SV88 )
= zero_zero_multiset_a )
= $true )
| ( ( SV88 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1258,plain,
! [SV88: multiset_nat] :
( ( ( SV88 = zero_z2005226153et_nat )
= $true )
| ( ( SV88 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1259,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $true )
| ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1260,plain,
! [SV18: nat > nat,SV89: multiset_nat] :
( ( ( SV89 = zero_z2005226153et_nat )
= $true )
| ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1261,plain,
! [SV89: multiset_nat,SV18: nat > nat] :
( ( ( ( image_mset_nat_nat @ SV18 @ SV89 )
= zero_z2005226153et_nat )
= $true )
| ( ( SV89 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1262,plain,
! [SV89: multiset_nat] :
( ( ( SV89 = zero_z2005226153et_nat )
= $true )
| ( ( SV89 = zero_z2005226153et_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1263,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( SV48 = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1264,plain,
! [SV48: $o] :
( ( $true = $true )
| ( SV48 = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1265,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( $true = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1266,plain,
! [SV48: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV48 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1267,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( SV48 = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1192]) ).
thf(1268,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( SV48 = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1192]) ).
thf(1269,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( $false = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1270,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1271,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1272,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1273,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1274,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1275,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1276,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1277,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1278,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1279,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1280,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1281,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1282,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1283,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1284,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1285,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1286,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1287,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1288,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $true )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1289,plain,
! [SV54: nat] :
( ( ( SV54 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1290,plain,
! [SV54: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV54 )
= $true )
| ( ( SV54 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1291,plain,
! [SV54: nat] :
( ( ( SV54 != zero_zero_nat )
= $true )
| ( ( SV54 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1292,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1293,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1213]) ).
thf(1294,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1213]) ).
thf(1295,plain,
! [SV115: nat,SV57: nat,SV165: nat,SV150: nat] :
( ( ( ~ ( ord_less_nat @ SV150 @ SV165 ) )
= $true )
| ( ( SV57 = SV150 )
= $true )
| ( ( ord_less_nat @ SV57 @ SV115 )
= $false )
| ( ( ( set_or562006527an_nat @ SV57 @ SV115 )
= ( set_or562006527an_nat @ SV150 @ SV165 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1296,plain,
! [SV60: nat > $o,SV117: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK4_SY221 @ SV117 @ SV60 ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1297,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( ~ ~ ( SV60 @ ( sK4_SY221 @ SV117 @ SV60 ) ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1298,plain,
! [SV60: nat > $o,SV117: nat] :
( ( ( ~ ! [SY313: nat] :
~ ~ ( ~ ( ord_less_nat @ SY313 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ SY313 ) ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1299,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $true )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1300,plain,
! [SV118: nat,SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $true )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1301,plain,
! [SV118: nat,SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 != zero_zero_nat )
= $true )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1302,plain,
! [SV63: nat] :
( ( ( SV63 != zero_zero_nat )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1303,plain,
! [SV63: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1304,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1305,plain,
! [SV64: int] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK5_SY225 @ SV64 ) )
= $true )
| ( ( SV64
= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1306,plain,
! [SV64: int] :
( ( ( SV64
= ( uminus_uminus_int @ ( semiri2019852685at_int @ ( sK5_SY225 @ SV64 ) ) ) )
= $true )
| ( ( SV64
= ( semiri2019852685at_int @ ( sK2_SY224 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1307,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
| ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1226]) ).
thf(1308,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1226]) ).
thf(1309,plain,
! [SV66: list_a > $o,SV120: list_a,SV170: list_a] :
( ( ( ~ ( ord_less_nat @ ( size_size_list_a @ SV170 ) @ ( size_size_list_a @ ( sK3_SY230 @ SV120 @ SV66 ) ) ) )
= $true )
| ( ( SV66 @ SV170 )
= $true )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1310,plain,
! [SV70: nat] :
( ( ( SV70 != zero_zero_nat )
= $true )
| ( ( SV70 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1229]) ).
thf(1311,plain,
! [SV70: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $true )
| ( ( SV70 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1312,plain,
! [SV70: nat] :
( ( ( SV70 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1313,plain,
! [SV73: nat,SV125: nat,SV168: nat,SV154: nat] :
( ( ( ~ ( ord_less_nat @ SV154 @ SV168 ) )
= $true )
| ( ( SV125 = SV168 )
= $true )
| ( ( ord_less_nat @ SV73 @ SV125 )
= $false )
| ( ( ( set_or562006527an_nat @ SV73 @ SV125 )
= ( set_or562006527an_nat @ SV154 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1314,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1315,plain,
! [SV127: a > $o,SV169: list_a] :
( ( ( ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1316,plain,
! [SV128: nat > $o,SV76: nat,SV171: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV171 @ SV76 )
| ~ ( SV128 @ SV171 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1317,plain,
! [SV128: nat > $o,SV76: nat,SV172: nat] :
( ( ( ~ ( ~ ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SV172 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1318,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) ) )
= $false )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1319,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $false )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1320,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV129 @ SV77 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV77 @ SV156 ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1321,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1322,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ! [SY314: a] :
~ ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SY314 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1323,plain,
! [SV130: nat > a > $o,SV78: nat,SV173: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV173 )
!= SV78 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_nat @ SY315 @ SV78 )
| ( SV130 @ SY315 @ ( nth_a @ SV173 @ SY315 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1324,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1325,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1326,plain,
! [SV81: nat,SV131: nat > $o] :
( ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1327,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1328,plain,
! [SV82: list_a,SV132: list_a] :
( ( ( ord_less_nat @ ( sK9_SY301 @ SV132 @ SV82 ) @ ( size_size_list_a @ SV82 ) )
= $true )
| ( ( SV82 = SV132 )
= $true )
| ( ( ( size_size_list_a @ SV82 )
= ( size_size_list_a @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1329,plain,
! [SV1: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1330,plain,
! [SV9: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1331,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false )
| ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1263]) ).
thf(1332,plain,
! [SV48: $o] :
( ( ( SV48 = $false )
= $true )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1263]) ).
thf(1333,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false )
| ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1334,plain,
! [SV48: $o] :
( ( ( SV48 = $false )
= $true )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1264]) ).
thf(1335,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false )
| ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1265]) ).
thf(1336,plain,
! [SV48: $o] :
( ( ( SV48 = $false )
= $true )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1265]) ).
thf(1337,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false )
| ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1266]) ).
thf(1338,plain,
! [SV48: $o] :
( ( ( SV48 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1266]) ).
thf(1339,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( SV48 = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1340,plain,
! [SV48: $o] :
( ( $false = $true )
| ( SV48 = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1341,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( $false = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1342,plain,
! [SV48: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV48 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1343,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1271]) ).
thf(1344,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1271]) ).
thf(1345,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1272]) ).
thf(1346,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1272]) ).
thf(1347,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1273]) ).
thf(1348,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1273]) ).
thf(1349,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1274]) ).
thf(1350,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1274]) ).
thf(1351,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1275]) ).
thf(1352,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1353,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1354,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1278]) ).
thf(1355,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1279]) ).
thf(1356,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1279]) ).
thf(1357,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1280]) ).
thf(1358,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1280]) ).
thf(1359,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1281]) ).
thf(1360,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1281]) ).
thf(1361,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1282]) ).
thf(1362,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1282]) ).
thf(1363,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1283]) ).
thf(1364,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1284]) ).
thf(1365,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1366,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1367,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 != SV162 )
= $false )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1368,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1369,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
= $true )
| ( ( ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $true )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1370,plain,
! [SV54: nat] :
( ( ( SV54 = zero_zero_nat )
= $false )
| ( ( SV54 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1371,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1372,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1373,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1374,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1375,plain,
! [SV115: nat,SV57: nat,SV165: nat,SV150: nat] :
( ( ( ord_less_nat @ SV150 @ SV165 )
= $false )
| ( ( SV57 = SV150 )
= $true )
| ( ( ord_less_nat @ SV57 @ SV115 )
= $false )
| ( ( ( set_or562006527an_nat @ SV57 @ SV115 )
= ( set_or562006527an_nat @ SV150 @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1376,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( ~ ( SV60 @ ( sK4_SY221 @ SV117 @ SV60 ) ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1377,plain,
! [SV60: nat > $o,SV117: nat] :
( ( ( ! [SY313: nat] :
~ ~ ( ~ ( ord_less_nat @ SY313 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ SY313 ) ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1378,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) )
= $false )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1379,plain,
! [SV62: nat,SV118: nat] :
( ( ( SV118 = zero_zero_nat )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1380,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1381,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1382,plain,
! [SV66: list_a > $o,SV120: list_a,SV170: list_a] :
( ( ( ord_less_nat @ ( size_size_list_a @ SV170 ) @ ( size_size_list_a @ ( sK3_SY230 @ SV120 @ SV66 ) ) )
= $false )
| ( ( SV66 @ SV170 )
= $true )
| ( ( SV66 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1383,plain,
! [SV70: nat] :
( ( ( SV70 = zero_zero_nat )
= $false )
| ( ( SV70 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1384,plain,
! [SV73: nat,SV125: nat,SV168: nat,SV154: nat] :
( ( ( ord_less_nat @ SV154 @ SV168 )
= $false )
| ( ( SV125 = SV168 )
= $true )
| ( ( ord_less_nat @ SV73 @ SV125 )
= $false )
| ( ( ( set_or562006527an_nat @ SV73 @ SV125 )
= ( set_or562006527an_nat @ SV154 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1385,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ( list_ex_a @ SV127 @ SV169 ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1386,plain,
! [SV127: a > $o,SV169: list_a] :
( ( ( ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1387,plain,
! [SV127: a > $o,SV169: list_a,SV174: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SV174 ) ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1388,plain,
! [SV128: nat > $o,SV76: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV76 )
| ~ ( SV128 @ SV171 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1389,plain,
! [SV128: nat > $o,SV76: nat,SV172: nat] :
( ( ( ~ ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SV172 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1317]) ).
thf(1390,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $true )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1318]) ).
thf(1391,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $true )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1392,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ~ ( ord_less_nat @ SV77 @ SV156 ) )
= $true )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1393,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1394,plain,
! [SV175: a,SV78: nat,SV130: nat > a > $o] :
( ( ( ~ ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1395,plain,
! [SV130: nat > a > $o,SV78: nat,SV173: list_a] :
( ( ( ( ( size_size_list_a @ SV173 )
!= SV78 )
| ~ ! [SY315: nat] :
( ~ ( ord_less_nat @ SY315 @ SV78 )
| ( SV130 @ SY315 @ ( nth_a @ SV173 @ SY315 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1323]) ).
thf(1396,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1397,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $false )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1398,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1399,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) )
| ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1400,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $false )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1327]) ).
thf(1401,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1327]) ).
thf(1402,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false ) )
= $true )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1403,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false ) )
= $true )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1404,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false ) )
= $true )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1405,plain,
! [SV48: $o] :
( ( ( ~ ( SV48
| $false ) )
= $true )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1406,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1407,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1408,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1409,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1410,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1411,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1412,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1413,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1414,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 = SV162 )
= $true )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1415,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $true )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1416,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $true )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1417,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1418,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1419,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1373]) ).
thf(1420,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1373]) ).
thf(1421,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1422,plain,
! [SV117: nat,SV60: nat > $o] :
( ( ( SV60 @ ( sK4_SY221 @ SV117 @ SV60 ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1423,plain,
! [SV60: nat > $o,SV117: nat,SV176: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV176 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ SV176 ) ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1424,plain,
! [SV118: nat,SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $false )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1425,plain,
! [SV62: nat,SV118: nat] :
( ( ( SV118 != zero_zero_nat )
= $false )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1426,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
| ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1427,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $false )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1428,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( list_ex_a @ SV127 @ SV169 )
= $true )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1429,plain,
! [SV127: a > $o,SV169: list_a] :
( ( ( ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $true )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1430,plain,
! [SV127: a > $o,SV169: list_a,SV174: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SV174 ) ) ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1431,plain,
! [SV128: nat > $o,SV76: nat,SV171: nat] :
( ( ( ~ ( ord_less_nat @ SV171 @ SV76 ) )
= $true )
| ( ( ~ ( SV128 @ SV171 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1432,plain,
! [SV128: nat > $o,SV76: nat,SV172: nat] :
( ( ( ~ ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) ) )
= $true )
| ( ( ~ ( SV128 @ SV172 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1433,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) )
= $false )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1434,plain,
! [SV129: nat,SV156: nat,SV77: nat] :
( ( ( ord_less_nat @ SV77 @ SV156 )
= $false )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ~ ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1435,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1436,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1437,plain,
! [SV175: a,SV78: nat,SV130: nat > a > $o] :
( ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1438,plain,
! [SV130: nat > a > $o,SV78: nat,SV173: list_a] :
( ( ( ( size_size_list_a @ SV173 )
!= SV78 )
= $true )
| ( ( ~ ! [SY315: nat] :
( ~ ( ord_less_nat @ SY315 @ SV78 )
| ( SV130 @ SY315 @ ( nth_a @ SV173 @ SY315 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1439,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1440,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1441,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1442,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1443,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $false )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1444,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ~ ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $false )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1445,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1446,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1447,plain,
! [SV48: $o] :
( ( ( SV48
| $false )
= $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1448,plain,
! [SV48: $o] :
( ( ( SV48
| $false )
= $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1449,plain,
! [SV48: $o] :
( ( ( SV48
| $false )
= $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1450,plain,
! [SV48: $o] :
( ( ( SV48
| $false )
= $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1451,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1452,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1453,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1454,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1455,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1456,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1457,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1458,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1459,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $false )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1460,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1461,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1462,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1463,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1464,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1465,plain,
! [SV60: nat > $o,SV117: nat,SV176: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV176 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ SV176 ) ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1466,plain,
! [SV118: nat,SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $true )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1424]) ).
thf(1467,plain,
! [SV62: nat,SV118: nat] :
( ( ( SV118 = zero_zero_nat )
= $true )
| ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1468,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
!= ( semiri2019852685at_int @ SV118 ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1469,plain,
! [SV118: nat,SV62: nat] :
( ( ( ~ ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1470,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1471,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $false )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1472,plain,
! [SV127: a > $o,SV169: list_a] :
( ( ( ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1473,plain,
! [SV127: a > $o,SV169: list_a,SV174: nat] :
( ( ( ~ ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SV174 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1474,plain,
! [SV128: nat > $o,SV76: nat,SV171: nat] :
( ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( ~ ( SV128 @ SV171 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1475,plain,
! [SV128: nat > $o,SV76: nat,SV172: nat] :
( ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( ~ ( SV128 @ SV172 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1476,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV129 @ SV77 ) )
= $false )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1477,plain,
! [SV129: nat,SV156: nat,SV77: nat] :
( ( ( ~ ( ord_less_nat @ SV77 @ SV156 ) )
= $false )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1478,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
| ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1479,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1480,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1481,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1482,plain,
! [SV130: nat > a > $o,SV78: nat,SV173: list_a] :
( ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ~ ! [SY315: nat] :
( ~ ( ord_less_nat @ SY315 @ SV78 )
| ( SV130 @ SY315 @ ( nth_a @ SV173 @ SY315 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1483,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1484,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1485,plain,
! [SV131: nat > $o,SV81: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ SV177 @ SV81 )
| ( SV131 @ SV177 ) )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1486,plain,
! [SV131: nat > $o,SV81: nat,SV178: nat] :
( ( ( ~ ( member_nat @ SV178 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SV178 ) )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1487,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY299: nat] :
( ~ ( ord_less_nat @ SY299 @ SV81 )
| ( SV131 @ SY299 ) ) )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1488,plain,
! [SV131: nat > $o,SV81: nat] :
( ( ( ! [SY300: nat] :
( ~ ( member_nat @ SY300 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SY300 ) ) )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1489,plain,
! [SV131: nat > $o,SV81: nat,SV179: nat] :
( ( ( ~ ( ord_less_nat @ SV179 @ SV81 )
| ( SV131 @ SV179 ) )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1490,plain,
! [SV131: nat > $o,SV81: nat,SV180: nat] :
( ( ( ~ ( member_nat @ SV180 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SV180 ) )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1491,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1492,plain,
! [SV48: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1493,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1494,plain,
! [SV48: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1495,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1496,plain,
! [SV48: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1497,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1498,plain,
! [SV48: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV48
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1499,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1500,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1501,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1502,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1503,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1504,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1505,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1506,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1507,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1508,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1509,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1510,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1511,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1512,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1513,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1514,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1515,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1516,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $false )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1517,plain,
! [SV109: list_a,SV162: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1460]) ).
thf(1518,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1519,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1520,plain,
! [SV56: nat,SV149: nat,SV164: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1521,plain,
! [SV60: nat > $o,SV117: nat,SV176: nat] :
( ( ( ~ ( ord_less_nat @ SV176 @ ( sK4_SY221 @ SV117 @ SV60 ) )
| ~ ~ ( SV60 @ SV176 ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1465]) ).
thf(1522,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ SV62 ) )
= ( semiri2019852685at_int @ SV118 ) )
= $true )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1523,plain,
! [SV118: nat,SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) ) )
= $true )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1524,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $false )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1525,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ( SV65 != SV151 )
| ( SV119 != SV166 ) )
= $true )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1526,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK11_SY311 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ ( sK11_SY311 @ SV127 @ SV169 ) ) ) ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1472]) ).
thf(1527,plain,
! [SV127: a > $o,SV169: list_a,SV174: nat] :
( ( ( ~ ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) ) )
= $true )
| ( ( ~ ( SV127 @ ( nth_a @ SV169 @ SV174 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1528,plain,
! [SV76: nat,SV171: nat,SV128: nat > $o] :
( ( ( SV128 @ SV171 )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1529,plain,
! [SV76: nat,SV172: nat,SV128: nat > $o] :
( ( ( SV128 @ SV172 )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1530,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $true )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1531,plain,
! [SV129: nat,SV156: nat,SV77: nat] :
( ( ( ord_less_nat @ SV77 @ SV156 )
= $true )
| ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1532,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( ~ ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1533,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1534,plain,
! [SV130: nat > a > $o,SV78: nat,SV181: nat] :
( ( ( ~ ( ord_less_nat @ SV181 @ SV78 )
| ~ ! [SY316: a] :
~ ( SV130 @ SV181 @ SY316 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1535,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1536,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1537,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1538,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY315: nat] :
( ~ ( ord_less_nat @ SY315 @ SV78 )
| ( SV130 @ SY315 @ ( nth_a @ SV173 @ SY315 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1539,plain,
! [SV131: nat > $o,SV81: nat,SV182: nat] :
( ( ( ~ ( ord_less_nat @ SV182 @ SV81 )
| ( SV131 @ SV182 ) )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1540,plain,
! [SV131: nat > $o,SV81: nat,SV183: nat] :
( ( ( ~ ( member_nat @ SV183 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SV183 ) )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1541,plain,
! [SV131: nat > $o,SV81: nat,SV177: nat] :
( ( ( ~ ( ord_less_nat @ SV177 @ SV81 ) )
= $true )
| ( ( SV131 @ SV177 )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1542,plain,
! [SV131: nat > $o,SV81: nat,SV178: nat] :
( ( ( ~ ( member_nat @ SV178 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) ) )
= $true )
| ( ( SV131 @ SV178 )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1543,plain,
! [SV131: nat > $o,SV81: nat,SV184: nat] :
( ( ( ~ ( ord_less_nat @ SV184 @ SV81 )
| ( SV131 @ SV184 ) )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1544,plain,
! [SV131: nat > $o,SV81: nat,SV185: nat] :
( ( ( ~ ( member_nat @ SV185 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
| ( SV131 @ SV185 ) )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1545,plain,
! [SV131: nat > $o,SV81: nat,SV179: nat] :
( ( ( ~ ( ord_less_nat @ SV179 @ SV81 ) )
= $true )
| ( ( SV131 @ SV179 )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1546,plain,
! [SV131: nat > $o,SV81: nat,SV180: nat] :
( ( ( ~ ( member_nat @ SV180 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) ) )
= $true )
| ( ( SV131 @ SV180 )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1547,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( SV48 = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1548,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( $false = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1549,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( SV48 = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1550,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( $false = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1551,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( SV48 = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1552,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1553,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( SV48 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1554,plain,
! [SV48: $o] :
( ( ( ~ SV48
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1555,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1556,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1557,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1558,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1559,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1560,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1561,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1562,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1563,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1564,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1565,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1566,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1567,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1568,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1569,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1570,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1571,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $true )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1572,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $true )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1516]) ).
thf(1573,plain,
! [SV109: list_a,SV162: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1517]) ).
thf(1574,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1517]) ).
thf(1575,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1576,plain,
! [SV149: nat,SV56: nat,SV164: nat,SV114: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1577,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1578,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
| ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1579,plain,
! [SV60: nat > $o,SV117: nat,SV176: nat] :
( ( ( ~ ( ord_less_nat @ SV176 @ ( sK4_SY221 @ SV117 @ SV60 ) ) )
= $true )
| ( ( ~ ~ ( SV60 @ SV176 ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1580,plain,
! [SV118: nat,SV62: nat] :
( ( ( ( SV62 != zero_zero_nat )
| ( SV118 != zero_zero_nat ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1581,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1582,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $false )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1583,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( SV65 != SV151 )
= $true )
| ( ( SV119 != SV166 )
= $true )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1584,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK11_SY311 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ ( sK11_SY311 @ SV127 @ SV169 ) ) ) ) )
= $true )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1585,plain,
! [SV127: a > $o,SV169: list_a,SV174: nat] :
( ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( ~ ( SV127 @ ( nth_a @ SV169 @ SV174 ) ) )
= $true )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1586,plain,
! [SV171: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1587,plain,
! [SV172: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) )
| ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1588,plain,
! [SV156: nat,SV129: nat,SV77: nat] :
( ( ( member_nat @ SV77 @ ( set_or562006527an_nat @ SV129 @ SV156 ) )
= $true )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1532]) ).
thf(1589,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1590,plain,
! [SV130: nat > a > $o,SV78: nat,SV181: nat] :
( ( ( ~ ( ord_less_nat @ SV181 @ SV78 ) )
= $true )
| ( ( ~ ! [SY316: a] :
~ ( SV130 @ SV181 @ SY316 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1591,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK12_SY297 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY317: nat] :
( ~ ( ord_less_nat @ SY317 @ SV78 )
| ( SV130 @ SY317 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SY317 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1535]) ).
thf(1592,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1593,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1594,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
| ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1538]) ).
thf(1595,plain,
! [SV131: nat > $o,SV81: nat,SV182: nat] :
( ( ( ~ ( ord_less_nat @ SV182 @ SV81 ) )
= $true )
| ( ( SV131 @ SV182 )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1596,plain,
! [SV131: nat > $o,SV81: nat,SV183: nat] :
( ( ( ~ ( member_nat @ SV183 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) ) )
= $true )
| ( ( SV131 @ SV183 )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1597,plain,
! [SV131: nat > $o,SV81: nat,SV177: nat] :
( ( ( ord_less_nat @ SV177 @ SV81 )
= $false )
| ( ( SV131 @ SV177 )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1598,plain,
! [SV131: nat > $o,SV81: nat,SV178: nat] :
( ( ( member_nat @ SV178 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $false )
| ( ( SV131 @ SV178 )
= $true )
| ( ( SV131 @ ( sK7_SY299 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1599,plain,
! [SV131: nat > $o,SV81: nat,SV184: nat] :
( ( ( ~ ( ord_less_nat @ SV184 @ SV81 ) )
= $true )
| ( ( SV131 @ SV184 )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1600,plain,
! [SV131: nat > $o,SV81: nat,SV185: nat] :
( ( ( ~ ( member_nat @ SV185 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) ) )
= $true )
| ( ( SV131 @ SV185 )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1601,plain,
! [SV131: nat > $o,SV81: nat,SV179: nat] :
( ( ( ord_less_nat @ SV179 @ SV81 )
= $false )
| ( ( SV131 @ SV179 )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1602,plain,
! [SV131: nat > $o,SV81: nat,SV180: nat] :
( ( ( member_nat @ SV180 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $false )
| ( ( SV131 @ SV180 )
= $true )
| ( ( SV131 @ ( sK8_SY300 @ SV131 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1603,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( SV48 = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1604,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( SV48 = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1605,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( $false = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1606,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1607,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( SV48 = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1608,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( SV48 = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1549]) ).
thf(1609,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( $false = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1610,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1611,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( SV48 = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1551]) ).
thf(1612,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( SV48 = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1551]) ).
thf(1613,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1614,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1615,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( SV48 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1616,plain,
! [SV48: $o] :
( ( ( ~ $false ) = $false )
| ( SV48 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1617,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1618,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1619,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1620,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1621,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1622,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1623,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1624,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1625,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1626,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1627,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1628,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1629,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1630,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1560]) ).
thf(1631,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1632,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1633,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1634,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1635,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1636,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1637,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1638,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1639,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1640,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1641,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1642,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1643,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1644,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1645,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1646,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1647,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1648,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1649,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1650,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1651,plain,
! [SV162: list_a,SV109: list_a,SV186: nat] :
( ( ( ~ ( ord_less_nat @ SV186 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SV186 )
= ( nth_a @ SV162 @ SV186 ) ) )
= $true )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1652,plain,
! [SV109: list_a,SV162: list_a] :
( ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ~ ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1653,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1654,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1655,plain,
! [SV149: nat,SV56: nat,SV164: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1656,plain,
! [SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1657,plain,
! [SV56: nat,SV164: nat,SV114: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1658,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ~ ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1659,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1660,plain,
! [SV60: nat > $o,SV117: nat,SV176: nat] :
( ( ( ord_less_nat @ SV176 @ ( sK4_SY221 @ SV117 @ SV60 ) )
= $false )
| ( ( ~ ~ ( SV60 @ SV176 ) )
= $true )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1661,plain,
! [SV118: nat,SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1662,plain,
! [SV62: nat,SV118: nat] :
( ( ( SV118 != zero_zero_nat )
= $false )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1663,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $true )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1664,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $true )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1665,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( SV65 = SV151 )
= $false )
| ( ( SV119 != SV166 )
= $true )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1666,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK11_SY311 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ ( sK11_SY311 @ SV127 @ SV169 ) ) ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1667,plain,
! [SV174: nat,SV169: list_a,SV127: a > $o] :
( ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( ~ ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1668,plain,
! [SV171: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1669,plain,
! [SV171: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1670,plain,
! [SV172: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1671,plain,
! [SV172: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1672,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV129 @ SV77 )
| ~ ( ord_less_nat @ SV77 @ SV156 ) )
= $false )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1673,plain,
! [SV130: nat > a > $o,SV78: nat,SV181: nat] :
( ( ( ord_less_nat @ SV181 @ SV78 )
= $false )
| ( ( ~ ! [SY316: a] :
~ ( SV130 @ SV181 @ SY316 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1674,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK12_SY297 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY317: nat] :
( ~ ( ord_less_nat @ SY317 @ SV78 )
| ( SV130 @ SY317 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SY317 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1675,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat,SV187: nat] :
( ( ( ~ ( ord_less_nat @ SV187 @ SV78 )
| ~ ! [SY318: a] :
~ ( SV130 @ SV187 @ SY318 ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1676,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1677,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1678,plain,
! [SV78: nat,SV173: list_a,SV130: nat > a > $o] :
( ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1679,plain,
! [SV131: nat > $o,SV81: nat,SV182: nat] :
( ( ( ord_less_nat @ SV182 @ SV81 )
= $false )
| ( ( SV131 @ SV182 )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1680,plain,
! [SV131: nat > $o,SV81: nat,SV183: nat] :
( ( ( member_nat @ SV183 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $false )
| ( ( SV131 @ SV183 )
= $true )
| ( ( ord_less_nat @ ( sK7_SY299 @ SV131 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1681,plain,
! [SV131: nat > $o,SV81: nat,SV184: nat] :
( ( ( ord_less_nat @ SV184 @ SV81 )
= $false )
| ( ( SV131 @ SV184 )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1682,plain,
! [SV131: nat > $o,SV81: nat,SV185: nat] :
( ( ( member_nat @ SV185 @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $false )
| ( ( SV131 @ SV185 )
= $true )
| ( ( member_nat @ ( sK8_SY300 @ SV131 @ SV81 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1683,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( SV48 = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1684,plain,
! [SV48: $o] :
( ( $false = $true )
| ( SV48 = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1685,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( $false = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1686,plain,
! [SV48: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV48 = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1687,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( SV48 = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1688,plain,
! [SV48: $o] :
( ( $false = $true )
| ( SV48 = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1689,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( $false = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1690,plain,
! [SV48: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV48 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1691,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( SV48 = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1692,plain,
! [SV48: $o] :
( ( $false = $true )
| ( SV48 = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1693,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1694,plain,
! [SV48: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV48 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1695,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( SV48 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1696,plain,
! [SV48: $o] :
( ( $false = $true )
| ( SV48 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1697,plain,
! [SV48: $o] :
( ( SV48 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1698,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1699,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1700,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1701,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1702,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1703,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1704,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1705,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1706,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1707,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1708,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1709,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1710,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1711,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1712,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1713,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1714,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1715,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1716,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1717,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1718,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1719,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1720,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1721,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1641]) ).
thf(1722,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1723,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1724,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1725,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1726,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1727,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1728,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1729,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1730,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1731,plain,
! [SV162: list_a,SV109: list_a,SV186: nat] :
( ( ( ~ ( ord_less_nat @ SV186 @ ( size_size_list_a @ SV109 ) ) )
= $true )
| ( ( ( nth_a @ SV109 @ SV186 )
= ( nth_a @ SV162 @ SV186 ) )
= $true )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1732,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( SV109 != SV162 )
| ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1733,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 != SV162 )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1734,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1735,plain,
! [SV114: nat,SV56: nat,SV149: nat] :
( ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1736,plain,
! [SV56: nat,SV164: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1737,plain,
! [SV164: nat,SV149: nat,SV114: nat,SV56: nat] :
( ( ( ord_less_eq_set_nat @ ( set_or562006527an_nat @ SV56 @ SV114 ) @ ( set_or562006527an_nat @ SV149 @ SV164 ) )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1738,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ( ord_less_eq_nat @ SV114 @ SV56 )
| ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1739,plain,
! [SV117: nat,SV176: nat,SV60: nat > $o] :
( ( ( ~ ( SV60 @ SV176 ) )
= $false )
| ( ( ord_less_nat @ SV176 @ ( sK4_SY221 @ SV117 @ SV60 ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1740,plain,
! [SV118: nat,SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1741,plain,
! [SV62: nat,SV118: nat] :
( ( ( SV118 = zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV118 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1742,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ( SV65 != SV151 )
| ( SV119 != SV166 ) )
= $false )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1743,plain,
! [SV151: nat,SV65: nat,SV166: nat,SV119: nat] :
( ( ( SV119 = SV166 )
= $false )
| ( ( SV65 = SV151 )
= $false )
| ( ( ~ ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1744,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ( ord_less_nat @ ( sK11_SY311 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1745,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ~ ( SV127 @ ( nth_a @ SV169 @ ( sK11_SY311 @ SV127 @ SV169 ) ) ) )
= $false )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1746,plain,
! [SV174: nat,SV169: list_a,SV127: a > $o] :
( ( ( ~ ( list_ex_a @ SV127 @ SV169 )
| ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1747,plain,
! [SV171: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1748,plain,
! [SV171: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1749,plain,
! [SV172: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1750,plain,
! [SV172: nat,SV128: nat > $o,SV76: nat] :
( ( ( ~ ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1751,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV129 @ SV77 ) )
= $false )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1752,plain,
! [SV129: nat,SV156: nat,SV77: nat] :
( ( ( ~ ( ord_less_nat @ SV77 @ SV156 ) )
= $false )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1753,plain,
! [SV78: nat,SV181: nat,SV130: nat > a > $o] :
( ( ( ! [SY316: a] :
~ ( SV130 @ SV181 @ SY316 ) )
= $false )
| ( ( ord_less_nat @ SV181 @ SV78 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1754,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ( ( size_size_list_a @ ( sK12_SY297 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY317: nat] :
( ~ ( ord_less_nat @ SY317 @ SV78 )
| ( SV130 @ SY317 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SY317 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1755,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat,SV187: nat] :
( ( ( ~ ( ord_less_nat @ SV187 @ SV78 ) )
= $true )
| ( ( ~ ! [SY318: a] :
~ ( SV130 @ SV187 @ SY318 ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1756,plain,
! [SV78: nat,SV130: nat > a > $o,SV175: a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY319: nat] :
( ~ ( ord_less_nat @ SY319 @ SV78 )
| ( SV130 @ SY319 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SY319 ) ) ) ) )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1676]) ).
thf(1757,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ~ ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1758,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1759,plain,
! [SV162: list_a,SV109: list_a,SV186: nat] :
( ( ( ord_less_nat @ SV186 @ ( size_size_list_a @ SV109 ) )
= $false )
| ( ( ( nth_a @ SV109 @ SV186 )
= ( nth_a @ SV162 @ SV186 ) )
= $true )
| ( ( SV109 = SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1760,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 != SV162 )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1761,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1762,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 = SV162 )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1733]) ).
thf(1763,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1764,plain,
! [SV164: nat,SV149: nat,SV56: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) ) )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1765,plain,
! [SV117: nat,SV176: nat,SV60: nat > $o] :
( ( ( SV60 @ SV176 )
= $true )
| ( ( ord_less_nat @ SV176 @ ( sK4_SY221 @ SV117 @ SV60 ) )
= $false )
| ( ( SV60 @ SV117 )
= $true )
| ( ( SV60 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1766,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( SV65 != SV151 )
= $false )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1767,plain,
! [SV151: nat,SV65: nat,SV166: nat,SV119: nat] :
( ( ( SV119 != SV166 )
= $false )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1768,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
| ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $false )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1769,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( ord_less_nat @ ( sK11_SY311 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
= $true )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1770,plain,
! [SV169: list_a,SV127: a > $o] :
( ( ( SV127 @ ( nth_a @ SV169 @ ( sK11_SY311 @ SV127 @ SV169 ) ) )
= $true )
| ( ( list_ex_a @ SV127 @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1771,plain,
! [SV174: nat,SV169: list_a,SV127: a > $o] :
( ( ( ~ ( list_ex_a @ SV127 @ SV169 ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1772,plain,
! [SV174: nat,SV127: a > $o,SV169: list_a] :
( ( ( ~ ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1773,plain,
! [SV171: nat,SV128: nat > $o,SV76: nat] :
( ( ( ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1774,plain,
! [SV171: nat,SV128: nat > $o,SV76: nat] :
( ( ( ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1775,plain,
! [SV172: nat,SV128: nat > $o,SV76: nat] :
( ( ( ! [SY292: nat] :
~ ~ ( ~ ( ord_less_nat @ SY292 @ SV76 )
| ~ ( SV128 @ SY292 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1776,plain,
! [SV172: nat,SV128: nat > $o,SV76: nat] :
( ( ( ! [SY293: nat] :
~ ~ ( ~ ( member_nat @ SY293 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ SY293 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1777,plain,
! [SV156: nat,SV77: nat,SV129: nat] :
( ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $true )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1778,plain,
! [SV129: nat,SV156: nat,SV77: nat] :
( ( ( ord_less_nat @ SV77 @ SV156 )
= $true )
| ( ( ord_less_eq_nat @ SV129 @ SV77 )
= $false )
| ( ( ord_less_nat @ SV77 @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1779,plain,
! [SV78: nat,SV181: nat,SV130: nat > a > $o] :
( ( ( ~ ( SV130 @ SV181 @ ( sK15_SY316 @ SV78 @ SV181 @ SV130 ) ) )
= $false )
| ( ( ord_less_nat @ SV181 @ SV78 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1753]) ).
thf(1780,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ( size_size_list_a @ ( sK12_SY297 @ SV130 @ SV78 ) )
!= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1781,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY317: nat] :
( ~ ( ord_less_nat @ SY317 @ SV78 )
| ( SV130 @ SY317 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SY317 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1782,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat,SV187: nat] :
( ( ( ord_less_nat @ SV187 @ SV78 )
= $false )
| ( ( ~ ! [SY318: a] :
~ ( SV130 @ SV187 @ SY318 ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1783,plain,
! [SV78: nat,SV130: nat > a > $o,SV175: a] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY319: nat] :
( ~ ( ord_less_nat @ SY319 @ SV78 )
| ( SV130 @ SY319 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SY319 ) ) ) ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1784,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) )
| ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1785,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1786,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1787,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( SV109 = SV162 )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1788,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1789,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1790,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 )
| ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1791,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( SV65 = SV151 )
= $true )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1792,plain,
! [SV151: nat,SV65: nat,SV166: nat,SV119: nat] :
( ( ( SV119 = SV166 )
= $true )
| ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1793,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
!= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $false )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1768]) ).
thf(1794,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ~ ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $false )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1768]) ).
thf(1795,plain,
! [SV174: nat,SV169: list_a,SV127: a > $o] :
( ( ( list_ex_a @ SV127 @ SV169 )
= $true )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1796,plain,
! [SV174: nat,SV127: a > $o,SV169: list_a] :
( ( ( ~ ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1797,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) @ SV76 )
| ~ ( SV128 @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1773]) ).
thf(1798,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1774]) ).
thf(1799,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) @ SV76 )
| ~ ( SV128 @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1775]) ).
thf(1800,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ~ ( ~ ( member_nat @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1776]) ).
thf(1801,plain,
! [SV78: nat,SV181: nat,SV130: nat > a > $o] :
( ( ( SV130 @ SV181 @ ( sK15_SY316 @ SV78 @ SV181 @ SV130 ) )
= $true )
| ( ( ord_less_nat @ SV181 @ SV78 )
= $false )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1802,plain,
! [SV78: nat,SV130: nat > a > $o] :
( ( ( ( size_size_list_a @ ( sK12_SY297 @ SV130 @ SV78 ) )
= SV78 )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1803,plain,
! [SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY317: nat] :
( ~ ( ord_less_nat @ SY317 @ SV78 )
| ( SV130 @ SY317 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SY317 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1804,plain,
! [SV175: a,SV78: nat,SV187: nat,SV130: nat > a > $o] :
( ( ( ! [SY318: a] :
~ ( SV130 @ SV187 @ SY318 ) )
= $false )
| ( ( ord_less_nat @ SV187 @ SV78 )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1805,plain,
! [SV78: nat,SV130: nat > a > $o,SV175: a] :
( ( ( ( ( size_size_list_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY319: nat] :
( ~ ( ord_less_nat @ SY319 @ SV78 )
| ( SV130 @ SY319 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SY319 ) ) ) )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1806,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1807,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1808,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1809,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1810,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
| ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1811,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1812,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1813,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV149 @ SV56 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1814,plain,
! [SV149: nat,SV56: nat,SV164: nat,SV114: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV114 @ SV164 ) )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1815,plain,
! [SV166: nat,SV151: nat,SV119: nat,SV65: nat] :
( ( ( ( set_or562006527an_nat @ SV65 @ SV119 )
= ( set_or562006527an_nat @ SV151 @ SV166 ) )
= $true )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1793]) ).
thf(1816,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ~ ( ( SV65 != SV151 )
| ( SV119 != SV166 ) ) )
= $true )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1817,plain,
! [SV174: nat,SV127: a > $o,SV169: list_a] :
( ( ( ! [SY311: nat] :
~ ~ ( ~ ( ord_less_nat @ SY311 @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ SY311 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1818,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) @ SV76 )
| ~ ( SV128 @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1819,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ( ~ ( member_nat @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1820,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) @ SV76 )
| ~ ( SV128 @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) ) ) )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1821,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ( ~ ( member_nat @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) ) ) )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1822,plain,
! [SV130: nat > a > $o,SV78: nat,SV188: nat] :
( ( ( ~ ( ord_less_nat @ SV188 @ SV78 )
| ( SV130 @ SV188 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SV188 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(1823,plain,
! [SV78: nat,SV175: a,SV187: nat,SV130: nat > a > $o] :
( ( ( ~ ( SV130 @ SV187 @ ( sK20_SY318 @ SV175 @ SV78 @ SV187 @ SV130 ) ) )
= $false )
| ( ( ord_less_nat @ SV187 @ SV78 )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1804]) ).
thf(1824,plain,
! [SV78: nat,SV130: nat > a > $o,SV175: a] :
( ( ( ( size_size_list_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) )
!= SV78 )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(1825,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY319: nat] :
( ~ ( ord_less_nat @ SY319 @ SV78 )
| ( SV130 @ SY319 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SY319 ) ) ) )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(1826,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY295: nat] :
( ~ ( ord_less_nat @ SY295 @ SV78 )
| ~ ! [SY296: a] :
~ ( SV130 @ SY295 @ SY296 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1827,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1828,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV189: nat] :
( ( ( ~ ( ord_less_nat @ SV189 @ SV78 )
| ~ ! [SY320: a] :
~ ( SV130 @ SV189 @ SY320 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(1829,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1830,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
!= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1831,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ~ ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1832,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1833,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1834,plain,
! [SV164: nat,SV114: nat,SV56: nat,SV149: nat] :
( ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1835,plain,
! [SV149: nat,SV56: nat,SV164: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $true )
| ( ( ord_less_eq_nat @ SV114 @ SV56 )
= $true )
| ( ( ord_less_eq_nat @ SV149 @ SV56 )
= $false )
| ( ( ord_less_eq_nat @ SV114 @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1836,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( ( SV65 != SV151 )
| ( SV119 != SV166 ) )
= $false )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1837,plain,
! [SV169: list_a,SV127: a > $o,SV174: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1817]) ).
thf(1838,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ( ord_less_nat @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) @ SV76 )
| ~ ( SV128 @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1839,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ( member_nat @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1840,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ( ord_less_nat @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) @ SV76 )
| ~ ( SV128 @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1841,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ( member_nat @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
| ~ ( SV128 @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1842,plain,
! [SV130: nat > a > $o,SV78: nat,SV188: nat] :
( ( ( ~ ( ord_less_nat @ SV188 @ SV78 ) )
= $true )
| ( ( SV130 @ SV188 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SV188 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(1843,plain,
! [SV78: nat,SV175: a,SV187: nat,SV130: nat > a > $o] :
( ( ( SV130 @ SV187 @ ( sK20_SY318 @ SV175 @ SV78 @ SV187 @ SV130 ) )
= $true )
| ( ( ord_less_nat @ SV187 @ SV78 )
= $false )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1844,plain,
! [SV78: nat,SV130: nat > a > $o,SV175: a] :
( ( ( ( size_size_list_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) )
= SV78 )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1845,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY319: nat] :
( ~ ( ord_less_nat @ SY319 @ SV78 )
| ( SV130 @ SY319 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SY319 ) ) ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1846,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV190: nat] :
( ( ( ~ ( ord_less_nat @ SV190 @ SV78 )
| ~ ! [SY321: a] :
~ ( SV130 @ SV190 @ SY321 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(1847,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY297: list_a] :
~ ~ ( ( ( size_size_list_a @ SY297 )
!= SV78 )
| ~ ! [SY298: nat] :
( ~ ( ord_less_nat @ SY298 @ SV78 )
| ( SV130 @ SY298 @ ( nth_a @ SY297 @ SY298 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1848,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV189: nat] :
( ( ( ~ ( ord_less_nat @ SV189 @ SV78 ) )
= $true )
| ( ( ~ ! [SY320: a] :
~ ( SV130 @ SV189 @ SY320 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1849,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY322: nat] :
( ~ ( ord_less_nat @ SY322 @ SV78 )
| ( SV130 @ SY322 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SY322 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1829]) ).
thf(1850,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(1851,plain,
! [SV162: list_a,SV109: list_a] :
( ( ( ! [SY310: nat] :
( ~ ( ord_less_nat @ SY310 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SY310 )
= ( nth_a @ SV162 @ SY310 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(1852,plain,
! [SV162: list_a,SV109: list_a,SV191: nat] :
( ( ( ~ ( ord_less_nat @ SV191 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SV191 )
= ( nth_a @ SV162 @ SV191 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(1853,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( SV65 != SV151 )
= $false )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1854,plain,
! [SV151: nat,SV65: nat,SV166: nat,SV119: nat] :
( ( ( SV119 != SV166 )
= $false )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1855,plain,
! [SV169: list_a,SV127: a > $o,SV174: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1856,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ( ord_less_nat @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) @ SV76 ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1857,plain,
! [SV76: nat,SV171: nat,SV128: nat > $o] :
( ( ( ~ ( SV128 @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1858,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ~ ( member_nat @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1859,plain,
! [SV76: nat,SV171: nat,SV128: nat > $o] :
( ( ( ~ ( SV128 @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) ) )
= $false )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1860,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ( ord_less_nat @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) @ SV76 ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1861,plain,
! [SV76: nat,SV172: nat,SV128: nat > $o] :
( ( ( ~ ( SV128 @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1862,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ~ ( member_nat @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1863,plain,
! [SV76: nat,SV172: nat,SV128: nat > $o] :
( ( ( ~ ( SV128 @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) ) )
= $false )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1864,plain,
! [SV130: nat > a > $o,SV78: nat,SV188: nat] :
( ( ( ord_less_nat @ SV188 @ SV78 )
= $false )
| ( ( SV130 @ SV188 @ ( nth_a @ ( sK12_SY297 @ SV130 @ SV78 ) @ SV188 ) )
= $true )
| ( ( ord_less_nat @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1865,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV78 )
| ( SV130 @ SV192 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SV192 ) ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(1866,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV190: nat] :
( ( ( ~ ( ord_less_nat @ SV190 @ SV78 ) )
= $true )
| ( ( ~ ! [SY321: a] :
~ ( SV130 @ SV190 @ SY321 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1867,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ~ ~ ( ( ( size_size_list_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY323: nat] :
( ~ ( ord_less_nat @ SY323 @ SV78 )
| ( SV130 @ SY323 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SY323 ) ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1847]) ).
thf(1868,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV189: nat] :
( ( ( ord_less_nat @ SV189 @ SV78 )
= $false )
| ( ( ~ ! [SY320: a] :
~ ( SV130 @ SV189 @ SY320 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(1869,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY322: nat] :
( ~ ( ord_less_nat @ SY322 @ SV78 )
| ( SV130 @ SY322 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SY322 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1870,plain,
! [SV162: list_a,SV109: list_a,SV193: nat] :
( ( ( ~ ( ord_less_nat @ SV193 @ ( size_size_list_a @ SV109 ) )
| ( ( nth_a @ SV109 @ SV193 )
= ( nth_a @ SV162 @ SV193 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(1871,plain,
! [SV162: list_a,SV109: list_a,SV191: nat] :
( ( ( ~ ( ord_less_nat @ SV191 @ ( size_size_list_a @ SV109 ) ) )
= $true )
| ( ( ( nth_a @ SV109 @ SV191 )
= ( nth_a @ SV162 @ SV191 ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(1872,plain,
! [SV166: nat,SV119: nat,SV151: nat,SV65: nat] :
( ( ( SV65 = SV151 )
= $true )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1873,plain,
! [SV151: nat,SV65: nat,SV166: nat,SV119: nat] :
( ( ( SV119 = SV166 )
= $true )
| ( ( SV65 = SV151 )
= $false )
| ( ( SV119 = SV166 )
= $false )
| ( ( ord_less_nat @ SV151 @ SV166 )
= $false )
| ( ( ord_less_nat @ SV65 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1854]) ).
thf(1874,plain,
! [SV169: list_a,SV127: a > $o,SV174: nat] :
( ( ( ~ ( ord_less_nat @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
| ~ ( SV127 @ ( nth_a @ SV169 @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1875,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( ord_less_nat @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) @ SV76 )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1876,plain,
! [SV76: nat,SV171: nat,SV128: nat > $o] :
( ( ( SV128 @ ( sK16_SY292 @ SV171 @ SV128 @ SV76 ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1877,plain,
! [SV76: nat,SV128: nat > $o,SV171: nat] :
( ( ( member_nat @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(1878,plain,
! [SV76: nat,SV171: nat,SV128: nat > $o] :
( ( ( SV128 @ ( sK17_SY293 @ SV171 @ SV128 @ SV76 ) )
= $true )
| ( ( ord_less_nat @ SV171 @ SV76 )
= $false )
| ( ( SV128 @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1879,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( ord_less_nat @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) @ SV76 )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1880,plain,
! [SV76: nat,SV172: nat,SV128: nat > $o] :
( ( ( SV128 @ ( sK18_SY292 @ SV172 @ SV128 @ SV76 ) )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1881,plain,
! [SV76: nat,SV128: nat > $o,SV172: nat] :
( ( ( member_nat @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1882,plain,
! [SV76: nat,SV172: nat,SV128: nat > $o] :
( ( ( SV128 @ ( sK19_SY293 @ SV172 @ SV128 @ SV76 ) )
= $true )
| ( ( member_nat @ SV172 @ ( set_or562006527an_nat @ zero_zero_nat @ SV76 ) )
= $false )
| ( ( SV128 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1863]) ).
thf(1883,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat,SV192: nat] :
( ( ( ~ ( ord_less_nat @ SV192 @ SV78 ) )
= $true )
| ( ( SV130 @ SV192 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SV192 ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1884,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV190: nat] :
( ( ( ord_less_nat @ SV190 @ SV78 )
= $false )
| ( ( ~ ! [SY321: a] :
~ ( SV130 @ SV190 @ SY321 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1885,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ~ ( ( ( size_size_list_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY323: nat] :
( ~ ( ord_less_nat @ SY323 @ SV78 )
| ( SV130 @ SY323 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SY323 ) ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(1886,plain,
! [SV173: list_a,SV78: nat,SV189: nat,SV130: nat > a > $o] :
( ( ( ! [SY320: a] :
~ ( SV130 @ SV189 @ SY320 ) )
= $false )
| ( ( ord_less_nat @ SV189 @ SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1887,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ( ( size_size_list_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY322: nat] :
( ~ ( ord_less_nat @ SY322 @ SV78 )
| ( SV130 @ SY322 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SY322 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1888,plain,
! [SV162: list_a,SV109: list_a,SV193: nat] :
( ( ( ~ ( ord_less_nat @ SV193 @ ( size_size_list_a @ SV109 ) ) )
= $true )
| ( ( ( nth_a @ SV109 @ SV193 )
= ( nth_a @ SV162 @ SV193 ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1889,plain,
! [SV162: list_a,SV109: list_a,SV191: nat] :
( ( ( ord_less_nat @ SV191 @ ( size_size_list_a @ SV109 ) )
= $false )
| ( ( ( nth_a @ SV109 @ SV191 )
= ( nth_a @ SV162 @ SV191 ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ( nth_a @ SV109 @ ( sK10_SY310 @ SV162 @ SV109 ) )
= ( nth_a @ SV162 @ ( sK10_SY310 @ SV162 @ SV109 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1890,plain,
! [SV169: list_a,SV127: a > $o,SV174: nat] :
( ( ( ~ ( ord_less_nat @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1891,plain,
! [SV174: nat,SV169: list_a,SV127: a > $o] :
( ( ( ~ ( SV127 @ ( nth_a @ SV169 @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1892,plain,
! [SV175: a,SV130: nat > a > $o,SV78: nat,SV192: nat] :
( ( ( ord_less_nat @ SV192 @ SV78 )
= $false )
| ( ( SV130 @ SV192 @ ( nth_a @ ( sK14_SY297 @ SV175 @ SV130 @ SV78 ) @ SV192 ) )
= $true )
| ( ( SV130 @ ( sK6_SY295 @ SV130 @ SV78 ) @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1893,plain,
! [SV173: list_a,SV78: nat,SV190: nat,SV130: nat > a > $o] :
( ( ( ! [SY321: a] :
~ ( SV130 @ SV190 @ SY321 ) )
= $false )
| ( ( ord_less_nat @ SV190 @ SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1894,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ( ( size_size_list_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
| ~ ! [SY323: nat] :
( ~ ( ord_less_nat @ SY323 @ SV78 )
| ( SV130 @ SY323 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SY323 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1895,plain,
! [SV78: nat,SV173: list_a,SV189: nat,SV130: nat > a > $o] :
( ( ( ~ ( SV130 @ SV189 @ ( sK24_SY320 @ SV173 @ SV78 @ SV189 @ SV130 ) ) )
= $false )
| ( ( ord_less_nat @ SV189 @ SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1886]) ).
thf(1896,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ( size_size_list_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(1897,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY322: nat] :
( ~ ( ord_less_nat @ SY322 @ SV78 )
| ( SV130 @ SY322 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SY322 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(1898,plain,
! [SV162: list_a,SV109: list_a,SV193: nat] :
( ( ( ord_less_nat @ SV193 @ ( size_size_list_a @ SV109 ) )
= $false )
| ( ( ( nth_a @ SV109 @ SV193 )
= ( nth_a @ SV162 @ SV193 ) )
= $true )
| ( ( ( size_size_list_a @ SV109 )
= ( size_size_list_a @ SV162 ) )
= $false )
| ( ( ord_less_nat @ ( sK10_SY310 @ SV162 @ SV109 ) @ ( size_size_list_a @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1899,plain,
! [SV169: list_a,SV127: a > $o,SV174: nat] :
( ( ( ord_less_nat @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) @ ( size_size_list_a @ SV169 ) )
= $true )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1900,plain,
! [SV174: nat,SV169: list_a,SV127: a > $o] :
( ( ( SV127 @ ( nth_a @ SV169 @ ( sK21_SY311 @ SV174 @ SV127 @ SV169 ) ) )
= $true )
| ( ( ord_less_nat @ SV174 @ ( size_size_list_a @ SV169 ) )
= $false )
| ( ( SV127 @ ( nth_a @ SV169 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1901,plain,
! [SV78: nat,SV173: list_a,SV190: nat,SV130: nat > a > $o] :
( ( ( ~ ( SV130 @ SV190 @ ( sK25_SY321 @ SV173 @ SV78 @ SV190 @ SV130 ) ) )
= $false )
| ( ( ord_less_nat @ SV190 @ SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1893]) ).
thf(1902,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ( size_size_list_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) )
!= SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1894]) ).
thf(1903,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ~ ! [SY323: nat] :
( ~ ( ord_less_nat @ SY323 @ SV78 )
| ( SV130 @ SY323 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SY323 ) ) ) )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1894]) ).
thf(1904,plain,
! [SV78: nat,SV173: list_a,SV189: nat,SV130: nat > a > $o] :
( ( ( SV130 @ SV189 @ ( sK24_SY320 @ SV173 @ SV78 @ SV189 @ SV130 ) )
= $true )
| ( ( ord_less_nat @ SV189 @ SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(1905,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ( size_size_list_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) )
= SV78 )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(1906,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY322: nat] :
( ~ ( ord_less_nat @ SY322 @ SV78 )
| ( SV130 @ SY322 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SY322 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1907,plain,
! [SV78: nat,SV173: list_a,SV190: nat,SV130: nat > a > $o] :
( ( ( SV130 @ SV190 @ ( sK25_SY321 @ SV173 @ SV78 @ SV190 @ SV130 ) )
= $true )
| ( ( ord_less_nat @ SV190 @ SV78 )
= $false )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(1908,plain,
! [SV78: nat,SV130: nat > a > $o,SV173: list_a] :
( ( ( ( size_size_list_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) )
= SV78 )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1909,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat] :
( ( ( ! [SY323: nat] :
( ~ ( ord_less_nat @ SY323 @ SV78 )
| ( SV130 @ SY323 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SY323 ) ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(1910,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ SV194 @ SV78 )
| ( SV130 @ SV194 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SV194 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(1911,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV195: nat] :
( ( ( ~ ( ord_less_nat @ SV195 @ SV78 )
| ( SV130 @ SV195 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SV195 ) ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(1912,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV194: nat] :
( ( ( ~ ( ord_less_nat @ SV194 @ SV78 ) )
= $true )
| ( ( SV130 @ SV194 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SV194 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1913,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV195: nat] :
( ( ( ~ ( ord_less_nat @ SV195 @ SV78 ) )
= $true )
| ( ( SV130 @ SV195 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SV195 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1914,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV194: nat] :
( ( ( ord_less_nat @ SV194 @ SV78 )
= $false )
| ( ( SV130 @ SV194 @ ( nth_a @ ( sK22_SY297 @ SV173 @ SV130 @ SV78 ) @ SV194 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( SV130 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ ( nth_a @ SV173 @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1915,plain,
! [SV173: list_a,SV130: nat > a > $o,SV78: nat,SV195: nat] :
( ( ( ord_less_nat @ SV195 @ SV78 )
= $false )
| ( ( SV130 @ SV195 @ ( nth_a @ ( sK23_SY297 @ SV173 @ SV130 @ SV78 ) @ SV195 ) )
= $true )
| ( ( ( size_size_list_a @ SV173 )
= SV78 )
= $false )
| ( ( ord_less_nat @ ( sK13_SY315 @ SV173 @ SV130 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1916,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[454,1915,1914,1908,1907,1905,1904,1900,1899,1898,1892,1889,1882,1881,1880,1879,1878,1877,1876,1875,1873,1872,1864,1850,1844,1843,1835,1834,1832,1815,1802,1801,1795,1792,1791,1787,1778,1777,1770,1769,1765,1762,1759,1741,1740,1737,1736,1735,1730,1729,1728,1727,1726,1725,1724,1723,1722,1721,1720,1719,1718,1717,1716,1715,1714,1713,1712,1711,1710,1709,1708,1707,1706,1705,1704,1703,1702,1701,1700,1699,1698,1697,1696,1695,1694,1693,1692,1691,1690,1689,1688,1687,1686,1685,1684,1683,1682,1681,1680,1679,1663,1655,1654,1602,1601,1598,1597,1588,1571,1531,1530,1522,1467,1466,1462,1428,1422,1417,1414,1390,1384,1383,1382,1380,1375,1370,1366,1365,1364,1363,1362,1360,1358,1356,1354,1353,1352,1351,1350,1348,1346,1344,1342,1341,1340,1339,1338,1336,1334,1332,1330,1329,1328,1312,1311,1308,1306,1305,1304,1303,1299,1296,1290,1289,1262,1261,1260,1259,1258,1257,1256,1255,1254,1253,1251,1250,1248,1232,1228,1223,1208,1187,1186,1185,1184,1183,1182,1181,1180,1179,1178,1177,1176,1175,1174,1173,1172,1171,1170,1169,1168,1167,1166,1165,1164,1163,1162,1161,1160,1159,1158,1157,1156,1155,1154,1153,1152,1143,1142,1141,1140,1139,1135,1030,1025,1024,1011,1010,966,951,949,947,942,940,905,904,902,896,892,884,878,874,871,868,863,855,854,853,852,845,841,838,836,832,822,820,809,798,789,787,785,783,781,780,779,778,777,776,775,774,773,771,754,746,736,726,724,721,720,719,717,715,713,711,709,707,705,692,691,690,687,686,685,684,682,680,679,678,677,676,675,674,673,664,638,635,629,618,616,598,597,596,594,540,536,526,525,524,459,458,457,455]) ).
thf(1917,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP078^1 : 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
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 11:17:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 152.05/25.65 ..
% 152.05/25.65
% 152.05/25.65 No.of.Axioms: 93
% 152.05/25.65
% 152.05/25.65 Length.of.Defs: 0
% 152.05/25.65
% 152.05/25.65 Contains.Choice.Funs: false
% 152.05/25.65 ......................................
% 152.05/25.65
% 152.05/25.65 ********************************
% 152.05/25.65 * All subproblems solved! *
% 152.05/25.65 ********************************
% 152.05/25.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:93,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:1916,loop_count:0,foatp_calls:1,translation:fof_full)
% 152.05/25.65
% 152.05/25.65 %**** Beginning of derivation protocol ****
% 152.05/25.65 % SZS output start CNFRefutation
% See solution above
% 152.05/25.67
% 152.05/25.67 %**** End of derivation protocol ****
% 152.05/25.67 %**** no. of clauses in derivation: 1654 ****
% 152.05/25.67 %**** clause counter: 1916 ****
% 152.05/25.67
% 152.05/25.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:93,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:1916,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------